The growing amount of orbital space debris surrounding Earth is becoming a significant issue as space exploration continues to expand and satellite communication networks continue to grow. Over time the amount of debris will grow exponentially, even without future space launches, because the debris will collide with itself and break into smaller pieces. Scientists and engineers worldwide have proposed numerous methods of removing these potentially dangerous orbital objects. The present challenge for any company that wants to prevent catastrophe by reducing the danger to their spacecraft and satellites is deciding which alternative to invest in.

We have created a mathematical model which evaluates an active space debris removal (ADR) method and produces an associated return of investment (ROI) that can be compared to other ADR methods. This model takes into consideration an ADR method’s altitude and mass range, rate of debris removal per year, and cost. It also requires a list of orbital debris that is currently in space whose size, velocity, and altitudes are known. After analyzing the efficiency and capability of an ADR method, our model calculates the new risk that a spacecraft would assume after the ADR method has been implemented. This new, and hopefully decreased, risk is converted to a monetary gain normally used in ROI estimation. The total cost of the ADR method represents the cost of investment.

Our research has led us to consider four ADR methods that have been developed and analyzed by scientists during the past decade. These alternatives have different ranges of altitude that they are capable of reaching, but all are within the low-Earth orbit (LEO, 200-2000km altitude). Our study focuses on LEO because this is where the highest density of space debris is and it is also where much of government and industry space traffic occurs. Each ADR methods guides objects into a lower orbit where the debris spirals toward Earth and eventually burns up as it skims the atmosphere.This process is known as deorbiting. The ADR methods are listed below:

1. Ion Beam Shepherd: A spacecraft uses a high velocity concentrated ion beam to guide objects of all sizes into lower orbit without contact . This method can remove large objects up to 5000 kg, but only at a rate of almost two per year.

2. Robot Arm -— Solid Rocket Propellant: This spacecraft grabs a piece of debris with a robot arm and attaches a thruster de-orbiting kit (TDK) to the object. The kit uses solid rocket propellant to thrust the debris into a lower orbit. This procedure can be completed up to five times per year, over seven years, provided that the spacecraft is restocked with TDKs and fueled by another ship every year.

3. Robot Arm —- Electrodynamic Tether: This method is similar to the method above in that it grabs an object with a robot arm, but it uses electro-dynamic tether (EDT) to lower the orbit of debris. The EDT consists of a conductive tether that sends current to the debris which generates a force created from the electric charge interacting with the magnetic field. This force slows the debris down into a lower orbit. This eliminates the need for propellant, but this method can only remove one object per year.

4. Electrodynamic Debris Eliminator: Also known as EDDE, this method implements the same EDT technology with some modifications. It is intended for debris of smaller mass (2-50kg) but it can remove many more objects per year.

As noted above, each of these ADR removal methods has an upper limit of objects removed per year. In addition, each operates at certain altitudes and is capable of eliminating debris within a specific mass range. These constraints reduce the effect each ADR method has on the collision risk to a mission spacecraft. Our model used current NORAD data to simulate the current population of space debris in LEO and predict how each ADR method and pairs ADR methods would be able to eliminate portions of the debris. Our comparative baseline for collision risk was the estimate that Hubble like missions have a 1 in 221 chance of a catastrophic collision with space debris. Each method or pair eliminated a portion of debris, resulting in a lowered risk to spacecraft in LEO. To better understand the benefit of lowering the risk, our model converted the risk reduction of each method or pair to a return on investment (ROI). The results of each ADR method, implemented over a period of 5 years, are listed below:

Since each individual option incurs a significant fiscal loss, our findings do not encourage investment into any one or pair of these four ADR methods. Instead, we propose the implementation of mitigation measures which are aimed at curtailing the future growth of debris rather than actively removing existing debris. On a policy level, we recommend a tax rebate system be implemented which encourages industry to design spacecraft for self-removal. This has been shown to be cost effective. For a private company, instead of investing in ADR technology, we recommend investing in strengthening spacecraft and improving debris avoidance capabilities.