**Abstract**

This study proposes a novel method of space debris collection from Earth's orbit using electromagnets and taking advantage of the Moon's gravity. The increasing accumulation of space debris is a growing concern for the future, and current methods, such as laser destruction and net collection, have limitations. The proposed system is supported by mathematical calculations and offers an ideal solution for space garbage collection.

With the Kessler syndrome mentioned in the study, the amount of space garbage around Earth is constantly increasing. The method developed for the collection of space garbage is that a rocket which can be controlled from Earth is to be sent to space with an electromagnet attracting the ferromagnetic space garbage with the help of the magnetic field it has in different orbits where the space garbage is located, and then leaves this garbage in the gravitational field of the Moon, moving this debris to different orbits to where the space garbage was located.

The result obtained as a result of calculations is that the proposed method is expected to send a rocket with an escape velocity of 35.120,354 km/s into space, and to complete a tour around the Earth in 2,117 hours with an orbital speed of 24,833,8404 km/h. In this process, the mechanical energy that the system will have is calculated as 23.793.199.139.8 J, and it is suggested that the fuel should be adjusted according to this value. For a 500 kg space junk, the number of turns an electromagnet should have has been calculated as approximately 113. It has been proposed to prepare an electromagnet with a winding close to this value.

The difference of the developed method from previous studies is that it uses more space garbage collection capacity by moving between orbits, benefiting from the gravity of the Moon and the electromagnet which can be controlled from the Earth.

**Keywords:** Space Trash, Gravitational Force, Electromagnet, Earth, Moon

**1. Purpose**

The aim of the project is to reduce and prevent space pollution, which is a substantial problem today. There are three main methods developed today for this problem. These methods are the destruction of space debris with the help of a laser, the collection of space debris with the help of a huge net, and the extraction of space debris with the help of an electromagnet. This study will focus on the collection of space debris with the help of an electromagnet. Researchers believe this technique could be used to safely slow down the rolling motion of space debris and then pull it into a lower orbit for destruction. This technique could also be used to stop a damaged satellite from spinning so it can be repaired— something which is currently not possible. As it is non-contact, it could also allow engineers to manipulate particularly fragile objects. (Dumé, 2021) In addition, the electromagnet will only be able to pick up ferromagnetic substances that can be attracted by the magnet, so it will not be effective for non-ferromagnetic space junk. In order for non-magnetic materials such as aluminum to gain magnetic properties, several electromagnets must be operated around the object by changing the currents and thus the magnetism they apply, respectively.

*Image 1: Image of the process required to demagnetize non-magnetic material. In this numerical simulation, a copper sphere is manipulated using six sources of dipole fields surrounding the object. The goal is to move the copper ball along the sides of a cube while keeping its direction constant. This requires checking all three force degrees of freedom and all three torque degrees of freedom. The method uses only one field source at a time, which is depicted by highlighting the active field source. (Abbott, 2021)*

In this study, a method has been developed to increase the capacity of the electromagnet sent to space as much as possible, following the studies on the electromagnets to attract non-ferromagnetic materials. It is aimed for the electromagnet to move between orbits and collect all the space garbage behind and ahead of it, consequently leaving this garbage in the gravitational field of the Moon after filling its capacity. It will then return to orbit and repeat its mission until it is complete.

**2. Introduction**

Space junk or space debris is any machinery or debris left in space by humans. It may refer to large objects such as satellites that fail or remain in orbit at the end of their mission. It can also refer to smaller things, such as pieces of debris from a rocket or smudges of paint. (O'Callaghan, no date)

The subject of the research study is to discuss calculations behind a proposed method developed to collect the space garbage that continues to accumulate in the Earth's orbit, even as space technologies develop.

The aim of the study is to develop a method for the collection of space garbage, which may cause great problems for humans in the future, and for this method to be applied by engineers. In this way, if this method succeeds, the problems discussed afore may be greatly reduced.

**3. Method**

This study will test the applicability of the space debris collection method developed with mathematical calculations, using data obtained from sources, and to consequently present results of the study.

**4. Project Work-Timeline**

**5. Findings**

There are about 23,000 pieces of debris larger than a softball orbiting the Earth. They travel at speeds of up to 17,500 mph, which is fast enough for a relatively small piece of orbital debris to damage a satellite or a spacecraft. There are half a million pieces of rubble the size of marble or larger (up to 0.4 inches or 1 centimeter), and about 100 million pieces of rubble about 0.04 inches (or one millimeter) and larger. There is even smaller micrometer-sized (0.00039 inch

diameter) debris. (National Aeronautics and Space Administration, 2021)

**5.1. Kessler Syndrome**

Kessler Syndrome is the probability of more collisions occurring when vehicles sent into Earth orbit collide, causing more debris. In short, they are chain accidents that may occur with the increase in the number of spacecrafts in orbit. Undoubtedly, these collisions also caused a garbage dump in space. (Altun, 2021) The garbage created as a result of Kessler syndrome may pose a risk for the satellites/telescopes that will be sent to space in the future, problems may occur in the signals sent to the earth and may pose a danger to the health of astronauts.

**5. 2. The Method Developed for the Collection of Space Garbage**

The first step in the method developed in this study is to send the rocket from the Earth to the Earth orbit, to which a powerful electromagnet is attached through which its direction and power can be controlled from the Earth. The numerical characteristics of this electromagnet and rocket will be specified in the next calculations section.

*Figure 2: The largest electromagnet ever built. The 1,000-metric-ton solenoid at the center of ITER Tokamak will have 5.5 gigajoules of stored energy and will be approximately 18 meters or 60 feet long. (Degitz, 2014)*

After the electromagnet, which can be managed from Earth, is sent to space, it is planned to return to Earth's orbit. The movements of the electromagnet and the data received will be monitored by sensitive detectors placed on the electromagnet, and the magnetic field can be adjusted according to the size and characteristics of the space junk it approaches. In this way, light space debris will be collected with a weaker magnetic field, and heavy and large space debris will be collected with the help of a stronger magnetic field. The current value of the electromagnet can be controlled from the Earth. With this method, the possibility of the electromagnet going out of orbit will be reduced when it attracts space junk. In addition, the magnetic field of the electromagnet will be turned off when it comes near the working and functioning satellites in orbit. In this way, the satellites operating in orbit will not be damaged.

After the electromagnet collects the space junk, it will be controlled from the Earth and its direction will be changed to the adequate position. This location should be a suitable location where the electromagnet can leave the Earth's orbit and travel towards the Moon's orbit. Considering that the direction of the electromagnet is successfully changed and it enters the orbit of the Moon, it can leave these garbage in a center that can be created on the Moon, where the garbage will come out of the Earth's orbit and the dangers it may pose will be eliminated.

The system to be established on the Moon will be a garbage center. All garbage will be brought to this center and their safety will be ensured here. Afterwards, the pile of space garbage in this system can be destroyed on the Moon, if desired.

**5.3. Calculation of the Developed Method**

A spacecraft leaving the Earth's surface would have to travel at about 11 kilometers per second (7 miles) or 40,000 kilometers per hour (25,000 miles per hour) to enter orbit. Achieving escape velocity is one of the biggest challenges facing space travel. The vehicle requires an enormous amount of fuel to break Earth's gravity. All that fuel adds significant weight to the spacecraft, and when an object is heavier, more thrust is required to lift it. (NASA, 2009) This expression can be used for the rate at which the electromagnet escapes from Earth orbit:

When we write the values in the formula, the mass of the Earth becomes 1 M = 5,9722 × 10 24 kg, the universal gravitational constant G = 6,67 × 10 -11 N m 2 kg -2 . 70% of known and tracked space junk is about 2,000 km above Earth. (Space Camp Turkey, 2020) The radius of the Earth is 6371 km. Based on this information, it can be taken as r = 2000 km + 6371 km = 8371 km. In this way, the formula can be arranged as follows and escape velocity can be found:

The escape velocity from Earth was found to be approximately 35.120 km/h to send the electromagnet to a distance of 2000 km where space debris is located.

Satellites are instruments manufactured to enter elliptical or circular orbits around a central body (such as earth, planet, sun). (GÜLSEÇEN, 2014) Considering that the electromagnet will also collect the wrecked satellites, it can be concluded that it will follow the same orbit as the satellites. Considering that the electromagnet will follow a circular orbit, the orbital velocity (v_c) can be found by the formula:

When the values used in calculating the escape velocity are placed, the orbital velocity of the electromagnet, its velocity value while following the trajectory, can be found as follows:

Compared to the escape velocity, the orbital velocity of the electromagnet decreased by about 10.286,5 km/h. Considering that the electromagnet will change its trajectory to collect space debris, r (the distance from the center of the Earth), the orbital velocity will decrease by the square root of r as it will increase as the electromagnet moves away from the Earth. The same is true when the electromagnet approaches Earth.

The orbital period of the electromagnet, the time it takes to make one revolution around the Earth, can be calculated using the following formula:

In the formula, the period T represents the distance between the Earth's center of mass and the object, and represents the orbital velocity found previously. When the values are replaced in the formula, the period is found as follows:

The electromagnet will complete one revolution around the Earth in approximately 2.1 hours. It will be very difficult for the electromagnet to pick up the space debris in that orbit with just one turn. So, the electromagnet must go around the Earth at least a few times. During these tours, scientists from Earth should carefully follow the movements of this electromagnet, because while collecting space debris, it should not attract orbiting satellites and change their orbits. Therefore, the magnetic strength of the electromagnet must be reduced by tracking it near the working spacecraft. Finally, the mechanical energy of the electromagnet can be calculated before moving on to changing the trajectory of the electromagnet. The mechanical energy of bodies following a circular orbit can be expressed as:

Mechanical energy is obtained by adding kinetic and potential energy. Potential energy is calculated with the formula

at far distances from Earth and is negative. Potential energy is considered positive for easy calculation at close distances to Earth but is actually negative. The total mass of all space objects in Earth orbit is 9,800 tons, and the number of debris objects regularly monitored and cataloged by Space Surveillance Networks is approximately 30,040 (Space Debris by the Numbers, 2022). From these values, the mass of an average space junk can be found as 326,23 kg. The mass of the electromagnet can be taken as 1.000 kg, which is more than the average space junk, but this number can change with more detailed engineering calculations. From this result, the energy of the electromagnet can be found as follows:

The mechanical energy that the electromagnet will have has been found to be approximately 23 billion Joules. This means that sending the electromagnet from Earth will be a fuel-intensive process because the electromagnet will convert its mechanical energy from chemical fuel energy. After the electromagnet collects the space debris in a certain orbit around the Earth, its orbit will be changed, and it will move towards the Moon's orbit. This state must be adjusted by the engineers following the electromagnet. When it is concluded that it has collected a sufficient amount of space debris by monitoring it through sensitive detectors placed on the electromagnet, its direction should be changed so that it travels towards the Moon while the electromagnet is closest to the Moon in Earth's orbit. It is aimed that the electromagnet, whose direction has changed, will go towards the Moon and, after being affected by the gravity of the Moon, enter the gravitational field of the Moon together with the space debris, and leave the space garbage, the rocket will continue its mission and continue to collect space debris until its fuel and energy are sufficient.

Apart from the electromagnet and the mechanics of the rocket, the magnetic field created by the electromagnet is also important. The electromagnet will approach the space debris from certain distances and collect it in itself. “This type of non-contact magnetic effect will operate from a distance of about 10-15 m and will offer positioning accuracy within 10 cm with a position accuracy of 1–2º.” (European Space Agency, 2017) The speed of space garbage can reach 30,000, 50,000 or even 70,000 kilometers per hour. (Dr. Mahir E. January, 2019) The magnetic force that the electromagnet can apply can be found with the following formula:

F = force, i = current, g = length of gap between the solenoid and a piece of metal, A = Area, n = number of turns in the solenoid and magnetic constant is:

Considering an example of a situation where an electromagnet with a radius of 2 m attracts a space debris with a mass of 500 kg, 15 m away with an acceleration of * *a= 2m/s^2, the magnetic force applied by the electromagnet would be F = 1,000 N. When the current value is accepted as i = 5 Amperes, n/g value can be found as follows. This value is the ratio of the number of turns in the solenoid in the electromagnet to the gap between the solenoid and the metal. This can be expressed as:

If we give g, the gap between the solenoid and the metal, 5 cm, the value for n, the number of turns in the solenoid, comes from approximately 113.

**n=112,539**

It can be understood from this that in a situation under the conditions mentioned above, approximately 113 turns of winding must be made in the electromagnet. The rocket, which has an electromagnet with about 113 turns of winding, will change its direction from Earth after departing from Earth and collect space debris in different orbits. Later, when its capacity is full, it will leave this garbage in the gravitational field of the Moon, continue its task, and when its fuel / energy decreases, it will return to the Earth. The number of different orbits it can travel will initially depend on the amount of fuel the rocket will have.

**6. Conclusion and Discussion**

In this study, a solution to the space garbage problem was developed supported by calculations. As a result, an electromagnet in a rocket with an escape velocity of 35.120,354km/s can be sent into orbit at a distance of 2,000 km from the Earth's surface, where space debris is concentrated. This electromagnet and rocket will complete a revolution around the Earth in hours with an orbital speed of 24. 833,8404km/h. The mechanical energy of the rocket and electromagnet system in this process was found to be 23.793.199.139.8 J. Therefore, it will be a costly fuel consumption. After this system collects enough space debris in one orbit, it will be directed to another orbit with different space debris, controlled by engineers on Earth and changing its direction. Afterwards, after the space garbage collection capacity is full, it will travel towards the Moon and enter the gravitational field of the Moon. After leaving space junk on the Moon, it continues its mission until its fuel is sufficient, and when its fuel is low, the rocket will return to Earth. The number of turns an electromagnet should have for a 500 kg space junk is calculated as 113. These calculations can be repeated many times, depending on the mass of the average space junk. As a result of the immense cost of electromagnets engineers must perform such calculations beforehand, rather than implementing this method through simply trying it. The feature that distinguishes the method developed for the collection of space garbage in this study from the previously developed methods is that it gains more space garbage collection capacity by repeating the task of the electromagnet many times with the help of a rocket, changing the orbit and collecting the space garbage in front and behind.

**7. Suggestions**

After the calculations are made in detail, it is necessary to develop a system in which the movements of the rocket can be continuously monitored so that it can be controlled from the Earth in terms of controlling the rocket from the Earth. This system can be provided with detectors to be placed on the electromagnet. These detectors in the electromagnet must be capable of calculating the distance, approximate volume and mass of the approaching space junk. After these data are obtained, the magnetic force required for the electromagnet and space junk to attract each other can be adjusted. In this way, the electromagnet will not deviate from its orbit while attracting space debris of different masses. Increasing or decreasing the current value according to the mass of the space junk can be controlled by a software developed. The transfer of these data to the world at the same time will be useful in terms of checking the accuracy.

Another issue in the realization of the method is fuel. A lot of fuel and investment is required both for the movement of the electromagnet between orbits and for its journey to the Moon. Since the propulsion cannot be provided by solar energy, the electromagnet will need a large investment for its fuel. In order to reduce the cost of this fuel need, it can be recommended to develop systems to reduce the production and transportation of liquid hydrogen, the fuel used in rockets.

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