# PRE2018 3 Group1

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## Group members

Name Student ID Major
Max van Mulken 1006576 Software Science
Mart Hagedoorn 1021524 Software Science
Niels Verstappen 0999624 Software Science
Rani van Hoof 1026024 Biomedical Engineering
Kees Voorintholt 1005136 Software Science

## Introduction

This wiki is an information page about a study on a huge problem that is known as the Kessler Syndrome, which is basically a form of cascade failure. It starts with for example two satellites colliding; this collision will cause a lot of debris to fly around in orbital space. This debris will then again collide with other debris, space stations or satellites, which can eventually lead to a shield of debris around the planet Earth.

The importance of this problem will be further explained and solutions in the form of robot designs will be considered and discussed, ultimately leading to the best space debris cleaning robot.

This study is done for a TU Eindhoven course: Robots Everywhere (0LAUK0). While studying this problem and its possible solutions, it is made sure that the three USE aspects: User, Society and Enterprise, are central.

## Problem definition

As mentioned in the introduction, the problem that will be studied is the Kessler Syndrome. In the long term this shield of debris around the Earth can have disastrous consequences. Starting with the consequence of not being able to send any new satellites into orbital space as they would get smashed by orbital debris immediately. At the speed of which these objects travel, they will just shatter in tons of smaller objects and travel straight ahead. This means that now all these smaller pieces make a cloud of debris of which the total area is bigger than it was before it crashed. This cloud will destroy everything it encounters, only making the cloud of debris bigger and bigger.

To have some kind of visualization of how much orbital debris is already out there, there are about 650.000 objects with a size in between the size of a softball and a fingernail. Next to that, there exist approximately 170 million pieces of space junk that are smaller than the tip of a pencil[1]. All of this together with the roughly 23.000 satellites, rocket bodies and other human made objects, make a huge amount of objects flying around in orbit.

Almost all of this orbital space debris is in Low Earth Orbit (LEO), at an altitude of at most 2.000 km. However, the biggest concentrations of space debris are found at an altitude of 800 to 850 km. This is a relatively low orbital altitude, which means that the orbital drag will be pretty big here compared to higher altitudes. This means that if we start slowing down these pieces, we will decrease their orbital life time from several decades to several months[2].

But why would this affect the ordinary human being living his life on planet Earth, the orbital debris is in space right, why would we care? Well, at the point where we have no more satellites in orbital space there will be quite some changes to our way of life. How would we make the important business call to a CEO on the other side of the world? How would we know what the weather will be for the coming weeks? All these things will become impossible without satellites.

Also, it might seem like a future problem that we could maybe still prevent, however that is not true, in fact it has already started a long time ago. There are numerous reports of orbital debris colliding with satellites or space stations; the US government logged 308.984 close calls and 665 emergency alerts in 2017 alone[1]. Furthermore, on average a satellite crashes to the Earth once every week which causes a rain of space junk that will burn up on the way to the Earth. However, some of this space junk may stay in orbit, which means the amount of orbital debris keeps increasing.

So, if you had the impression that this problem is not very relevant, think again, because it will change our ways of living drastically.

## Objectives

While studying the subject we have set several objectives for ourselves:

• We will do a literature study and based on these studies we will choose the best solution for the Kessler Syndrome.
• The best solution should be based on several criteria like: safety, cost and effectiveness.
• A solution in the form of a robot.
• We want to make a clear design on how such a robot should be created.
• After this design is created, we want to model this solution to be able to run simulations on it.
• Using these simulations we want to make visual representations.
• To support the feasibility of the best solution, we will also use a simulation.

## USE aspects

While the problem described above is a very ambitious one to solve entirely, we believe the work we can do in 8 weeks is more than enough to impact multiple stakeholders. We will identify stakeholder groups and look at what our project can do for these groups.

### Society

The product aims to prevent or even solve the problem that the Kessler Syndrome poses, in the extent to which that is still possible. If prevention of or a solution to this problem is no longer possible, it will at least attempt to reduce the consequences and growth of the problem. The Kessler Syndrome poses multiple complications that will influence society in a major way.

Since the Kessler Syndrome will cause everything in orbit to be in danger of being damaged and/or destroyed, it will be very hard for humans to launch and maintain satellites into orbit. This has a number of consequences, since satellites are very important for society today. First of all, they allow us to do a lot of research of the entire solar system and even beyond the solar system, expanding our knowledge of our place between the stars. Perhaps even more important to some people, satellites have allowed us to be way more accurate when predicting weather forecasts and potential storms, which is not only nice when you are planning a camping trip but can also be a lifesaver when it concerns a hurricane prediction. Also, since communication over large distances works in straight lines, satellites have greatly increased the distance over which communication can work correctly, along with increasing quality of communication. Instead of having a direct communication channel between two points which can be blocked by a large building or a mountain, communication via a satellite allows the communication to avoid large obstacles. Society has prospered and greatly benefitted from these communication channels, delivering the Internet, modern television and even radio stations to millions of people around the world. Finally, satellites play a key role in navigation. The GPS (Global Positioning System), which is used by every piece of modern navigation technology, has not only allowed individuals to find their way around but it is also used by giant infrastructures like air traffic control, and is used by corporations like Google to provide society with an all-inclusive map of the entire world. It is safe to say that satellites are key to modern society, meaning development of the Kessler Syndrome to disallow satellites would be disastrous.

While the project and product themselves do not entail a lot of direct consequences for the people, if something were to go wrong while disposing of orbital debris and a large piece of metal would, for example, come crashing down on a residential area, people would suddenly have a huge stake in the project as well. Society would be outraged. Thus, it is very important that if an orbital cleaning were to be put into practice, that it is done right.

During later stages of the Kessler Syndrome, a cloud of space debris in orbit would make it too dangerous to send any spacecraft either into or past orbit. This not only limits satellites, but we would no longer be able to send out missions to other planets or moons because of a fear of the spacecraft getting destroyed. We as a society would be forever stuck on Earth, unable to accomplish the dreams science-fiction has set out for us.

### Enterprise

Enterprises that would suffer from this problem, were it not to be addressed, would be both enterprises that focus on space exploration and any enterprise that benefits from sending satellites into orbit. As discussed above, there are a lot of enterprises which would suffer from a lack of satellites since communication methods would suffer severely. Next to these indirect consequences, more direct consequences are suffered by enterprises like SpaceX and Orbital. These enterprises focus on space exploration and flight research to bring multiple benefits and large chunks of knowledge to the general public. Both of these tasks, especially space exploration, will become a lot harder were the close Earth orbit to be home to huge amounts of debris. It would greatly increase the risk of crafts being damaged when send into or beyond orbit. Thus, it is in these enterprise’s best interest that the Kessler Syndrome’s effect is reduced.

## State of the Art

One of the most important things to do at the start of this project is to understand the state of the art of the current technology. The literature study is divided in two relevant topics: How to track space debris? How to remove space debris?

The first will cover the state of the art in finding and tracking debris in space. Where the second will focus on the methods on how to remove pieces of debris from space. We will divide the topic on how to remove space debris in several parts, such that all parts focus on the state of the art of one method.

### Literature study on tracking space debris

There is already a lot of information available on debris that is in orbit around the Earth[3] The sources of this debris are normal launch operations, certain operations in space, fragmentations as a result of explosions and collisions in space, firings of satellite solidrocket motors, material ageing effects, and leaking thermal-control systems[4]. To track those pieces of debris several techniques are developed. At this moment the pieces of debris that are bigger than 10 cm can be tracked. Nowadays, space-object tracking is done with radar technology. To track debris, a radar beam is aimed to a predetermined position in space. When a piece of debris is observed, this piece will be tracked and the motion of the debris is saved. With the motion data of the debris the orbit can be calculated[4]. With this technology we can track pieces of at least 10 cm, but pieces of debris greater than 1 cm can seriously damage satellites. At this moment tracking of debris that is smaller than 1 cm is extremely hard because of the size, but also the reduced orbital stability. Also the total number of objects we have to track when we reduce the size threshold exponentially increase[5].

In July/August and April/May 2013 a new technique for space debris tracking was tested[6]. Here a laser was fired and the reflected signal was received. Then the time between the laser that was fired and the received signal can be used to calculate the distance. These techniques of tracking space debris can be used for tracking satellites with reflectors, but not yet to track smaller pieces of debris. To be able to track smaller pieces of debris, we need to upgrade the laser power, laser irradiance and efficiency[5].

### Literature study on removing space debris

• RemoveDebris

An experimental satellite called RemoveDebris was launched by the International Space Station in 2018. This satellite will perform three experiments with regard to remove space debris. The first experiment was performed in October 2018, RemoveDebris captured a dummy satellite with a net in low orbit. The research group says: “Our small team of engineers and technicians have done an amazing job moving us one step closer to clearing up low Earth orbit”. The idea of this technique is that satellites in the future can identify pieces of space debris and capture them with a net that is tethered to the satellite. Once such an object is captured small rockets can be used to drag the satellite and object back in the atmosphere. There is all a danger to this technique, it is possible that the captured space debris and the satellite collide and increase the space debris problem instead of solving it[7].

The second experiment will be with the use of a harpoon, soon in early 2019 RemoveDebris will shoot a pen-sized harpoon at a composite target that will be deployed by the International Space Station. This technique is similar to that of the capture with a net, capture a piece of space debris and return it to the atmosphere, a harpoon can be used to capture larger objects that can’t be captured with a net. However a harpoon could also break an object in two which makes the overall space debris problem worse[8].

In the third experiment RemoveDebris will deploy a drag sail that would speed up the deorbiting process of the satellite. A drag sail will be deployed so the satellite can re-enter the atmosphere and this will be the final experiment of RemoveDebris.

• Ion beam

Ion-beams can be used to remove debris from space. An ion beam is a type of charged particle beam consisting of ions, this can be used in space to transmit a force to a nearby piece of debris. This force can change the course of the debris, but it can also be used to slow down the debris such that it will crash towards the Earth. Depending on the size and material the debris will (partly) burn up in the atmosphere. In the literature study of PRE2016 3 Group19, we found more information about the ion beam. The most advanced technology that uses an ion beam is the Ion Beam Shepherd (IBS)[9]. The concept of IBS is that the spacecraft is located not too far from the debris and is pointing his ion thruster towards the debris. The ions with a high velocity will transmit their velocity to the asteroid and the asteroid will change it direction and possibly slow down. There is another thruster that will cancel out the motion caused by pushing the debris.

• Laser

The idea is simple, take a laser and gradually evaporate space debris till it doesn’t exist anymore or it changes of orbit. A lot of research has been done into this solution, it has been estimated that with a ground based laser it would be possible that under the right circumstances an object could be slowed down by 1 millimeter a second[10]. For most objects it would still take a long time before they are slowed down enough for them to break up in the atmosphere, but with this technique it would be possible to avoid major collisions. A downside is that a ground-based laser can only be used when the conditions are right, a laser wouldn’t be able to penetrate clouds. Another danger is that when the laser is aimed at a wrong part of a piece of space debris such a piece might explode of break apart[11].

• Gecko-inspired robot

Another technique on removing space debris is inspired from a gecko, the gripper that is used can be compared with the fingers and toes of the gecko. A gecko can hang upside down by their toes, since the toes are covered in a kind of bristles that stick when moved in one way and can easily be removed when moved in the other way. The grabber used the same adhesion technique, when the grabber is moved in the right direction, the debris will stick to it. The robot was tested in a zero gravity environment and could grab debris in a shape of a cube or an beach ball. This technique is not yet fully developed, next steps could be to develop sensors that could help monitor adhesion and the robot still needs to be tested outside the space station in a more extreme environment[12].

• Magnets

The last technique we will cover is using magnets to deorbit pieces of debris. This solution does not require contact with the debris, because magnetic fields can influence each other without contact. Therefore it is safer for the robot to use magnets, since no contact is required. The technique is based on magnetic field, these fields can attract or repel pieces of debris, to change the orbit or to completely deorbit it[13]. To create a magnetic field, superconducting wires are used that are cooled to extreme low temperatures. These field can then influence the orbit of multiple pieces of debris at once. A disadvantage of using magnets, is that they will not influence pieces of glass or aluminium and therefore the robots using magnets are only useful for debris that is made from elements that react to magnetic fields.

### Best solution

From the work done by PRE2016 3 Group19, they concluded the the ion beam technology is the best solution for the space debris problem. We will discuss the solution shortly and then draw our own conclusion. The experimental satellite RemoveDebris uses harpoons and nets to catch pieces of debris to remove them, therefore it needs physical contact with the debris for these techniques. There is a disadvantage to physical contact, since there is a risk that the piece of debris is not caught and it will drift away. Furthermore when the net or harpoon is stuck to a piece of debris it might not be functional anymore. Like RemoveDebris, the gecko solution also tries to grab the debris and collect it. The biggest difference between those techniques is that there is almost no force needed for the gecko solution to grab the debris and thus the chance on pushing it away is smaller. We think that using this technique is the most desirable technique using physical contact.

The next possible solution is to use a laser to evaporate the debris. This will be safer for the Earth, but it takes a lot of time to completely remove the debris. To use the laser it takes loads of energy, so it is almost not possible from space and a laser from the ground can only be used in the right conditions. Using a laser is not the only technique that does not use physical contact, we can also use magnets to change the orbit of debris. The biggest advantage of using magnets is that it can handle multiple pieces of debris at the same time and thus cleaning can be a lot faster. But it is only able to remove pieces of metal, thus glass and other debris will not be affected by magnets. The last, we think the best, solution is the ion beam. Since it is more precise than magnets and can easier be charged than an robot that uses a laser, the ion beam method seems like the best method.

### Additional resources

A lot of additional research has already been done in this field of research. In the following section we will show the separate papers:

• There are over 500.000 pieces of space debris that are currently tracked, these pieces move with speeds up to 17.000 miles/hour[14].
• General overview of the problem, with the addition of why the general public should care about the problem[15].
• The Kessler Syndrome explained[16].
• Threat of the Kessler Syndrome[17].
• Some possible solutions to the Kessler Syndrome[18].

## Study on ion beam

IBS slowing down a piece of orbital debris.

Since we chose the option of using ion beams to mitigate the orbital space debris, we will try to fully understand the way these beams work. This way we can design the robot in the best way possible.

An ion beam is an charged particle beam that consists of ions. Ions are atoms or molecules with an electrical net charge. The unit of the ion current density is: mA/(cm)2 (milliampère per cm2), while its energy is measured in eV (electron volt).

There has already been quite some research on the use of ion beams to get rid of the orbital space debris, in this research the robot that is used is referred to as: the Ion Beam Shepherd. This IBS is deployed with 2 ion beams, one of these will fire a beam of quasi-neutral plasma against the surface of the targeted debris. However when this would be the only beam that is fired, the IBS itself will move the other way because of Newton’s third law. So there is a second ion beam that points in the exact opposite direction of the first beam, this will fire a beam with the exact same intensity whenever the other beam fires. This way the reaction force on the IBS will be compensated and the IBS will not shoot through space itself. This compensation is necessary, because the ions that are fired towards the surface of the space debris can be accelerated up to 30 km/s and more[19].

Next we want to know what the IBS should be able to do to complete its task in the best way. The IBS should be able to fly in the proximity of its target and stay there at a constant distance. Then it should aim the ion beam along the tangent of the targets orbit, this way it can slow down the debris by firing at it. The main challenges while doing this are: the guidance and control of the IBS to get it to fly in the proximity of the target and collision avoidance.

Ion beams always have a certain divergence of the fired ions. This means that the further the ions have to travel to the target, the further they will spread in width. When the IBS has detected a target and has managed to get into the proximity of the target, it wants to have a certain distance to the target such that ion beam divergence can not cause part of the particles to miss the target. This can happen when the distance between the IBS and the target is too big. It will cause a decrease in the total momentum that is transmitted to the targeted object, which can be a problem if the computation of the amount of force to apply depends on the assumption of all the particles hitting the target.

## Getting rid of orbital debris

We considered two possible ways to get rid of the orbital debris by using an ion beam attached to the robot. We will discuss the pros and cons of these options and based on these we will choose one of them.

### Push the debris in the atmosphere

The first possibility that we will consider is pushing the debris in the atmosphere of the Earth. This will be done by shooting the ion beam towards the debris in such a way that the debris will get pushed out of orbit towards the Earth. Then because of the huge amount of speed it reaches it will slowly burn up in the atmosphere of the Earth. This is especially convenient for space debris in the low Earth orbit, because it does not require too much energy. The only downside of this option is that large pieces of debris might not fully burn up, which means that they will crash into the Earth. This can be a great danger if the debris will crash in an inhabited area. However, there has already been found a solution for this, namely steering the crashing piece of debris in a direction such that it will land in the pacific ocean. This solution has already been realised and put into use. It is done by computing how to hit the piece of debris such that it will get directed to this “spacecraft cemetery” in the pacific ocean. In this way the larger pieces of debris will not cause any danger for humanity when they survive the crash through the atmosphere. On the other hand, it does not seem very optimal to have a big pile of space junk in the pacific ocean, so that’s still a bit of a downside.

### Push debris to a graveyard orbit

The second possibility is pushing the space debris to a graveyard orbit about 300 km above the geostationary orbit[20] by using the same ion beam as mentioned before. This method is convenient for space debris that is farther away from Earth, because way more energy would be needed to push these satellites all the way to the atmosphere. Sending space debris into this graveyard orbit, these pieces of debris will no longer cause any harm to currently active satellites. However, this is a temporary solution, since eventually a shield of debris will occur in this higher orbit. Nevertheless, pushing debris to a higher orbit gives us the opportunity to find a real solution in time, because higher orbits have a larger path length, so it takes more time before a shield of debris will occur.

On the other hand, this method is less convenient for lower orbiting space debris, because it would require a huge amount of energy to push them in the graveyard orbit. Most of the space debris is present in the low Earth orbit, therefore, this method would not be convenient for the overall clean up of space.

### Conclusion

After considering the pros and cons of these two possibilities, we came to the conclusion that pushing debris in the atmosphere is more favorable. This option has only one downside of creating a pile of space junk in the pacific ocean over time. However, the second option seems very hard to realise because of the amount of energy that is needed. Besides, the second method will not entirely solve the actual problem that we are dealing with, since the debris is only shifted and not removed from orbit.

## Orbit failure

An orbit is the perfect balance between a satellite’s inertia and the gravitational pull on it. If space would be a perfect vacuum, meaning there was absolutely nothing in it, spacecraft would stay in orbit as long as we liked because of this balance. However, space is almost but not completely empty. Dust, dirt and gasses collide with spacecraft resulting in forces that act as resistance. Although these forces are very small, over long periods of time, the effect of the colliding particles is significant and slows down the spacecraft, eventually leading to a degradation of the spacecraft’s orbit. For example, spacecraft of the size of a passenger plane can stay in orbit for about one month before these forces cause it to fall out of orbit. Spacecraft could also collide with space debris of larger sizes and either gain or lose speed depending on the direction of the collision. Speeding up causes spacecraft to spin off into space, slowing down would cause them to crash into Earth. Collisions of debris could also knock spacecraft closer or farther from Earth. If they move closer to the Earth, gravitational pull increases, it they more farther, gravitational pull decreases. In both cases, spacecraft’s orbit changes[21][22]. To prevent orbit failure, regular adjustments are necessary.

Furthermore, Earth’s gravity is stronger in some places compared to others, leading to unevenness in experienced gravity. Together with the gravitational pull from other major members of the solar system like the Sun, Moon and Jupiter, this unevenness causes a change in inclination of spacecraft’s orbit. Regular adjustments of inclination are needed to maintain orbit[23][24].

Spacecraft are also pulled out of orbit by atmospheric drag. Although spacecraft travel through the uppermost, thinnest layers of the atmosphere, air resistance is still strong enough to pull them closer to Earth where gravity causes them to speed up. Atmospheric drag increases during times when the Sun is active. The Sun adds extra energy, causing the low density layers of the atmosphere to rise and replacing them by higher density layers that were previously on lower altitudes. As a result, spacecraft are moving through a higher density layer and experience more resistance. These drag forces eventually lead to atmospheric re-entry; spacecraft burn or fall down to Earth. To prevent re-entry, regular adjustments are needed to maintain the correct orbit. When the Sun is quiet, spacecraft need to boost their orbits about four times per year, but when solar activity is high, they have to be maneuvered every two or three weeks to maintain orbit[23].

## Solution Criteria

We assessed the following requirements and preferences for the robot design. Each requirement has been given a priority of Must Have, Should Have, Could Have or Won't Have.

### Requirements

Requirement ID Requirement description Priority
R01 The size of the robot must not be larger than 25 m Must Have
R02 The weight of the robot must not be larger than 500 kg Must Have
R03 The cost of the robot must not be larger than 2 billion dollars Must Have
R04 At end of life, all parts from the robot must be removed from orbit Must Have
R05 The robot must have appropriate fuel tanks such that it can get in orbit Must Have
R06 The robot should be able to move around in space by changing its direction and speed Should Have
R07 The robot needs to reach a minimal speed of approximately 17,000 mph[25] to stay in orbit Should Have
R08 The robot should be able to precisely detect orbital debris within a range of at least 50 m Should Have
R09 The robot must be able to push space debris it detects into the atmosphere where it will burn up Must Have
R10 The robot must be able to target objects in 360-degree space Must Have
R11 The robot must have a energy source to charge the ion beams Must Have
R12 The robot should get a continuous steam of data from Earth on where the orbital debris currently is Could Have
R13 The robot must be able to avoid collisions with satellites and other spacecraft Must Have
R14 The robot must be able to withstand extreme temperatures Must Have
R15 The robot should be able to withstand friction and supplementary heat Could have
R16 The robot must be able to withstand micro gravity situations Must Have
R17 The robot must be able to withstand harsh-radiation Must Have
R18 The robot must be able to withstand heat flux Must Have
R19 The robot should be able to operate for at least 10 years Should Have

#### Remarks

R07 - The orbital velocity of the spacecraft depends on its altitude above Earth. The nearer to Earth, the faster the required orbital velocity. To stay in orbit at an altitude of 124 miles (200 kilometers), an orbital velocity of a little more than 17,000 mph is required[25].

R11 - Solar panels could be used to charge the ion beams.

R13 - SPACETRACK is the current program for worldwide Space Surveillance Network (SSN). It consists of multiple, dedicated, electro-optical, passive, radio frequency and radar sensors. The purpose of the SSN is not only space debris cataloging and identification but also satellite attack warning and space treaty monitoring. In total the SSN tracked 39,000 space objects.

### Preferences

• The detection range should be as large as possible.
• The robot should detect and clean as much orbital debris as possible in a given time period.
• The robot needs to be efficient, it should not waste energy when cleaning space.
• The robot should be operational for as long as possible.
• The costs need to be as low as possible.
• The robot should have a sufficient reacting time for detection of space debris.

## General design concept

There are multiple actions the robot should be able to take in order to perform its task adequately. These are:

• Get up into orbit after launch
• Track pieces of debris
• Decide what piece to clear
• Plan/predict trajectory
• Move towards the debris
• Aim and decelerate
• Where to shoot from

### Getting to orbit after launch

There are multiple alternatives to getting an object into orbit. We will discuss some of them separately. The criteria to assess these methods are:

• Feasibility
• Technical
• Practical
• Costs
• Safety
• Pollution
• Reliability

#### Expendable Launch Vehicle

A launch vehicle or system that is used only once to carry a payload into space. It is not recovered. This is the only way a craft has been able to get into orbit so far.

Criteria assessment

• Feasibility

This option is very feasible, most likely the most out of all options. It is already widely used to get objects into orbit meaning it is both practically and technically possible.

• Costs

The costs of this option are relatively low on the short term. Since a lot of other methods in this list are giant structures that likely cost billions of dollars to build, this method seems to be a cheaper one. However, on the long term costs start to build up. Rocket fuel is very expensive. With this method, costs for sending only 1 kilogram of payload into space costs about 20.000 US dollars[26]. That’s 1.3 million dollars for the average human being. Thus, it seems that costs are a lot higher than it looks like at first with this method.

• Safety

The safety of this option is quite high in the spectrum compared to other options. While it can sometimes go wrong since we would be working with combustibles, the overall chance of it going wrong is quite small. This option has been tested and used very often and successfully meaning it can likely be used without too much risk.

• Pollution

Orbital pollution is of course a bit of a kink in the plan. Since empty fuel canisters and worn-out boosters are dropped off in this option, it adds to the problem our robot is aiming to solve by (potentially) adding its empty canisters to the debris belt in orbit. However, if the robot is able to drop the canisters in time so that they fall back to Earth then this problem is possibly avoided. Pollution in terms of the environment on Earth is not too bad. Since the takeoff is a one-time occurrence, the amount of pollution is not very significant.

• Reliability

Reliability of the expendable boosters is quite high. Again, since this method has been used many times before it has been honed to not go wrong very often. Thus, this method is quite reliable.

#### Space Elevator

A proposed type of planet-to-space transportation system, whose main component is a cable/tether that is anchored to the surface of the Earth and extends into space.

A space elevator would consist of a cable anchored to the Earth's surface, reaching into space.

Criteria assessment

• Feasibility

It is very hard to say whether a space elevator is actually something that can be built. It is safe to say that a structure this big would be the biggest humanity has ever built. The tether itself would have to be made from a material that is light, strong, weather/radiation resistant and not too costly. Unfortunately, such a material is not currently known to mankind. Additionally, climbing the elevator could take a very long time. It is difficult to power the cart going up and down reliably.

• Costs

The costs for building would, of course, be enormous. However, estimations predict that having built a space elevator will reduce the cost of sending loads into space tenfold, to 200 US dollars per kilogram[26]. This means that, if an inexpensive space elevator would cost 20 billion dollars to build, the elevator would pay for itself after sending one million tonnes into space. This is a bit more than twice the weight of the International Space Station[27].

• Safety

Safety is something that should be of utmost concern when building a structure like this. Were the elevator to break, the results could be disastrous. The upper part of the tether would drift off into space, potentially adding a large amount of extra debris into orbit. The bottom part of the tether could whip around the Earth and also remain in orbit, which results in a large ring of tether around the Earth meaning big problems for satellites and space flight.

• Pollution

Orbital pollution will only be a problem were construction of the space elevator to go wrong. Then, orbital pollution will be off the charts. However, were the construction to be a success the space elevator may actually be a help in cleaning the debris, since the end of the tether could be made into a station the robots could go to to refuel or repair. Pollution on Earth is a different story. A space elevator would require enormous amounts of energy to function properly. This energy has to come from somewhere. Since the most energy producing ways on Earth are not very environment friendly, the space elevator may have a big impact on the environment. However, were the “green” energy production methods to be greatly improved within the next few years, this problem may be rectified.

• Reliability

The reliability of the space elevator would depend on the material of its tether along with the amount of energy it has access to. Again, it is of utmost importance that the tether does not break since the results would be disastrous. The energy cannot run out either, since then the cart would stop and start falling back down to Earth. Since there is no material currently known to be strong enough for a space elevator, and no energy production method (other than a nuclear reactor on board of the cart) that could provide for the space elevator’s needs, a space elevator seems to be not that reliable of an option.

#### Skyhook/Rotavator

The rotating concept. If the orbital velocity and the tether rotation rate are synchronized, the tether tip moves in a constant curve. At the lowest point it is momentarily stationary with respect to the ground, where it can 'hook' a payload and swing it into orbit.

A proposed momentum exchange tether whose main component is a heavy orbiting station, connection to a cable which extends down towards the upper atmosphere. Payloads are hooked to the end of the cable as it passes and flung into orbit by rotation of the cable around the centre of mass. If the tether is long enough and the rotation rate high enough, it is possible for the lower endpoint to completely cancel the orbital speed of the tether such that the lower endpoint is stationary with respect to the planetary surface that the tether is orbiting.

Criteria assessment

• Feasibility

At first this idea seems completely moronic. Flinging payload into orbit with a giant rotating tether does not seem like it would work very well. However, a study by the NASA Institute for Advanced Concepts published in 2000 proposed a 600 km long tether rotating with a speed of 3.6 km/s at the tip of the tether[28]. This speed could be matched by a hypersonic airplane at about 100 km height to transfer the payload over. The aim of the study was to show that a structure like this is in fact possible with existing materials such as Spectra 2000, which is an ultra-high-molecular-weight polyethylene[29] (meaning it is very strong and light), and the heat resistant Zylon. A further study in 2001 by the same team proposed increasing the rotation speed, increasing the height of the tether and changing the transfer method to a reusable rocket propelled vehicle. This would reduce the mass required by the tether by a factor of 3[30]. The study concluded that “There are no fundamental show-stoppers”, that there are still some technological challenges to be overcome before the HASTOL (Hypersonic Airplance Space Tether Orbital Launch) system can be developed properly. It does tell us, however, that a system like this may actually be possible in the foreseeable future, both practically and technologically.

• Costs

The costs of building such a system would of course be very large, but while there are no exact numbers available, estimates predict that the subsequent operational costs would be very low, and that the structure would pay for itself within a relatively small time frame[28].

• Safety

The study referenced above described a system that takes safety very seriously. With every single step taken the safety factor is taken into account. This results in a tether that can withstand multiple cuts on a single level, and even if the primary tether is completely cut it described a secondary tether that can withstand the strain as well. Thus, that leads us to believe that the Rotovator structure is quite safe[28].

However, if the tether breaks the results would be even more devastating that the tether of the space elevator breaking. Since this tether already has a speed of 3.6 km/s when working properly, breaking of the tether could destroy large areas on Earth, as well as destroying a lot of systems in orbit already.

• Pollution

Orbital pollution could be avoided were the tether not to break. However, it is important that the Rotovator is on a different orbit than any other satellite or system in orbit already, since collision with the rotovator would destroy the satellite colliding with it, as well as it may disrupt the rotation speed of the rotovator itself. Pollution on Earth would be negligible, since the structure would not even touch the Earth. Also, the energy needed to keep it functioning is quite low since there is very little friction in orbit.

• Reliability

Once set up, the structure works very reliably. The strain on the tether can be tested before construction, and the meeting of the airplane carrying the payload and the end of the tether can be plotted reliably beforehand. Thus, the system would be quite reliable.

#### Space Fountain

A proposed form of an extremely tall tower extending into space. A stream of pellets is accelerated upwards at a ground station. At the top it is deflected downwards. The necessary force for this deflection supports the station at the top and payloads going up the structure.

Hyde design space fountain.

Criteria assessment

• Feasibility

While this structure may work on paper, in practice it may prove a lot more challenging. While a space fountain like this would not need materials as strong as the structures described above, the particles would need to be accelerated to such speeds that it required amounts of energy we do not currently have access to. Thus, this structure is not very feasible[31].

• Costs

The costs of building the structure is not only enormous like with most of the proposed methods, but since the structure requires a lot of particles to be constantly accelerated at all times, the upkeep costs of this structure are very high as well.

• Safety

The structure ought to be quite safe. While it is very costly, the structure has very little chance of falling back down because of the enormous force produced by the particles going up the tube. However, because of the amount of energy needed to accelerate the particles as well as the energy needed to climb the tubes with some sort of cart, the risk that the amount of energy that can be produced is not enough is quite high.

• Pollution

While orbital pollution is not worsened by this structure, environmental pollution on Earth may be quite bad. Again, because of the fact that most large energy production methods are not clean and the fact that this structure requires enormous amounts of energy, pollution is boosted.

• Reliability

If built properly and somehow we find a method to produce infinite amounts of energy, this method can be quite reliable. However, since it is likely that we cannot produce the amount of required energy reliably, the structure is likely not a good option.

#### Orbital Ring

Orbital ring.

A concept for a space elevator that consists of an artificial ring placed around the Earth.

Criteria assessment

• Feasibility

An orbital ring is relatively feasible, even while it might not look like it at first. The materials requirements are not as harsh as, for example, those of the space elevator, since a ring has quite a strong structural integrity by design, and it would . It would, of course, still be a giant undertaking to get the ring into space, but the materials and techniques are already existent[32].

• Costs

The costs of creating an orbital ring is estimated at about 20 billion dollars. This is, of course, a lot of money. However, the costs of sending payload into space would be reduced drastically. Predictions say that, if an orbital ring is in space, trips to orbit would become as costly as a regular train ticket to a neighbouring city[33]. This means that the ring would pay back for itself very quickly.

• Safety

The ring itself is very safe in normal operation. It is almost like a train track around the Earth. However, were the ring to be hit by a large asteroid or another piece of space debris large enough to make a big impact, the results would be disastrous. In less than two hours, all the lifting elements will have reached the impact site. All the elevators to the ring as well as much of the ring itself would fall to the planet surface. An impressive cloud of orbital debris would remain in orbit for some time.

• Pollution

Orbital pollution would, on normal operation, be negligible. There would of course be a giant ring in space that would have to be avoided, but this could be done relatively easily. Environmental pollution would not be that bad either. The trains on the rings would not require that much more energy than current trains on Earth need, and elevators up to the ring would not require more energy than the elevators described previously.

• Reliability

The issue with orbital rings is that everything has to go right the very first time it is attempted. One single mistake while building or utilizing the ring could lead to a disaster that is irreversible.

#### Launch Loop

A proposed system for launching objects into orbit using a moving cable-like system situated inside a sheath attached to the Earth at two ends and suspended above the atmosphere in the middle. The design concept was published by Keith Lofstrom and describes an active structure maglev cable transport system that would be around 2,000 km (1,240 mi) long and maintained at an altitude of up to 80 km (50 mi). A launch loop would be held up at this altitude by the momentum of a belt that circulates around the structure. This circulation, in effect, transfers the weight of the structure onto a pair of magnetic bearings, one at each end, which support it.

Launch loop.

Criteria assessment

• Feasibility

The option is not really feasible, since it will almost be impossible to get the whole structure of 2000 km to a height of 80 km. There should be materials developed that could handle the tensions and forces to keep the launch loop in the air.

• Costs

The costs are not too high, since it should be build once and then the structure can be reused. The costs are estimated between the 10 and 30 billion dollars.

• Safety

When one big part of the system would fail the system may explode with the power of a nuclear bomb. But when this system will be built far away from habitation, the impact will be small if something goes wrong, since no nuclear radiation will be emitted.

• Pollution

There is almost no pollution with this launch technique, since no greenhouse gases will be created. The energy needed can be from clean power sources. No space debris will be created, since the objects will reach orbit without any help of other thrusters.

• Reliability

If the system works, it is reliable, since the velocity of the object fired from the launch loop can easily be measured.

#### KITE Launcher

The KITE Launcher - using momentum to accelerate the payload.

This is a form of an endo-atmospheric tether. The idea involves towing an aerodynamic payload behind a large subsonic, or low supersonic aircraft with a very long (20 km+) cable. At high altitude, the aircraft executes a change of direction, and the resulting centripetal action, the intensity of which is dependent on the length of the cable and the rate of turn, will fling the payload into space.

Criteria assessment

• Feasibility

There should exist a cable of more than 20 km that can also hold the payload. The other aircraft should be able to carry this payload in the air. Also the payload should get a huge amount of energy to get into space, that may not be created with the aircrafts we have right now.

• Costs

The costs are not too high, since no structure should be created. The only problem that would cost money is creating a cable that can carry the payload.

• Safety

The KITE launcher can be relatively safe, if there is no other aircraft nearby. Also when the cable breaks, the payload should be able to safely come down to the ground, this problem can be solved by adding a parachute to the payload and open this parachute if needed.

• Pollution

This technique still creates pollution, since it will use an aircraft to fling the payload in space. No space debris will be created.

• Reliability

This method is not reliable, there are lots of different factors that have an influence on how and with what velocity the object is launched. First of all the method is not precise, the method only focuses on the velocity the object should get, but one cannot control where the object will go. Furthermore, wind, speed of the aircraft and the change of direction influence the velocity the object will get when launched. This means that it can get too much or not enough velocity when launched.

#### StarTram

A proposal to launch vehicles directly to space by accelerating them with a mass driver. Vehicles would float by maglev repulsion between superconductive magnets on the vehicle and the aluminum tunnel walls while they were accelerated by AC magnetic drive from aluminum coils. The power required would probably be provided by superconductive energy storage units distributed along the tunnel. Vehicles could coast up to low or even geosynchronous orbital height; then a small rocket motor burn would be required to circularize the orbit.

Electro-dynamic interactions in the railgun used in the StarTram.

Criteria assessment

• Feasibility

This technique requires an enormous structure of at least 22 km high and a length between 1000 and 1500 km. Also it should be able to create huge amounts of energy 22 km above sea level, which can be quite hard. This structure would require materials that have a lot of strength, but these materials do not exist.

• Costs

The costs of the StarTram for transport of humans will be around the 70 billion dollars. So this technique is relatively expensive. Also there should be a lot of materials developed which also costs lots of money.

• Safety

The StarTram is quite safe, the vehicle will be attached to a rail and have nowhere to go. Since it has a path over which it is accelerated, it is relatively precise.

• Pollution

The vehicles still need a small rocket to get to their orbit height, so depending on the technique space debris will be created, but also there will be pollution in terms of greenhouse gases.

• Reliability

The StarTram is relatively reliable, the object is accelerated along a fixed path. And with the additional thruster that is needed to bring the object into space, one can correct the path of the object. Therefore the StarTram is relatively reliable.

#### Space Gun

A proposed method of launching an object into outer space using a large gun, or cannon. Gun launch concepts do not always use combustion. In pneumatic launch systems, a projectile is accelerated in a long tube by air pressure, produced by ground-based turbines or other means. In a light-gas gun, the pressurant is a gas of light molecular weight, to maximize the speed of sound in the gas.

Criteria assessment

• Feasibility

The technique of guns is already known, and thus it should also be possible to make this in the large. The technique does not require to make an enormous structure or make use of materials that do not exist yet. The only problem with this technique that the projectile will gain so much speed in not that much time, that it is not possible to launch humans with this technique. It also need the projectile to have the shape of a bullet, otherwise things might break. The speed the space gun can give to the projectile depends on the mass the projectile has, the heavier a projectile the more pressure needed to give the same speed to this projectile.

• Costs

The costs of the project are not high, since no new technique need to be developed. The space gun can also be reused for other launches. The only costs for development will be for the space gun and everytime a satellite is shot in space there should be a new capsule.

• Safety

The system is relatively safe, when something goes wrong, probably only the projectile is lost, but new projectiles can still be fired.

• Pollution

A space gun does not make use of thrusters that burn fuel, but it makes use of the difference in pressure in front of the projectile and behind the projectile. This difference in pressure can be generated by turbines that work on electricity. This electricity can be generated by clean sources. The satellite that is launched by a space gun should have the shape of a bullet, this can be achieved by making a capsule around the satellite. This capsule should be removed when the satellite is in space, this may create new space debris, or the satellite should push the capsule back to Earth.

• Reliability

The reliability of the space gun would depend on the accuracy of the gun and if it the projectiles get enough velocity. If the accuracy is bad, the space gun might miss the place where the satellite is planned, or the satellite might not reach space at all. But when it is better, it can be a cheap way to shoot satellites, not humans, to space.

#### Ram Accelerator

The ram accelerator is a device for accelerating projectiles to an extremely high speed. The idea consists of a long barrel, filled with flammable gases. The gases are contained in the tube by a diaphragm at both ends. To accelerate the projectile the projectile is fired with a supersonic speed through the first diaphragm them the projectile burns the gasses as fuel and accelerates under jet propulsion[34].

RAM accelerator.

Criteria assessment

• Feasibility

The technique can only be used for payloads without humans, since the projectile will be accelerated to a very high speed in a small time, which will created a huge amount of G-forces.

• Costs

The costs are not too high, everytime something is accelerated to a high speed, the tube should be filled with new gas.

• Safety

When something goes wrong with the gases, for example when they ignite, there could be a huge explosion that will destroy the barrel, but probably also the area around it.

• Pollution

Every time a projectile is accelerated the gases are burnt. This means there will be greenhouse gases created from burning the other gases. No space debris will be created with this method.

• Reliability

This method is not tested in the large and there can be safety concerns. Also there cannot be controlled to what speed the projectile is accelerated, so it can be too slow, but it can also be too fast.

#### Slingatron

A slingatron accelerates a projectile in a tube or track that has circular or spiral turns. The projectile can be accelerated in the tube, by moving the tube in a constant circular motion. When the projectile reaches the end of the tube, it will be shot to space with a high velocity.

Criteria assessment

• Feasibility

To reach the speed needed to get a projectile to space we need an enormous tube and we need something that can make this tube rotate. This is not really feasible to move a structure like this at the right speed. Also the G-forces created by a slingatron are too much for a human body, so it is not able to shoot people to space.

• Costs

The costs of a slingatron are not too high, since the structure does not consist of materials that are hard to make and it is not a structure that is hard to make or is of an enormous size.

• Safety

The method is safe, but not for humans to sit in the projectile. Also the projectile is hard to control after it is fired out of the slingatron, this means that if it is not fired in the right direction, it may never come in space and crash on Earth.

• Pollution

No pollution is emitted if the slingatron is rotated by an machine that makes use of energy that is generated by clean sources. Furthermore the projectile would get a speed to get it into space, so no other thrusters are needed and no space debris is created.

• Reliability

The slingatron is not reliable. First of all, once the movement has started, the projectile cannot be stopped anymore in a simple way. This means that if something goes wrong, the projectile will probably crash. Also the accuracy of the slingatron is not high, since the projectile is not really controllable in the tube, but also when fired, the trajectory of the projectile is fixed, this means that the satellite can end up in different places than planned.

#### Orbital Airship

The orbital airship is a technique being developed by JP Aerospace intended to launch airships into orbit. It makes use of three separate airships stages to reach orbit. The ascender, is the first stage and would be used to provide more lift to the airship that is launched The Dark Sky Station would be a permanent floating structure, that would allow transfer of cargo and personnel between the Ascender stage and the orbital stage. And it would also serve as the construction facility. Orbital Ascender would be the final stage for the airship. It would give more lift to the airship to lift it from 140000 to 180000 feet. To give enough lift to the airship, the Orbital Ascender should be over 1600 meters long to gain enough buoyancy. From 180000 feet it would accelerate with ion propulsion towards space.

Criteria assessment

• Feasibility

This method is not feasible in the near future. It is needed to create three different stages for this launch technique. The first one should be able to provide more lift to the airship, this will be hard to have a structure in the air where the airship can be connected to to give more lift. The stage should be able to provide enough lift to the airship, this will be a huge challenge, since an airship is quite heavy. The second stage should be a permanent floating structure at around 43 km high, which not feasible with the current technique. The last stage would require humans to have an structure in space that is over 1600 meters long, where the largest airplane in the world is not yet 100 meters long.

• Costs

Creating all three stages will cost loads of money. There are not estimations yet available about the cost of this project.

• Safety

The biggest concern in terms of safety will be the huge structures in space. If something goes wrong and those structures will come down, it may have huge consequences for the place they will crash. Furthermore to lift the aircraft to space, it should have contact with all three stages at least once to give the aircraft the boost it needs.This requires precision, since if something goes wrong with the contact, it will have consequences for the people in the aircraft.

• Pollution

The pollution emitted by the aircraft is the only pollution to get it into space, since the stages do not work with thrusters to gain height. There will not be any space debris, since the aircraft does not use fuel tanks that are later dropped by the aircraft.

• Reliability

If the orbital airship method can be executed there are still some risks when executing the method. For all stages it might be hard for the airship to profit from it. The airship should use the three stages, but to use them, it need to have some kind of contact to gain altitude. Also the first and the third stage are both really dependent on the weather. Since those are floating platforms in the air, they are relatively susceptible for the weather. If there is a lot of wind, they could drift off and then it costs energy to move them back to the right place.

#### Conclusion

We discussed 12 possible solutions to get the robot into space. For all methods we looked at the criteria that were the most important for us. These criteria were feasibility, costs, safety, pollution, reliability. Some methods are not feasible within ten years, therefore we cannot use them to get the robot into space. For other methods we do think that they ever be possible to use them to get objects to space. In the table below we ranked all methods on the criteria from 1 to 5. The lower the score the better the solution for that criteria. The sum is the total sum over all criteria, this means that if the sum is the lowest, it is the best solution over all criteria. We will not include some of the methods, since these methods will not be feasible at all.

The methods we will not rank are Orbital Airship, Orbital Ring, Space Fountain, Launch Loop, KITE Launcher, Space Elevator, StarTram and Skyhook/Rotovator. Except for the KITE Launcher, all methods above are not possible, because of the structure they require. The launch method require to have a structure in space or high up in the air, with the current technology it is not possible, since the materials do not exists to make it feasible. We think the KITE Launcher is not feasible, since the technique will not generate enough speed to get the satellite into space.

In the table we can see that the sum over all criteria is the lowest for the expendable launch vehicle. We think that this is also the easiest way of getting the robot in space, the only disadvantage is that there will be more space debris because an expendable launch vehicles create debris. Since the method is used nowadays it is very reliable and safe to use it to bring satellites into space.

The other three launch methods have a score that is worse than for the expendable launch vehicle. The slingatron has to best score of those three, the biggest advantage of this method is that it will not pollute the Earth, but it is not accurate, so one cannot say exactly where it will end up. For the Ram Accelerator and the Space gun this is also the case. The speed which the satellite gets during acceleration is not constant. The Ram Accelerator will also pollute the Earth, since it uses gasses that will inflame when the projectile gets accelerated.

We can conclude that the expendable launch vehicle stays the best solution to bring satellites into space. Since it is the most accurate and safe solution. Therefore we recommend to use this launch method to bring the satellite into space. The biggest disadvantage is that it will create new pieces of space debris that have to be removed by our robot.

Design Feasibility Costs (shortterm) Costs (longterm) Safety Pollution Reliability Score
Expendable Launch Vehicle 1 2 4 1 4 1 13
Space Elevator -- -- -- -- -- -- --
Skyhook/Rotovator -- -- -- -- -- -- --
Space Fountain -- -- -- -- -- -- --
Orbital Ring -- -- -- -- -- -- --
Launch Loop -- -- -- -- -- -- --
KITE Launcher -- -- -- -- -- -- --
StarTram -- -- -- -- -- -- --
Space Gun 4 3 1 5 3 4 20
Ram Accelerator 3 3 3 5 5 5 24
Slingatron 3 4 1 4 1 5 18
Orbital Airship -- -- -- -- -- -- --

### Track pieces of debris

There are a few ways of tracking space debris. The criteria to assess these methods are:

• Feasibility
• Accuracy
• Latency
• Range
• Reliability
• Cost

#### Tracking from Earth with radar

In the current day most space debris is being tracked with the use of radars. With the use of bistatic radars space debris can be tracked up to a certain level of accuracy. This accuracy is not extremely high, but when combined with the predicted flight path of launched object. A acceptable accuracy for collision prevention can be calculated[35].

##### Criteria assessment
• Accuracy

When the data from the radar is combined with data from flight paths, the position of is not accurate enough for our purpose of targeting a space object with an ion beam.

• Latency

Since we can predict where space objects will be next, latency is not a problem.

• Range

Objects are tracked all around the Earth, so the range of this detection method is unlimited.

• Reliability

The reliability is good, because even if one radar system fails, there are multiple stations. And predictions models can be used to furthermore ensure reliability.

• Cost

This method has already been implemented around the world, thus only little cost is required to link the data to our satellite systems.

#### Tracking from Earth with lasers

The idea is that with lasers objects in orbit can be tracked with a higher accuracy than with radar. The space debris reflects the laser to Earth where a receiver detects this reflected signal. With the time it takes from sending till receiving laser and the position and direction of multiple laser the location of the objects can be tracked accurately. A downside is that fewer objects can be tracked at the same time, as a laser only can track one item at a time. Also when the weather conditions are not right, lasers will not work.

##### Criteria assessment
• Accuracy

The accuracy of the position of object tracked with lasers is higher than when the position is tracked with radar. Combined with data from flight paths, it is possible to predict the position with high accuracy.

• Latency

Since we can predict where space objects will be next, latency is not a problem.

• Range

Objects can be tracked around the entire planet, so the range would be unlimited

• Reliability

When the weather conditions are unfit for lasers, for example through fog and clouds. The system can’t track objects, but we can still predict the location with the use of prediction models.

• Cost

This method is not extremely costly, as these are relatively cheap to produce and install[36].

#### Visual based navigation

Visual based navigation can be used to identify and position the satellite to make it able to aim at the piece of space debris. Optical, infrared and LIDAR cameras can be used together with image recognition to locate space debris. An advantage of this system is that it is also possible to determine information about the shape of the space debris[37].

##### Criteria assessment
• Accuracy

The accuracy is very high, because the information from the camera’s can interpreted very precisely to see where the ion beam has to be aimed.

• Latency

Because all information can be calculated on board of the satellite, this is highly depended of the processing power of the on-board computer chip. It would be ideal to have the calculated information in under 0.1 seconds.

• Range

The range of this system is very limited, because the objects have to be in range where the cameras can capture footage material of the space debris. However, optics can be used to increase this range.

• Reliability

This technique is reliable, LiDAR can be used no matter the light conditions. So, it does not matter if the satellite is in the shadow of the Earth or not.

• Cost

This technique will be relatively cheap, only cameras are needed that are likely to be included for navigation.

#### Conclusion

We have discussed three different methods of tracking space debris. The best way would be to have a combination of all three methods. For determining what pieces to clear we could track pieces from Earth with radar. To determine what pieces have the highest risk of colliding with another piece, the tracking data does not need to be very accurate. When the correct piece is chosen, laser tracking can be used to determine a more accurate position of the debris. With this accurate data the satellites can position and orientate themselves to get ready for clearing the piece of debris. Finally, the satellite can use LiDAR to fine tune it’s position and orientation with respect to the debris. LiDAR can also be used to get more information about the piece of debris. For example, the size and shape of the debris. This information can be used to precisely target the space junk.

### Prioritising

There are thousands of pieces of debris that are in orbit. The robot we would like to send into space has to clear pieces of debris, but does not know where to start. In this section we will discuss different approaches in choosing the next piece of space debris to clear.

#### Considerations

There are multiple aspects to consider when giving pieces of debris priority values. First of all, we should look at the probability for a piece of debris to collide with another object. When pieces of debris collide, they split into multiple pieces of fast-moving bullet sized objects that in turn can damage and destroy other orbiting objects[38]. This means that it is essential for our robot to clean up pieces of debris that are likely to collide soon, since when they collide the problem the object poses will multiply.

Secondly, the mass of the object should be considered. Not only will an object with a bigger mass likely have a bigger impact on collision, it also determines the amount of potential debris mass spread into pieces on contact. However, objects with a bigger mass require a lot more energy to slow down and bring back into the atmosphere. This means it might be a better idea to slow them down just enough to decrease their orbital lifetime substantially while taking care to plan the trajectory such that they are unlikely to collide with another piece.

Lastly, it would be a good idea to take a certain proximity to the robot into account. If there is a piece 20000 kilometres away from the robot that has a high priority, and a piece 2 kilometres away from the robot that has a slightly lower priority, it may still be a better idea to clean the piece that is closer first to save energy.

#### Concretisation

In 2006, NASA developed the LEO-to-GEO Environment Debris model (LEGEND)[39].

“LEGEND is a full-scale, three-dimensional, debris evolutionary model that is the NASA Orbital Debris Program Office’s primary model for study of the long-term debris environment.”

This quote is from the Astromaterials Research & Exploration Science (ARES) page on the NASA website which described the LEGEND model[40]. In Layman’s terms, the LEGEND model uses information from a recently updated historical satellite launch database (DBS database), two efficient state-of-the-art propagators (PROP3D and GEOPROP), and the NASA Standard Breakup Model to effectively simulate the historical and future debris environment from LEO to the geosynchronous orbit regions[40]. We can effectively use this LEGEND model to predict collisions. This is actually a key component in the LEGEND model: its collision probability estimation model.

The LEGEND model is capable of predicting trajectories for the debris objects. However, when two trajectories cross, there is still a chance that the two do not collide. Collision probabilities among orbiting objects are estimated with a fast, pairwise comparison algorithm, Cube[41][42]. Since debris objects in orbit often rotate wildly, Cube defines a cube for each object within which the object lies (“The cube dimension is characterized by the short-period perturbations on the positions of the objects.”)[43]. The cube wherein objects lie can be obtained in a straightforward manner. When two objects i and j lie within the same cube, their collision probability Pi,j. is given by:

Two objects (i and j) in their respective "cube hitboxes".

Pi,j = si sj Vimp σ dU

where si and sj are the spatial densities of objects i and j in their respective cubes, Vimp is the relative velocity between the two, dU is the volume of the cube, and σ is the collision cross-sectional area which can be computed with the formula[44]:

σ = π( ri + rj )2 ( 1 + Ve2 / Vimp2 )

where Ve, the escape velocity, is given by √( 2( m1 + m2 )G / ( ri + rj ) ), G is the universal gravity constant, and ri and rj the average radii of objects i and j.

Now, to get the priority list for the objects, the value of Ri is calculated for all objects i with a non-zero collision probability using the following formula:

Ri = Pi * mi

Where Pi is the collision probability defined above, and mi is the mass of object i.

Now, we’ve taken both the probability of a collision and the mass of the object into account. The third and last consideration is the distance to the object from the robot. To integrate this into the formula, we need to consider what the distance to the robot should do to its priority value. The further away the object is from the robot, the lower its priority should be. This can be achieved by dividing Ri by the product of the distance to the robot and some constant c. This gives us the following formula for the priority Oi of object i:

Oi = Ri / ( di*c )

where di is the distance from object i to the robot, and c is some constant that dictates the importance of the distance to the robot.

This priority list O is then sorted in descending order, and handled from top to bottom. This way, objects with the highest priority are handled before objects with lower priorities.

### Move towards the debris

After the robot chose a piece of debris that he will be pushing back into the atmosphere, the robot should move to the position from which it is able to remove the debris. The robot has two options to move itself. The first is the classic option of a propulsion system, these systems are mostly used to keep satellites in space. To move to other specified locations will cost much more fuel than keeping only a satellite in orbit. This will mean that the robot cannot be used very long, because of the limited fuel. Therefore, it would be better to have a moving mechanism that has unlimited energy. As mentioned earlier, the Ion Beam Shepherd has two ion cannons, one to push the space debris and the other ion cannon to keep itself in the same place[9]. The ion cannon can be charged with solar panels, thus the ion cannons do not depend on a limited source of fuel. A laboratory study[45] has shown that the ion cannons can be used for space debris removal, but that they can also work to accelerate the robot or to decelerate the robot. This can be done by firing only one of the ion cannons, which means that the robot will start accelerating in the opposite direction of which the ion cannon is fired. This would mean that there is a way to move the robot through space towards the right place to remove the debris. Using the ion cannons will also result in a longer life time, since the energy cannot be depleted.

Therefore, it would be better to use the ion cannons to move the robot in space, because no new technology needs to be installed on the robot and thus it will be smaller. Also, the lifetime of the robot will be longer and therefore the ion cannons would be the better choice.

### Aim and decelerate

An object in orbit being decelerated along its tangent. The green vector indicates the force exercised on the object, and the white line indicates the orbit of the object.
An object in orbit being accelerated towards Earth. The green vector indicates the force exercised on the object, and the white line indicates the orbit of the object.

Once the robot is close enough to the object to start decelerating it, the robot must decide on an angle and the amount of force to exercise on the object. Since the object must fall back to Earth, there are two options to decrease its orbit enough to fall back to Earth: the robot either slows the object down enough along its tangent for it to fall back into the atmosphere, or the robot accelerates the object towards the Earth which effectively “increases gravity”, meaning the debris will eventually crash down into the atmosphere as well.

There are two main things to consider when choosing between these two angles. We need to consider the hardware design requirements and the amount of force needed to decrease the orbit enough in both cases. In order to apply force along the tangent of the object’s trajectory, the robot will have to match to speed of the debris object and go fly “in front” of it, in the same orbit as the object. A safe distance from the robot to the debris piece at which the ion beam doesn’t diverge from its target too much is considered to be about 7 meters[46]. To maintain this distance, the robot must change its speed to match that of the debris piece at all times. This is the reason the robot must have two thrusters, one on each side. If the robot fires one stream of particles towards the debris, then by the third law of Newton the robot itself will be accelerated. To counteract this effect, it will need a second outlet on the opposite side of the robot.

To apply force towards the Earth, the robot must be in a slightly higher orbit than the object. Here, it is much harder to measure how fast the robot must go to stay alongside the object. Since the orbit of the robot is slightly higher, it must maintain a higher speed than that of the object in order to keep up with it. Since the robot will still need to counteract the force predicted by Newton’s third law, it may need a third ion beam in order to keep up its speed along its own tangent. Thus, as far as hardware complications go, deceleration the debris along its tangent is easier. However, the amount of force required may make up for it.

In order to check, we have modelled a piece of debris in orbit to see what the forces exercised on it do to the trajectory of said piece. The GIF on the left illustrates the orbit when the object is accelerated towards Earth, and the GIF on the right illustrates the orbit when the object is decelerated along the tangent. In both images, the force exercised on the object is equal (1000 Newton). As we can see, decelerating the object along its tangent decreases its orbit a lot more than accelerating towards Earth does. This is quite logical, since accelerating towards Earth is effectively equal to increasing its gravity. This means its orbit can be maintained, on a different level. Thus, it would require a lot more force to make the object crash into Earth, where deceleration along the tangent slows the object down and lets gravity do the rest.

Now of course in reality, a constant force of 1000 Newton is not something that can be achieved by an Ion beam. This force is enough to knock an object of 40 tonnes from an orbit 2000 kilometers from the surface back down to Earth within 4 hours. This time frame is not realistic, and is not something we aim to achieve. A more realistic estimate is that we will be handling objects of 1 to 2 tonnes in weight, and will be able to exercise a force of 60 mN. In that case, the object would take between 80 and 150 days to crash down[46].

## Risk analysis

The robot we are researching and designing at the moment is meant to make space safer for satellites and rockets and to make sure that space can be used in the future. To remove the debris from space, the robot will slow down the debris and then it will crash in the atmosphere. Most of the debris will be destroyed in the atmosphere, but some of the bigger heat resistance pieces of debris will crash on Earth. It requires utmost precision to make these pieces of debris crash in a designated area. There is an area in the pacific ocean which is the furthest away one can get from land without leaving Earth, this place is already used for old satellites and rocket bodies. Before re-entry of the atmosphere the orbit is calculated which the debris will follow and there is made sure that it will crash in this area.

There is a lot that can go wrong during the process of cleaning space debris. This will have consequences for the trajectory the piece of debris will follow and therefore the place it will crash will change. Below we will discuss the risks that we have in the stages of cleaning a piece of debris, we will also discuss the consequences for the stakeholders (society) when it will go wrong. We divided the process of removing debris in three stages. The first stage is before the robot will start to shoot an ion beam. The second stage will cover the problems and risks when shooting an ion beam at a piece of debris. The last stage is after the robot did its job and the piece of debris got slowed down and therefore will crash in the atmosphere.

#### Before slowing down

Before a piece of debris is decelerated by the IBS there are a couple of things that could go wrong.

• The IBS can crash into debris when trying to fly in the proximity of this debris

This would be a very big problem since then we would have to replace this IBS, which costs a lot of money and effort especially when this happens more often. This will also cause the IBS and the targeted debris to break down in a lot of small pieces of debris, which only increases the amount of orbital debris while we are trying to clean it up. This problem will also occur when the IBS collides with another piece of debris that it was not targeting. However the chance of colliding with the targeted debris is bigger since it will try to fly in its proximity. The society will be affected if this problem occurs since it will have the consequences of losing a cleaner and adding more debris to clean. This means that the entire process is being delayed, which can lead to the discussed problems like: losing satellites and not being able to space travel.

• The targeted piece of debris collides with another piece of debris

When the calculations have been done and the IBS has been given the command to target a certain piece of debris, it could be that while the IBS is moving in that direction the targeted piece of debris collides with another piece of debris. This will mean that the debris breaks up into multiple smaller pieces which all have a new mass and slightly different orbit. This implies that the calculations have to be done all over again or another piece of debris should be targeted. This risk however is not something that we could fully prevent with the use of an IBS. We can clean up pieces of debris that have a higher probability of crashing into another piece of debris first, but it can never be guaranteed there will never be a collision. It will not have great consequences for society as well, it will only cause a slight increase in amount of orbital debris.

#### During slowing down

• Debris will not be decelerated properly

There is a risk with this method that the ion beam will not slow down the debris enough to make it crash in the right place on Earth. The cause of this problem can be that the ion beam is not correctly functioning anymore and therefore it cannot deliver enough force to the object. It can also be the case that the piece of debris is rotating so much that the ion beam cannot focus on the debris and decelerate it. In the first case the robot is broken and if it is not repairable, the robot should destroy itself in the atmosphere. Then it will become a piece of debris that is slowed down and we will go to the next stage. In the other case the ion beam can try to decelerate the rotating piece of debris, but there is a chance that the ion beam cannot slow the debris down enough, such that it will crash in the pacific ocean. Then the consequence is that the debris will not enter the atmosphere and just that it got a different orbit, or the debris will enter the atmosphere in the wrong place. If this happens the debris could crash somewhere on Earth even in civilized areas. This will bring a risk that the debris will harm some people which is not desired. Therefore if the robot is uncertain if it is able to decelerate the debris and give it the right trajectory such that it will end in the pacific ocean it should not take this unnecessary risk where people can be harmed.

#### After slowing down (before re-entry)

• The debris collides with some other piece of debris

It is possible that the piece of debris that is slowed down such that it will crash down in the designated space-junk graveyard gets hit by some other piece of debris. This will cause both to break down into multiple smaller pieces of debris. Also the trajectory of the targeted piece of debris changes. This can have disastrous consequences when the trajectory changes in such a significant way that this new trajectory will end in an inhabited area on Earth. This is why it is of great importance that the trajectory and possible collisions after decelerating the targeted object are tracked. This way we can guarantee that the targeted object will not collide with any of the trackable pieces of debris. If the possibility that the targeted debris crashes into another piece of debris is larger than 0, we will simply not try to remove this piece. Of course there is still a tiny chance that there is some unknown piece of debris which will collide with the targeted piece of debris after decelerating. However we can never prevent this since the other piece of debris is unknown.

#### After slowing down (after re-entry)

• The debris crashes down in an inhabited area on Earth

There is a possibility that a piece of debris makes it through the atmosphere. In this case we want it to crash down in the designated space-junk graveyard in the pacific ocean. However there is ofcourse a possibility that the computation of the trajectory for the piece of debris is done wrong. This could have disastrous consequences if the piece crashes down in an inhabited area on Earth. If this happens it could kill hundreds of people in the worst case. The possibility that this happens is not very big, however the consequences are so high that as long as it can’t be guaranteed that this won’t happen, the entire space debris cleaning project should not be deployed.

• The debris crashes into an airplane or helicopter on the way down

It could happen that after a piece of debris has re-entered the atmosphere it will crash into an airplane or helicopter. This would also have great consequences as hundreds of lives can be lost when hitting a passenger plane. However it would be pretty easy to prevent this, namely by communicating with flight control when a piece of debris is going to re-enter the atmosphere. Another possibility would be to make the sky above this space-junk graveyard a no-fly zone. This would exclude all possible risks and the communication with flight control will not be needed anymore.

### Relation to the model

The risks described above need to be modelled and simulated in order to sketch the probability for them to occur. We will look at all risks and look at which ones we will simulate and how we will simulate them.

• The IBS can crash into the targeted debris when trying to fly in the proximity of this debris

The risk that the IBS could crash into some debris is likely to be quite small. With the path finding technology and AI NASA has access to today, it can make sure the ISS avoids collisions with debris[47]. Since the IBS is a much smaller satellite than the ISS, it is much more maneuverable and will be able to dodge debris even better than the ISS. However, when handling a specific piece the IBS has to fly quite close to a piece of debris. This may make the risk considerable, but while the results of a collision may be substantial, they do not endanger human populace more than the Kessler Effect itself does. This means that while a collision will slow down progress, it does not pose many big dangers to society, meaning this risk has a low modeling priority.

• The targeted piece of debris collides with another piece of debris

(before starting to slow down)

The probability of this risk is somewhat higher than the IBS crashing into a piece of debris, because the pieces of debris are uncontrolled so there is no way to avoid them crashing into each other. However, the consequences of this would not be so high, it would delay the cleaning process but there are no other big consequences. Because of this reason this risk also has a low modeling priority.

• Debris will not be decelerated properly

This risk is a major one. There are two scenarios that can occur when this happens. Either the debris enters a lower stable orbit, which means the problem is not solved but just moved to a lower orbit. This is not a big problem, since it does not pose any more danger than before. The second scenario is a bigger problem. There is a chance that if the debris is not decerelated properly, that it will crash into Earth in a wrong place. In this case, it might crash into another vehicle or onto an inhabited piece of land. Thus, this risk includes both the risks:

• The debris crashes down in an inhabited area on Earth
• The debris crashes into an airplane or helicopter on the way down

This risk poses a big threat to the safety of society. Thus, this will be the primary focus of the simulation.

In order to simulate this risk, the model needs variation on multiple areas since a lot of things could go wrong. The deceleration force could be smaller than intended, the deceleration time frame could be smaller than intended, the atmospheric pressure could differ from what was expected and the mass of the object may change due to burning in the atmosphere. All of these possibilities will need to be assessed and modelled in our model in order to evaluate the risks created by the IBS.

The model contains two main things, namely a piece of debris with a set weight, speed, starting height, air resistance coefficient, pulse timeframe and pulse strength and a simulated planet representing Earth containing a target with a radius of 1500 kilometers representing the spacecraft cemetery[48]. To simulate the trajectory of the debris, we will assume that the IBS is capable of exercising a force of 60 mN on the debris piece [46] and alter the duration of the pulse.

• The targeted piece of debris collides with another piece of debris

(while / after slowing down)

This risk does not have a very high probability. Almost all the pieces of debris are in a database that is accessible on Earth. This way the IBS also has access to the position and orbit of all these pieces, which means that it can try to compute a way of decelerating that no object will hit the targeted piece of debris. If the IBS notices that another piece of debris will hit the targeted piece on the way of decelerating, it will have no use to start cleaning this piece up. However, there is always a small possibility that an untraceable piece of debris crashes in to the targeted piece while slowing down. The consequences of this will not be very high, it will have done some work for nothing but that is not the biggest problem.

If the piece of debris gets hit after it has been slowed down enough by the IBS, it will still continue in the same direction because of the speed that the debris has. It will however break down in a lot of smaller pieces with a higher total width than the original piece had. However, since these new smaller pieces will still be directed towards the spacecraft cemetery, it will not be a very big problem. It could be a problem if the debris gets hit relatively high in orbit, since then the smaller pieces can each get a different orbit. This can lead to all the pieces crashing down somewhere on Earth, possibly in an inhabited area. This can have disastrous consequences if people or buildings get hit by the pieces of debris. Even though the probability is very low, because of these big consequences the modeling priority is high.

## Variables that influence orbital trajectories

### Orbital elements

Earth’s orbit around the sun, with the semi-major (a) and the semi-minor (b) axis, the apoapsis and periapsis and their radius lengths ra and rb.

Orbits and the location of the spacecraft within them are uniquely identified by six parameters[49]:

• Semi-major axis
• Eccentricity
• Inclination
Eccentricities ranging from 0 to 0.9 are shown increasing in steps of 0.1.
• Right ascension of the ascending node
• Argument of Perigee
• True anomaly at Epoch

Semi-major axis and eccentricity

The semi-major axis (a) is half the distance across the orbit’s major axis and defines the orbital size[50]. The major axis ranges from the periapsis (also called perigee), the closest point to Earth, until the apoapsis, the point farthest away from Earth. The length of the periapsis to Earth is denoted as rp; the length of the apoapsis to Earth is defined as ra. The semi-major axis is half of the distance between periapsis and apoapsis, that is a = (rp + ra)/2[51].

The eccentricity (e) is the amount by which the orbit deviates from the perfect circle, characterising orbital shape[50]. It is defined by ra and rp and can be calculated with e = (ra - rp)/(ra + rp). In case of a circle, ra equals rp resulting in an eccentricity of 0. An elliptical orbit has an eccentricity of 0 up to but not including 1[51].

Orbital plane with its inclination (i) with respect to the equatorial plane, right ascension of the ascending node (Ω), argument of Perigee (ω) and true anomaly (v). The vernal equinox, the ascending node, the perigee and the equatorial plane are represented.

Inclination and right ascension of the ascending node

The orbit’s orientation in space is defined by the inclination (i) and the right ascension of the ascending node (Ω). The inclination is the angle between the orbital plane and the Earth’s equatorial plan (plane of reference) and is measured at the ascending node[51]. Two major classes of orbits can be distinguished by the value of inclination: direct orbits and indirect orbits. Direct orbits have an angle ranging from 0 until 90 degrees with respect to the equatorial plane. Spacecraft in these orbits move in the same direction as Earth’s rotation. Angles ranging from 90 until 180 degrees result in indirect obrits, with spacecraft moving opposite to Earth’s rotation[50].

The orbital plane intersects the equatorial plane in two points; the ascending node, where the spacecraft crosses the equator going from south to north, and the descending node, where the spacecraft heads south when passing the equator. The right ascension of the ascending node (also called longitude of the ascending node) describes how the orbital plane is rotated in space; it defines the ascending and descending node locations with respect to Earth’s equatorial plane. By convention, the location of the ascending node is specified. The common latitude/longitude coordinate system cannot be used, because the Earth is spinning. Therefore, the right ascension/declination coordinate system is used, which does not spin with the Earth. Right ascension is another word for angle. In this case, the angle in the equatorial plane from the vernal equinox, a reference point where the right ascension is defined to be zero. Thus, the right ascension of the ascending node is the angle between the vernal equinox and the ascending node, in direction of the spacecraft’s motion[49][50][51][52].

Argument of Perigee

The argument of Perigee (ω) is the angle in the orbital plane between the ascending node and the perigee (point closest to Earth), measured in direction of the spacecraft’s motion. Actually, this is the angle between the orbit’s major axis and the line of nodes, which connects the ascending and the descending node. This angle defines the orientation of the orbit within the orbital plane[50][52][53].

True anomaly

Now that the size, shape and the orientation of the orbit are defined, the exact location of the spacecraft in its orbit needs to be specified. Since the spacecraft moves in its orbit, its location needs to be determined at a specific time (at Epoch). The true anomaly (v) represents this location. It is the angle between the spacecraft’s location and the perigee at Epoch time. This angle increases non-uniformly with time[49][50][52][53].

## Atmospheric entry heating

A piece of debris burns up in space if the friction caused by all the matter in the Earth’s atmosphere is very large. This friction gets larger as the speed of the debris that enters the atmosphere increases. Because of the friction, the particles of the debris and the atmosphere get broken down into glowing ionized particles. This means that the debris vaporizes and a flash of light can be seen from a distance[54].

### Influence of size, shape and type of material on the burning process

Microscopic dust from space most often reaches the surface of Earth. This is the case because they have such a low mass that they get decelerated very easy. This way they do not go through the atmosphere with ridiculous high speeds, they travel around 0.025 m/s[54]. This means that they do not experience the huge amount of friction that other pieces of debris do, which leads to the microscopic dust reaching the Earth’s surface. However, it is not really a problem if this microscopic debris makes it to the Earth’s surface, it is so small that it can not even be seen. Which means that it can also never have bad consequences if the pieces reach the Earth’s surface. Furthermore, the very big pieces of debris also have a big chance of making it to the Earth’s surface. This is for a different reason however, they burn up partially but because these pieces are so big a part will make it through the atmosphere. So, even in this case the pieces that actually crash down on the Earth’s surface will not be so big anymore, as the biggest part will already have been burned up. However, these pieces of debris can lead to problems depending on where it crashes down on Earth[55].

There was not a lot of research done on how the shape of debris influences the speed of the burning process, but for satellites this is done extensively. The hardest component of the burning process to compute is the drag coefficient, since it is impossible to test the shape with the speed it will get during re-entry[56]. When the satellite is streamlined it will decelerate much later than when it has a bigger drag coefficient. Also when it is streamlined, the heat will be concentrated on a smaller surface than when it not streamlined. Then the temperature will be much higher than when it has a bigger surface. When a satellite has a bigger surface that will create more drag it will be slowed down more, but the heat that will be created will be divided over a much bigger surface and thus it does not heat up as much as a streamlined satellite does.

The type of material also influences the burning process, because of differing material properties, like melting point, density and emissivity. Low melting point materials such as aluminum burn up faster, i.e. at higher altitudes, than materials with higher melting points such as titanium, stainless steel and carbon-carbon[57]. Therefore, pieces of debris with high melting points are less likely to burn completely in Earth’s atmosphere and fragments are more likely to crash down on Earth. Dense items are also more likely to partially survive re-entry to Earth[58], because the amount of substance to be burnt increases with density[59]. The emissivity of a material is its effectiveness in emitting energy, instead of absorbing it. Space debris with a high emissivity emits a larger fraction of the heat during re-entry, resulting in a slower burning process. Therefore, pieces of debris with a high emissivity are more likely to crash down on Earth than pieces with low emissivity.

### Influence of re-entry angle

For re-entry in the atmosphere the angle of re-entry is also important. The satellites that will reenter the Earth will have an optimal angle of re-entry. When they enter with this angle, the G-forces will not be deadly for humans and the heat shield will be able to withstand the heat that is created. There are two other cases that can occur. The angle of re-entry is smaller, then there exists a chance that the satellite skips on the atmosphere. This means that the satellite does not get decelerated enough and it remains in orbit around the Earth. When pushing the debris towards the Earth, we must make sure that the angle of re-entry is not too small. The other case is that the angle is bigger than the perfect angle. Then the G-forces will be much bigger on the piece, also it will have a higher velocity in lower altitudes. Because of the higher velocities the temperature will be much bigger and the debris will be more likely to burn-up in the atmosphere.

Furthermore, the spacecraft’s re-entry angle also affects the maximum heating rate. The maximum heating rate increases for increasing re-entry angles, because the vehicle travels deeper into the atmosphere before reaching maximum deceleration. A large flight-path angle results in a very high heating rate, however, only for a brief time. Therefore, the overall effect on the spacecraft may be small, resulting in less burning. Small flight-path angles lead to much lower heating rates, but the heating continues longer and the spacecraft is more likely to adsorb the produced heat, resulting in more damage done to the vehicle[56].

### Spacecraft’s protection against burning up

When spaceships re-enter the atmosphere to return to Earth, they will have a velocity which can be higher than 30.000 km/h. Because of the friction the temperatures can rise as high as 1700 degrees celsius. There are several Thermal Protection Systems developed to protect the spacecraft itself and the astronauts inside.

The most used idea is that the spaceship has a heat-shield that can protect the capsules during re-entry. The heat-shield is made of materials that can resist very high and very low temperatures. The idea behind the ablative heat-shield is that it lifts the hot layer of gas away from the outer wall such that there is a cooler layer created between the shield and the gasses. This protection layer of air can also remove the gaseous reaction products that are formed because of the heat.

Objects with a high emissivity, reach terminal equilibrium (emitted energy equals absorbed energy), at lower temperatures, because they emit most of their absorbed energy. Radiative cooling is used to reduce this equilibrium temperature by emitting most of the heat energy before the spacecraft’s structure can absorb it. This is done by using Shuttle tiles, which is a surface coating on top of a revolutionary insulator. The surface coating must radiate the heat caused by friction and requires high emissivity and high melting point, like ceramics. Ultra High Temperature Ceramics are currently used; they also have good oxidation resistance and reasonably good thermal shock resistance[60]. The insulator between the surface coating and the spacecraft’s aluminum skin must prevent the skin from melting, and is made of a highly refined silicate. Radiative cooling is thus a form of passively cooling[56].

It satellites do not have to return to space, these methods will not be used, since it will make it harder to destroy the satellites when they are used.

### Conclusion

Because of the differences between shape, velocity, mass, material, size and the angle of re-entry of the piece of debris, it is not possible to calculate how the piece of debris will burn in the atmosphere. Therefore, we cannot say that a piece will reach the ground or not. Most of the pieces that enter the atmosphere will not reach the ground, but very big pieces and/or pieces that are heat resistant are most likely to reach the Earth. Also, microscopic small pieces of debris will be able to reach the Earth, since they will not encounter as much air resistance as bigger pieces, thus they will not reach the temperature that the big pieces do.

This does not pose much of a problem for the model, however. Since the model is needed in order to check the certainty of the landing location, pieces that do not land on Earth are not interesting for the model. The change in mass could usually have quite the impact on the trajectory. However, the atmospheric burn doesn't start after the debris piece has actually entered the atmosphere. At this point, sideways movement is reduced to almost a relative halt. This means that the only thing dependent on the mass at this point is the downwards movement which is not very important for the location of the crash. Thus, the mass of the debris piece is not very important after the atmosphere has been entered, meaning the atmospheric burn due to its insignificance for the crash site and its difficulty to compute will not be incorporated into the model.

## The IBS Model

Approximation of the atmospheric pressure.

### Construction

In order to properly construct a model, some assumptions must be made prior to starting construction.

#### Assumptions

A model has been constructed that is capable of simulating debris trajectories. In order to accurately predict and model trajectories, a number of assumptions have to be made:

• The mass of the Earth: 5.972 * 1024 kg[61]
• The radius of the Earth: 6.378 * 106 m[61]
• The gravitational constant: 6.67408 × 10-11 m3kg-1s-2[61]
• The spacecraft cemetery is an area with a radius of 1500 kilometers, and the center is 2700 kilometers from the nearest landmass[62]
• The Earth has a rotational speed of 15 degrees per hour.
• The space object exerts a gravitational force, however since the Earth has a relatively large mass with regards to the space object, this gravitational force is negligible.
• The atmospheric pressure is can be approximated by a exponential formula. Based on data of a standard atmosphere. The formula is 1.28*e-1.2 * 10-4 * h[63]
• The IBS is capable of exercising a force of up to 60 mN on any debris piece for a maximum specific impulse of 2500 seconds[46].
The IBS model simulating the trajectory of one piece of debris. The red and yellow part of the Earth represents the spacecraft cemetery.

#### Design Choices

The model was created in Python 3 [64]. Python has a lot of useful package which help doing calculations and visualising the results. The packages used are:

The most important goal of the model should be that we are able to test properly to which degree a guarantee can be given on the crash location of the debris pieces. All design decisions and implemented functionality should directly or indirectly lead to this goal. This means that functionality that does not serve a significant purpose towards this goal should be given low priority such that other functions that benefit the goal have more time available to be implemented.

Given what is stated above, a decision was made to make the IBS model in two dimensions instead of three. This does not mean we are flat Earthers, but rather that a model in three dimensions is a lot harder to visualize on-screen than a 2D one. Also, it means that functions like determination of distance to a target are easier to implement. Since the robot itself is not essential to model the trajectory of the debris piece, the model will only support the force exercised by the robot on the debris piece.

The Earth is given as a turquoise sphere, which is the actual average color of the Earth. Around that, a small white circle orbits leaving behind a white line illustrating the debris piece and its trajectory. On Earth a target the relative size of the spacecraft cemetery is displayed as a yellow and red strip. The model is capable of measuring how far from the center of the target the crash site is located when the debris crashes down to Earth. There are three forces that work on the debris piece, namely Earth’s gravity, air resistance and the IBS’s ion beam. These forces all have an impact on the trajectory of the debris: the acceleration caused by these forces is added to the velocity of the debris piece each tick of the model.

### Sensitivity Analysis

In order to get an idea of the effect of different parameters on the trajectory of a piece of debris, tests are performed varying the known parameters a little each time. The tested parameters are mass, altitude, drag coefficient, pulse strength and pulse duration. The tests will be performed on a control simulation with an object of a mass of 50 kg, altitude of 200 kilometers, air resistance coefficient of 0.8, pulse strength of 60 mN and pulse duration of 279 seconds. Then, tests are performed where the values differ from their original value by 0.01%, 0.1%, 1%, 5% and 10%. The results can be found below.

Variable (100%) 90% 95% 99% 99.9% 99.99% 100% 100.01% 100.1% 101% 105% 110%
Mass (50 kg) 17203.36 11186.42 2204.56 220.97 24.80 1.47 17.22 217.85 2179.27 10760.11 18911.11
Altitude (200 km) 14863.17 20033.58 4100.81 12894.43 1304.39 1.47 1300.22 13202.88 12767.70 17459.68 18312.12
Drag coefficient (0.8) 19499.27 11338.13 5501.69 541.93 51.89 1.47 59.46 548.34 5396.35 14067.16 9531.69
Pulse Strength (0.06006 N) 3761.44 1876.98 370.97 33.91 2.53 1.47 5.47 41.49 378.32 1878.86 3750.94
Pulse Duration (279 s) 3761.38 1884.12 372.39 36.92 8.23 1.47 1.47 30.15 365.41 1871.62 3736.46

In the table above, the results of the tests are shown. The leftmost column show the variables altered along with their start values at 100% in brackets. The top row shows the tested value, in percentages of the starting value. In the cells the amount of meters away from the center of the target (being the spacecraft cemetery) is shown. The color of the cell indicates how acceptable the value is: green means the value is less than 100 meters away from the center (good), yellow means less than 1500 meters away from the center (acceptable) and red means more than 1500 meters away from the center (unacceptable).

The sensitivity analysis reveals much about the tolerance in measurement error of these variables. The pulse strength and pulse duration, for example, are very tolerant. A whole percent from the intended value still yield acceptable results, and since these two variables are controlled mostly by the IBS itself, these two will not present any big issues. The drag coefficient, mass and in particular altitude are very prone to errors.

Let’s start by looking at mass. Since we do not have a scale in orbit, the best way to approximate the mass of an object is by solving the equation v = √(G * m / h) for m, where m is the mass, v is the object’s velocity, h is the altitude of the object and G is the gravitational constant of the Earth which is equal to 6.67408 × 10-11 m3kg-1s-2. This means that we need the altitude and the velocity of the object, both of which can be approximated. It is likely that the approximation of the speed of an object is more accurate than that of the altitude, meaning that the accuracy of the approximation of the mass is dependent on the accuracy of the approximation of the altitude. This is fine, since the mass is more lenient on measurement errors than the altitude, so if the altitude measurement error falls within its bounds, then so will that of the mass.

This bring us to the altitude. The sensitivity analysis of the altitude shows us that any error larger than 0.01% gives us an unacceptable value. We are looking at debris in the Low Earth Orbit, which is the orbit between 100 and 2000 kilometers. This means that the error in altitude can be between 10 and 200 meters to get an acceptable result. Whether or not this is achievable will be discussed later.

Lastly, the drag coefficient. This variable poses a big problem. The drag coefficient is not as prone to errors as the altitude, but it is a lot harder to approximate. Since a single percent can make the result unacceptable, we will need to find a way to bypass this variable. This may be done by using a trained neural network with domain randomization. Domain randomization is a method to generalize an AI in order for it to be effective in a lot of different situations. What this allows us to do is, by randomizing the drag coefficient during training, make the neural net able to adapt to a lot of different drag coefficients. This way, it can approximate what to do after it has pushed the debris once and read the reaction to its push. Domain randomization has been used before by OpenAI to make a robot learn dexterity[72].

Under the header "Measurement methods" the methods to measure these variables and their likelihood for error will be discussed.

The Model can be found for own uses at the GitHub page.

## Measurement methods

To determine whether we can actually realize our design, we have to determine how accurate we can determine some of the variables that influence the place that a piece of debris will land. The three variables that we will consider for this are: altitude, velocity, and the drag coefficient. For the variables: altitude and velocity, a laser will be the best measuring method, where the drag coefficient is very hard to be measured in an accurate way. We will further discuss the accuracy of the laser measurement method to determine whether this design is realizable.

### Altitude and Velocity

To determine the altitude and velocity of a piece of debris we can use lasers that are situated on earth. These lasers will send about 1.000 beams of light per second towards a piece of debris for some small amount of time. These beams will then be reflected by the piece of debris back to the laser. Based on the time this takes the altitude of this piece of debris can be calculated. Based on the difference in position between the beams it can calculate the velocity of this piece.

There has been quite some research on how accurate a laser is able to track the altitude of a piece of space debris. For one of these researches some requirements were set, namely: the laser should be able to track pieces of 1 cm and bigger, the laser should be able to track these pieces with an accuracy of 1 meter and the laser should be able to track 150.000+ objects. [73].

There are some factors that have to be improved to contribute to the feasibility of these requirements. These factors are: Laser irradiance, Receiving aperture size and Receiver sensitivity. Laser irradiance is the flux of radiant energy per unit area, this can be scaled upwards by increasing the power of the laser, reducing the divergence of the beam of light and making the transmission losses as small as possible. Receiving aperture size is the size of the opening that will receive the reflected beam, a standard aperture size is 75cm for telescopes. Receiver sensitivity is the sensitivity of the part that receives the reflected beam.

The requirements set earlier can be realized with nowadays technology, the only thing that is not tested yet is the possibility to track pieces of 1cm and bigger. Until now it is certain that the orbit of pieces of 10 cm and larger can be tracked with an accuracy of 1 meter. However, it is believed that for the pieces of 1 cm and larger it is only a matter of confirming that it is possible by experiments.

So, we can safely say that it is realizable to make a robot that measures the altitude with an accuracy of 1 meter, and the velocity with approximately the same magnitude of accuracy. Given these statements, and the fact that mass can be calculated with the following formula: m = (v2 * h) / (G), where G is the gravitational constant of the Earth and h is the altitude. So if we know that v and h can be estimated with an accuracy of around 1 m/s and 1 m respectively, we can say that

### Drag coefficient

The drag coefficient is a variable that is a lot harder to estimate accurately. This is mainly because the shape of all the pieces of orbital debris is not known. However, the shape of an object highly influences its drag coefficient. After doing the research for a reliable measuring method for the drag coefficient of space debris, the following can be concluded: there is no measuring method that is accurate enough for our model. The variables that influence the drag coefficient, especially the shape of the debris, vary too much in space for this.

## Conclusion

The goal of the model was to determine whether it was possible to use the Ion Beam Shepherd to push debris into the spacecraft cemetery. It turned out that the location of the crash site varied too much; it varied between 0 and 1100 kilometers from the center of the target. Therefore, we cannot guarantee that pieces of debris successfully crash down into the target area, which could have disastrous consequences.

Considering the results of the model, we can conclude that the approach we took with the training of this model does not work. While the Q-learner is the appropriate agent for the job, it did not consistently receive satisfying results. The position where the debris crashed into the earth varied between 0 to 100 degrees from the target. After running 300 episodes, the agent did not perform better than after 50 episodes. There are a few possible things that can be the cause of this problem. For example, the state space fed into the Q-learner can be inconclusive or confusing for the agent. Another possible problem could be the output states, the agent only pushes along the tangent of the velocity vector for a specific time chosen by the agent. It is possible this is too specific or not specific enough to train the agent.

Since the input values are with some degree random it is also possible that the agent is not capable of solving this problem with this level of randomness. If this is the case, in the future we need to look at different ways of solving this problem. This could be done with stronger and more precise computing power, or an agent that is powered with another method than a Q-learner.

## Possible future extensions to the model

The model, of course, is by no means perfect. There are a lot of things that could be added to the model to have extra functionality or to make it more realistic.

### Realism

First and foremost, an added dimension (making the model 3D) would not go amiss when it comes to realism. This would allow us to do more with sideways movement of the debris, adding complexity but a lot of credibility as well. At the moment, the object does not lose any mass when entering the atmosphere. In real life, objects entering the atmosphere often combust, losing a lot of mass in the process. The amount of mass lost and the impact on the trajectory of the debris piece is very hard to compute and model, but it is something that could be added in the future to further increase its realism.

Support for multiple pieces of debris is something that could be added as well, in order to simulate pieces that can crash into each other. Steps could even be made towards modeling every single piece of debris currently within actual orbit in real life. While we’re in the process of adding multiple new bodies, the IBS itself could be added as well in order to simulate its own movement. This way we can approximate the difficulty of moving the IBS around in orbit.

### Functionality

With the realism described above come a lot of options for extra functionality. The extra dimension allows for the simulation of pieces whose orbit does not cross over the spacecraft cemetery, meaning the model would allow simulation of the IBS pushing the debris sideways to obtain an orbit over the spacecraft cemetery. It would also allow for orbits that are not perfect circles to be simulated more accurately and in multiple different ways.

The IBS’ movement could also be included in the model, moving itself around with the Ion Beam. This could include thrusting forwards and backwards, steering with extra smaller thrusters pointing sidewards and staying in front of the debris piece while slowing it down. When multiple other debris pieces are modelled, the model could also have the IBS learn to avoid other debris pieces when tracking the trajectory of the debris piece that is being slowed down.

## Approach

First of all, a literature study is performed to assess the state of the art regarding space debris orbiting the Earth and the Kessler Syndrome. To prevent the occurence of the Kessler Syndrome, the space debris should be removed from orbit before it can collide with other debris. The literature study resulted in multiple possible solutions for cleaning space debris. This is combined with the literature study of PRE2016 3 Group19, leading to the most promising solution. This solution is subsequently elaborated by determining the requirements for the robot. This robot design will then be specified based on these requirements, preferences and constraints. A model of the robot will be made to assess the effectiveness of the robot during its task of tracking and cleaning orbital debris. The robot will be put to the test by conducting simulation experiments for different USE-cases, to determine whether the robot works properly, whether it has negative side effects for the users, etc.

## Planning and division of work

Week Concern Responsible member(s)
1
• Define subject
• Work plan
• Literature study (10 references per member)
• Introduction, problem definition and objectives
• USE aspects
• State of the art
• Approach, planning, deliverables, milestones and work division
• Update wiki page
• Prepare tutor meeting 1
• All
• All
• All
• Niels
• Max
• Kees & Mart
• Rani & Max
• All
• All
2
• Tutor meeting 1
• Process tutor meeting 1
• Review of previous week
• Literature study
• References in APA style
• Update objectives
• Completed state of the art and selection of best solution
• Evaluate orbital launch methods
• Add details to planning
• Requirements, preferences and constraints for design
• Update wiki page
• Prepare tutor meeting 2
• All
• All
• All
• Mart
• Max
• Niels
• Kees
• Kees & Max
• Rani
• Niels & Rani
• All
• All
3
• Tutor meeting 2
• Process tutor meeting 2
• Review of previous week
• Evaluate ways of locating debris
• Finalize orbital launch methods
• Research into how an ion beam works
• Finalize requirements
• Evaluation of decision on what piece to handle
• Prioritisation
• Research into variables that influence orbital trajectories
• Update wiki page
• Prepare tutor meeting 3
• All
• All
• All
• Mart
• Kees & Max
• Niels
• Rani
• Kees & Max
• Max
• Rani
• All
• All
4
• Tutor meeting 3
• Process tutor meeting 3
• Review of previous week
• Aim and decelerate
• Finalize move towards the debris
• Orbit failure
• Start working on simulation
• Risk analysis
• Variables that influence orbital trajectories
• Update wiki page
• Prepare tutor meeting 4
• All
• All
• All
• Max
• Kees
• Rani
• Mart
• Niels & Kees
• Rani
• All
• All
5
• Tutor meeting 4
• Process tutor meeting 4
• Review of previous week
• Risk Analysis with regards to simulation
• Variables that influence orbital trajectories
• Space debris burning in Earth's atmosphere
• Update wiki page
• Prepare tutor meeting 5
• All
• All
• All
• Mart & Max & Niels
• Rani
• Niels & Kees & Rani
• All
• All
6
• Tutor meeting 5
• Process tutor meeting 5
• Review of previous week
• Simulation experiments (sensitivity analysis)
• Space debris burning in Earth's atmosphere
• Update wiki page
• Prepare tutor meeting 6
• All
• All
• All
• Mart & Max
• Niels & Kees & Rani
• All
• All
7
• Tutor meeting 6
• Process tutor meeting 6
• Review of previous week
• Finalize simulation experiments
• Future extensions
• Measurement Methods
• Prepare presentation
• All
• All
• All
• Mart
• Max
• Niels
• Kees & Rani
8
• Presentation
• Finalize wiki
• Kees & Rani
• All

### Milestones

Week Milestone Remarks
1
• Determine subject for the project
• Subject chosen: Cleaning up orbital debris
2
• Selection of best solution
• Finish literature study
• Finish state of the art analysis
• Best orbital debris cleaning method: ion beam
• Continue with Ion Beam Sheperd: design and simulations
3
• Requirements, preferences and constraints for design
• Simulation start
• -
• Simple 2D physics simulation
4
• Robot design
• IBS
5
• Finalized basic model
• -
6
• Sensitivity analysis
• Results found under "The IBS Model"
7
• Finish simulation experiments
• Finish preparation of presentation
• Q-learning neural network
• -
8
• Completed presentation
• Completed wiki page
• Performed by Rani & Kees
• -

## Deliverables

The deliverables are as follows:

• Wiki page

This wiki page will describe the project progress in detail and will be updated weekly. It will contain all relevant information about the project and links to the end products.

• Model

The trajectory of one piece of debris is simulated to visualize orbital cleaning by the Ion Beam Shepherd.

• Presentation

This presentation will be held during week 8 of the project and includes an introduction of the Kessler Syndrome and the possible solutions. The best solution is considered further by providing the robot design and a simulation of this robot.

## References

1. Mosher, D. (2018, april 15). The US government logged 308,984 potential space-junk collisions in 2017 — and the problem could get much worse. Retrieved february 7, 2019, from https://www.businessinsider.com/space-junk-collision-statistics-government-tracking-2017-2018-4?international=true&r=US&IR=T
2. Frequently Asked Questions: Orbital Debris. (z.d.). Retrieved february 8, 2019, from https://www.nasa.gov/news/debris_faq.html
3. Stuff in Space [Dataset]. (z.d.). Retrieved February 8, 2019, from http://stuffin.space/
4. Mehrholz, D., Leushacke, L., Flury, W., Jehn, R., Klinkrad, H., & Landgraf, M. (2002). Detecting, Tracking and Imaging Space Debris. Retrieved from http://www.pacaspacedebris.com/wp-content/uploads/2013/05/Detecting-space.pdf Cite error: Invalid <ref> tag; name "paca" defined multiple times with different content
5. Greene, B. (n.d.). Laser Tracking of Space Debris. Retrieved from https://cddis.nasa.gov/lw13/docs/papers/adv_greene_1m.pdf
6. Latifi, J. (2017). Literature Review: Space Debris, Track methods and the Danger of the Future Debris Environment. Retrieved from https://jblati14.files.wordpress.com/2017/03/gis636-space-debris-literature-review_latifi-jorida.pdf
7. University of Surrey. (2018, September 19). Net successfully snares space debris | University of Surrey. Retrieved February 9, 2019, from https://www.surrey.ac.uk/news/net-successfully-snares-space-debris
8. Pultarova, T. (2018, June 22). 1st Satellite Built to Harpoon Space Junk for Disposal Begins Test Flight. Retrieved February 9, 2019, from https://www.space.com/40960-removedebris-space-junk-cleanup-test-flight.html
9. Bombardelli, C., & Peláez, J. (2011a, July 1). Ion Beam Shepherd for Asteroid Deflection. Retrieved February 14, 2019, from http://sdg.aero.upm.es/PUBLICATIONS/PDF/2011/AIAA-51640-157.pdf
10. Mann, A. (2011, October 26). Space Junk Crisis: Time to Bring in the Lasers. Retrieved February 9, 2019, from https://www.wired.com/2011/10/space-junk-laser/
11. Bates, D. (2011, March 16). Nasa to shoot lasers at space junk around Earth to prevent collisions with satellites. Retrieved February 9, 2019, from https://www.dailymail.co.uk/sciencetech/article-1366838/Nasa-use-lasers-shoot-space-junk-Earth.html
12. Choi, C. Q. (2017, June 28). Gecko-Inspired Robot Could Snag Space Junk. Retrieved February 9, 2019, from https://www.space.com/37335-robotic-gecko-gripper-microgravity-space-junk.html
13. Williams, M. (2017, June 21). Let's Clean up the Space Junk with Magnetic Space Tugs - Universe Today. Retrieved February 9, 2019, from https://www.universetoday.com/136142/lets-clean-space-junk-magnetic-space-tugs/
14. Garcia, M. (2013, September 27). Space Debris and Human Spacecraft. Retrieved February 10, 2019, from https://www.nasa.gov/mission_pages/station/news/orbital_debris.html
15. Hull, S. (2015, October 30). Is the Sky Really Falling? An Overview of Orbital Debris. Retrieved February 10, 2019, from https://ntrs.nasa.gov/search.jsp?R=20150023281
16. La Vone, M. (n.d.). The Kessler Syndrome Explained. Retrieved February 10, 2019, from http://www.spacesafetymagazine.com/space-debris/kessler-syndrome/
17. Pelton, J. N. (2013). The Space Debris Threat and the Kessler Syndrome. In J. N. Pelton (Ed.), Space Debris and Other Threats from Outer Space (pp. 17–23). https://doi.org/10.1007/978-1-4614-6714-4_2
18. David, L. (2013, January 25). Space Junk Menace: How to Deal with Orbital Debris. Retrieved February 10, 2019, from https://www.space.com/19445-space-junk-threat-orbital-debris-cleanup.html
19. Bombardelli, C., & Peláez, J. (2011). Ion Beam Shepherd for Contactless Space Debris Removal. Retrieved February, 18, 2019 from
20. Bethesda, M. D. (2010, November 9). The GEO Graveyard May Not Be Permanent. Retrieved February 14, 2019, from http://www.spacedaily.com/reports/The_GEO_Graveyard_May_Not_Be_Permanent_999.html
21. What could cause an orbit to fail? (n.d.). Retrieved February 25, 2019, from http://www.qrg.northwestern.edu/projects/vss/docs/space-environment/3-orbit-fails.html
22. Once a ship is in orbit, do we have to do anything to keep it there? (n.d.). Retrieved February 25, 2019, from http://www.qrg.northwestern.edu/projects/vss/docs/navigation/1-maintain-an-orbit.html
23. Riebeek, H. (2009, September 4). Catalog of Earth Satellite Orbits. Retrieved February 24, 2019, from https://earthobservatory.nasa.gov/features/OrbitsCatalog
24. National Aeronautics and Space Administration (NASA). (1959). Space handbook: Astronautics and its applications. Retrieved from https://history.nasa.gov/conghand/spcover.htm
25. Brown, G. & Harris, W. (2018, March 8). Orbital Velocity and Altitude. Retrieved March 18, 2019, from https://science.howstuffworks.com/satellite6.htm
26. Kurzgesagt – In a Nutshell. (2016, April 8). Space Elevator - Science Fiction or the Future of Mankind? [Video file]. Retrieved February 16, 2019, from https://www.youtube.com/watch?v=qPQQwqGWktE
27. Melina, R. (2017, August 4). International Space Station: By the Numbers. Retrieved February 16, 2019, from https://www.space.com/8876-international-space-station-numbers.html
28. The Boeing Company. (2000). Hypersonic Airplane Space Tether Orbital Launch System. Retrieved from http://www.niac.usra.edu/files/studies/final_report/355Bogar.pdf
29. Stein, H. L. (1998). Ultrahigh molecular weight polyethylenes (uhmwpe). Engineered Materials Handbook, 2, 167–171
30. The Boeing Company. (2001). HYPERSONIC AIRPLANE SPACE TETHER ORBITAL LAUNCH (HASTOL) ARCHITECTURE STUDY. Retrieved from http://www.niac.usra.edu/files/studies/final_report/391Grant.pdf
31. Lucas, P. (2003, July 14). Orbital Railroads: Beanstalks and Space Fountains. Retrieved February 17, 2019, from http://strangehorizons.com/non-fiction/articles/orbital-railroads-beanstalks-and-space-fountains/
32. Birch, P. (1982). ORBITAL RING SYSTEMS AND JACOB'S LADDERS. Retrieved from https://www.orionsarm.com/fm_store/OrbitalRings-I.pdf
33. Arthur, I. (2017, June 29). Orbital Rings [Video file]. Retrieved February 17, 2019, from https://www.youtube.com/watch?v=LMbI6sk-62E
34. Ram Accelerator Profile [Illustratie]. (z.d.). Geraadpleegd op 16 februari 2019, van http://www.islandone.org/LEOBiblio/SPBI106.HTM
35. Muntoni, G., Schirru, L., Pisanu, T., Montisci, G., Valente, G., Gaudiomonte, F., Serra, G., Urru, E., Ortu, E., Fanti, A. (2017). Space Debris Detection in Low Earth Orbit with the Sardinia Radio Telescope. Retrieved from https://www.mdpi.com/2079-9292/6/3/59/pdf
36. Riede, W., Rodmann, J., Humbert, L., & Hampf, D. (2017). Laser Optical Tracking Technology For Space Debris Monitoring. Paper presented at Wissen für Morgen, Stuttgard, Germany. Retrieved from https://elib.dlr.de/117838/1/Riede_IAA-ICSSA-17-01-01.pdf
37. RemoveDebris - Satellite Missions. (n.d.). Retrieved February 18, 2019, from https://directory.eoportal.org/web/eoportal/satellite-missions/r/removedebris
38. Kurzgesagt – In a Nutshell. (2018, November 25). End of Space - Creating a Prison for Humanity [Video file]. Retrieved February 21, 2019, from https://www.youtube.com/watch?v=yS1ibDImAYU
39. Liou, J. C., & Johnson, N. L. (2006). Instability of the Present LEO Satellite Populations. Retrieved from https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20060024585.pdf
40. NASA. (n.d.-b). ARES: Orbital Debris Program Office Evolutionary Models. Retrieved February 21, 2019, from https://orbitaldebris.jsc.nasa.gov/modeling/evolmodeling.html
41. Liou, J. C., & Johnson, N. L. (2009, January 1). A sensitivity study of the effectiveness of active debris removal in LEO. Retrieved February 21, 2019, from https://www.sciencedirect.com/science/article/pii/S0094576508002634?via%3Dihub
42. J.-C. Liou, D.J. Kessler, M.J. Matney, E.G. Stansbery, A new approach to evaluate collision probabilities among asteroids, comets, and Kuiper Belt objects, in: Proceedings of Lunar and Planetary Science Conference, vol. 34, 2003, p. 1828.
43. Liou, J. C. (2004). Collision activities in the future orbital debris environment. Retrieved from https://ac.els-cdn.com/S0273117705008057/1-s2.0-S0273117705008057-main.pdf?_tid=0a53707c-bdd5-4b22-8c7d-3f0190373d95&acdnat=1550762781_cc9f416904aa1bf778994e3531b8ab1e
44. Kessler, D. J. (1981). Derivation of the Collision Probability between Orbiting Objects: The Lifetimes of Jupiter's Outer Moons. Retrieved from https://ac.els-cdn.com/0019103581901512/1-s2.0-0019103581901512-main.pdf?_tid=cb3520c7-7b5e-4beb-9983-f0e8f7f8d0c8&acdnat=1551086082_9dde33704dca4f7eb18da22045e123dc
45. Takahashi, K., Charles, C., Boswell, R. W., & Ando, A. (2018, 26 september). Demonstrating a new technology for space debris removal using a bi-directional plasma thruster. Geraadpleegd op 21 februari 2019, van https://www.nature.com/articles/s41598-018-32697-4#Sec7
46. Takahashi, K., Charles, C., Boswell, R. W., & Ando, A. (2018). Demonstrating a new technology for space debris removal using a bi-directional plasma thruster. Retrieved from https://www.nature.com/articles/s41598-018-32697-4#ref-CR16
47. Cain, F. (2017, February 27). How Do Astronauts Avoid Debris? - Universe Today. Retrieved March 11, 2019, from https://www.universetoday.com/121067/how-do-astronauts-avoid-debris/
48. Smith-Strickland, K. (2015, May 15). This Watery Graveyard Is the Resting Place for 161 Sunken Spaceships. Retrieved March 11, 2019, from https://gizmodo.com/this-watery-graveyard-holds-161-sunken-spaceships-1703212211
49. National Aeronautics and Space Administration (NASA). (n.d.). Orbital elements. Retrieved March 2, 2019, from https://spaceflight.nasa.gov/realdata/elements/
50. Describing orbits. (n.d.). Retrieved March 2, 2019, from https://www.faa.gov/about/office_org/headquarters_offices/avs/offices/aam/cami/library/online_libraries/aerospace_medicine/tutorial/media/III.4.1.4_Describing_Orbits.pdf
51. Introduction of the six basic parameters describing satellite orbits. (n.d.). Retrieved March 2, 2019, from https://www.narom.no/undervisningsressurser/sarepta/rocket-theory/satellite-orbits/introduction-of-the-six-basic-parameters-describing-satellite-orbits/
52. Keplerian Elements Tutorial. (n.d.). Retrieved March 2, 2019, from https://www.amsat.org/keplerian-elements-tutorial/
53. European Space Agency (ESA). (n.d.). The Ulysses orbit: Classical orbital elements. Retrieved March 2, 2019, from https://www.cosmos.esa.int/web/ulysses/orbital-elements
54. How big does a meteor have to be to make it to the ground? (2018, March 8). Retrieved March 14, 2019, from https://science.howstuffworks.com/question486.htm
55. Returning from space: Re-entry. (n.d.). Retrieved March 16, 2019, from https://www.faa.gov/about/office_org/headquarters_offices/avs/offices/aam/cami/library/online_libraries/aerospace_medicine/tutorial/media/III.4.1.7_Returning_from_Space.pdf
56. National Aeronautics and Space Administration (NASA). (n.d.). Orbital Debris Program Office Reentry. Retrieved March 21, 2019, from https://orbitaldebris.jsc.nasa.gov/reentry/
57. European Space Agency (ESA). (n.d.). Go for the burn: how to melt a satellite. Retrieved March 21, 2019, from http://m.esa.int/Our_Activities/Operations/Space_Safety_Security/Clean_Space/Go_for_the_burn_how_to_melt_a_satellite
58. Khalfi, A., Trouve, G., Delfosse, L., & Delobel, R. (2004). Influence of Apparent Density during the Burning of Wood Waste Furniture. Journal of Fire Sciences, 22(3), 229–250. https://doi.org/10.1177/0734904104040394
59. Dino, J. (n.d.). Thermal Protection System (TPS) and Materials. Retrieved March 18, 2019, from https://www.nasa.gov/centers/ames/research/humaninspace/humansinspace-thermalprotectionsystem.html
60. Bouwens, R. E. A., Nederlandse Vereniging voor het Onderwijs in de Natuurwetenschappen (NVON), & NVON-commissie. (2013). Binas: havo/vwo : informatieboek havo/vwo voor het onderwijs in de natuurwetenschappen (6e ed.). Groningen, Netherlands: Noordhoff Uitgevers.
61. Smith-Strickland, K. (2015, May 15). This Watery Graveyard Is the Resting Place for 161 Sunken Spaceships. Retrieved March 11, 2019, from https://gizmodo.com/this-watery-graveyard-holds-161-sunken-spaceships-1703212211
62. Engineering ToolBox, (2003). U.S. Standard Atmosphere. [online] Available at: https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html [11 March 2019].
63. Python Software Foundation. Python Language Reference, version 2.7. Available at http://www.python.org
64. Stéfan van der Walt, S. Chris Colbert and Gaël Varoquaux. The NumPy Array: A Structure for Efficient Numerical Computation, Computing in Science & Engineering, 13, 22-30 (2011), DOI:10.1109/MCSE.2011.37
65. Jones E, Oliphant E, Peterson P, et al. SciPy: Open Source Scientific Tools for Python, 2001-, http://www.scipy.org/ [Online; accessed 2019-03-25]
66. John D. Hunter. Matplotlib: A 2D Graphics Environment, Computing in Science & Engineering, 9, 90-95 (2007), DOI:10.1109/MCSE.2007.55
67. Fredrik Lundh, et al. Python Imaging Library (PIL), 2009, http://www.pythonware.com/products/pil/ [Online; accessed 2019-03-25]
68. Intel Corporation, Willow Garage, Itseez. OpenCV2, 2000. https://github.com/opencv/opencv [Online; accessed 2019-03-25]
69. Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan. PyTorch, 2016. https://pytorch.org/ [Online; accessed 2019-03-25]
70. ImageIO Python Library, 2014. https://imageio.github.io/ [Online; accessed 2019-03-25]
71. OpenAI. (2018, July 30). Learning Dexterity [Video file]. Retrieved April 4, 2019, from https://www.youtube.com/watch?v=jwSbzNHGflM