As mankind continues to launch more and more satellites, orbital debris is becoming an increasingly larger problem for spacecraft operators. Recent events such as the COSMOS-Iridium collision and the Chinese A-SAT weapons test have increased the amount of orbital debris by almost 50% since 2007. Projections from NASA's Orbital Debris office show the number of orbital debris increasing over the next 100 years. Thus, a proactive method of orbital debris removal will be needed to clear debris from low earth orbit, providing a safer environment for future space exploration and earth observation. Current proposals will be analyzed that involve actively changing the orbit of the debris so it will eventually disintegrate in the atmosphere. A relatively new proposal involves using high powered lasers to propel the debris into a decaying orbit. The analysis will be extended utilizing tracking data for space debris available on CelesTrak to determine the change in orbital elements and lifetime with debris modified by ablative laser propulsion. It was found that ablative laser propulsion provides enough deltaV to change the lifetime of debris produced from the Chinese A-SAT weapons test to an average of 1.6 years.
Space debris is not a new problem in astrodynamics, but rather one, like climate change, that has recently come to light due to the increase in the rate at which the change is occurring. Two recent events in the last few years, the COSMOS-Iridium collision in 2009 and the Chinese Anti-Satellite (A-SAT) weapon test in 2007, have increased the number of orbital debris in orbit by 50%. However, there a plethora of additional sources that produces space debris: discarded rocket bodies, defunct satellites, fragments from other man-made objects, and even natural debris such as micrometeorites.
Figure 1. Computer model (not to scale) of all man-made debris currently orbiting the earth.
Space debris is not a problem that will solve itself, at least in the near future. An active approach is needed to remove debris from orbit. Unfortunately, most proposed methods for space debris removal are just that: proposals. Many methods never get past the initial feasibility studies. From a space-based approach, a common proposal is the usage of a "trash-collector" spacecraft to capture and deorbit one or more pieces of space debris. This method has not been proven viable yet mainly due to the fuel required for rendezvous with debris for capture, then deorbit the debris or push it into a graveyard orbit. It is a costly endeavor to design and launch a spacecraft to remove a few pieces out of thousands of debris. Ground-based approaches involve utilizing electromagnetic properties, such as lasers, photon propulsion, and EM fields, to enact small deltaV's on the space debris to, over time, push them into a lower orbit. One such concept, the ablative laser propulsion technique, will be examined later on in this paper.
The guiding principles behind orbital debris removal are orbit maneuvers and atmospheric drag. Most debris in low earth orbit will be subject to small atmospheric drag, causing their orbits to decay over time, and eventually burn up in the atmosphere. The higher up a debris piece is, the longer it will take to decay due to a lower atmospheric density. Debris higher up may eventually decay, but it may be on the order of hundreds of years. An orbital maneuver will be required to push the debris into a lower orbit, causing it to decay into the atmosphere quicker. An impulsive or continuous deltaV can perform this task. In the case of the "trash-collector" approach, another spacecraft would provide the required deltaV.
Although meteoroids and micrometeoroids have been present orbiting the earth long before man put artificial satellites into orbit, the problem of space debris is a man-made one. Beginning with the launch of Sputnik in 1957, the North American Aerospace Defense Command has been logging and tracking every large man-made object in space. As of October 31, 2011, the current count for the amount of objects in space is over 22,000, of which 965 are operational satellites. Although today we mainly speak of two debris incidents, the COSMOS-Iridium collision and the Chinese A-SAT weapons test, the number of objects in space increased drastically during the height of the Cold War and the space race providing additional satellites and weapons tests into orbit.
Figure 2. The amount of objects in earth orbit has been increasing steadily since the beginning of the Cold War. The discrepancy between functional satellites and orbital debris is very large, leading to problems for satellite operators trying to avoid collisions.
The main concern surrounding space debris problem is the potential for collision of a functional, multi-million dollar satellite. As proven with the COSMOS-Iridium collision of 2009, not only will a satellite be rendered useless upon impact with a large enough piece of debris, but even create more debris. In 2007, the United Nations issued voluntary guidelines to prevent the creation of more orbital debris, including guidelines for satellites to have the ability to deorbit itself after their mission is completed. NASA and the European Space Agency have similar regulations in place to prevent the creation of more debris.
Space debris impacts on both manned and unmanned spacecraft are essentially a fact of life in spacecraft design and operations. Satellites can be designed to withstand small debris impacts through the usage of shielding on key components, but large surfaces such as solar arrays will suffer degradation over time due to small debris impacts. However, solar arrays can be designed with degradation over time in mind. Despite this fact, when it comes to large debris, the only option to avoid serious damage to the satellite is to perform a maneuver to prevent collision. The International Space Station recently had to fire its thrusters for the first time in 5 years to avoid a collision with a large piece of debris. Although it happens rarely, the cost of maneuvering the ISS to avoid collisions is very high fuel-wise, so much so that when maneuvers like this are required, ISS crew and operators prefer to use the docked resupply vessels to push the ISS out of harm's way.
Although a "trash-collector" based approach is easy to visualize and compute as an active method of orbital debris removal, it has not been proven a feasible approach to space debris removal. The collector satellite would have to rendezvous with each piece of debris it wishes to capture, match its velocity, and then capture it in the satellite. Each capture would require a large fuel sum to perform, and thus the spacecraft would be limited by its fuel to the number of debris pieces it can capture. There are currently several projects in development that would mitigate some of these issues. Canadian aerospace firm MDA is developing a geosynchronous refueling station, Space Infrastructure Servicing, which the collector satellite could use to get more fuel as needed to collect more debris than it could normally. A different mitigation of this issue is through the use of mini-collectors attached to a satellite bus. REDCROC, a senior design team from the University of Colorado, has developed mini-collectors that when attached to a satellite bus, deorbit debris pieces without the satellite bus being required to deorbit with it. Deorbiting the debris could be done in several ways, either with an applied delta V, a drag device such as an inflatable balloon, or collecting the debris on the satellite itself. Despite the risk mitigation being applied to the "trash-collector" approach to removing space debris, it is still a costly project to undertake. Even if each collector satellite could capture 20 pieces of debris, it would take over 1000 missions to capture the estimated 21,000+ pieces of debris.
This is where the new proposals, including electrodynamic tethering, particle momentum transfer, and ablative laser propulsion come into play. These devices don't use fuel to perform debris removal; rather they rely on electromagnetic and material properties to modify the orbit of the debris. Electrodynamic tethering generates an electromotive force from current generated through long wires to move a captured debris piece into a lower orbit. Particle momentum transfer involves bombarding a piece of debris with photons or ions continuously over time to slowly modify the object's orbit. Ablative laser propulsion uses a high powered laser to ablate the surface of the debris, generating a rocket-like propulsive force on the debris. The method of ablative laser propulsion will be examined in more detail later on. Both particle momentum transfer and ablative laser propulsion do not require rendezvous with the debris to deorbit it.
Deorbiting and Drag
Under standard two-body motion of satellites, an object in earth orbit will not come down to the earth's surface unless perturbed. To get that satellite to come back down to the earth, a change in velocity is required to maneuver the satellite into a different orbit. In reality, objects in LEO experience perturbations due to atmospheric drag, which changes the semi-major axis of the orbit, causing the satellite to eventually impact the earth or burn up in the dense atmosphere. If low enough, space debris will eventually burn up in the atmosphere due to the drag forces acting on it. The lifetime of said debris can be on the order of a few years, but debris in higher orbits may take hundreds of years to come down, possibly more. While in orbit, it poses a real threat to spacecraft operators, who must maneuver the satellite to avoid the debris to prevent damage or collision.
The guiding principle behind deorbiting is to give the satellite or piece of debris a delta V to push it into a lower orbit where drag will dominate, causing the satellite to loose altitude and bring it down into the dense atmosphere. Figure 1 shows the required delta V for a basic Hohmann transfer to lower altitudes from various circular orbits. Note that only the first segment of the Hohmann transfer was utilized, as drag will reduce the apoapse altitude over time.
Figure 3. Required deltaV to move into an orbit with a lower periapse altitude.
As expected, the larger change in periapse altitude, the larger the required deltaV to move the satellite or piece of debris is. Even for the largest change shown on the graph, from 500 km to 100 km, a deltaV of about 0.115 km/s is required to change the orbit. Once a piece of debris has been moved into a lower orbit, its orbital lifetime has been drastically decreased. Drag is a dominate force in low earth orbit. Without any active form of boosting the semi-major axis of a satellite in low earth orbit, it will fall back and burn up in the atmosphere. The same applies to space debris. Figure 4 displays historical data on spacecraft lifetimes in low earth orbit.
Figure 4. Historical lifetimes of satellites in low earth orbit.
As you increase in altitude, the lifetime of the satellite or debris piece increases exponentially. Above 700 km altitude, orbital lifetimes are very large, upwards of 30 years. Once below 300 km, the lifetime is less than a year. The satellite or debris piece will quickly burn up in the atmosphere or impact the surface of the earth. In order for debris higher up to be removed in a reasonable time fame, its orbit must be changed into a very low orbit where drag will dominate.
Ablative Laser Propulsion
Ablative laser propulsion is a rather new proposal to remove space debris from low earth orbit. Ablative laser propulsion relies on using a high-powered laser to ablate, a form of vaporization, the surface of the debris. As the vapor is ejected from the debris, it generates a momentum change similar to the impulse delivered by a rocket. Generally, the momentum change is delivered in the direction of the laser's incoming beam.
The obvious benefit of ablative laser propulsion is that the deorbit device is the actual debris itself. There is no need to rendezvous with the debris. Provided that the laser is high enough power to ablate the debris, which could be made of composites, aluminum, and any other space building materials, it could be placed on a specially designed satellite or even placed on the ground. This reduces the cost of deorbiting the debris significantly, particularly in the ground-based approach, where no new satellites would need to be placed into orbit to remove the debris.
However, there are a few downsides to this technology. Because the laser would have to be powerful enough to physically vaporize a small part of the debris in order to provide a momentum change to deorbit the debris, it also has a military application. Other countries could see this as a threat to their own space systems. The initial proposal to build ground-based high powered lasers to deorbit debris, set forward by the US Air Force, was declined for this very reason. An international task force would most likely need to be assembled to build high powered lasers for ablative propulsion, which isn't an easy thing to do from a political standpoint. Additionally, on the technical side, the lasers would need to be developed to produce high power outputs effective through the atmosphere and high quality optics to filter and focus the laser on the debris.
A common misconception in the usage of lasers is that lasers produce one-dimensional beams. In a classroom or hall, the size of the laser dot in your average presentation laser produces is essentially the same. At large distances, the divergence of the laser beam cannot be neglected. The beam of light produced by a laser slowly will diverge over distance. Although the dot you shine to point something on the projector screen is very small, by the time it reaches orbit, should you shine it there, could be several hundred feet in diameter, depending on the quality of the optics. Despite the divergence, orbital debris must be tracked very closely so when the high powered laser is actually fired on the debris, it hits the debris and doesn't miss. Thus the tracking of debris must be done very precisely and accurately to ensure that the momentum transfer is induced successfully on the debris, pushing it into a lower orbit.
The magnitude of the momentum change induced on a piece of debris - or any object, for that matter - is a function of the material properties, including reflectivity and absorption, along with the laser's firing wavelength and output power. The more power, the higher the momentum change. The more energy absorbed by the material, the more momentum change. Although complex in nature, the momentum change can be simplified to a basic expression shown in Equation 1. The momentum change is delivered in the direction of the vector between the laser itself and the piece of debris.
The coupling coefficient, cm, varies on the material of the debris. For an ideal case on aluminum, this coupling coefficient is cm = 2 x 10-5 Ns/J. The energy delivered, Ed, is a function of the laser power at the impact location (which in itself is a function of laser output power, atmospheric attenuation, space loss, optical properties, and much more), material absorptivity, and the area of the debris exposed to the laser's energy beam. Over the course of the laser's activation, the energy delivered is approximately a constant value. However, mass is not constant during this process. Mass is removed from the piece of debris at the ablation rate, μ. For aluminum, this value is approximately equal to μ = 80 x 10-9 kg/J, so the change in mass is Δm = μEd. As the laser outputs high-energy pulses at a particular frequency, for n amount of pulses, the change in velocity can be expressed in the form shown in Equation 2.
This issue now comes to the laser's output power. There have been incredible advances in laser technologies in the past few years. The US Department of Defense has been funding laser weapon technologies, such as the Airborne Laser. Thus high powered lasers are already in development that could be used in space debris removal. Table 1 displays a sampling of lasers and their output powers.
Table 1. Modern laser output power. 
Laser Pointer Pen
Advanced Tactical Laser
Northrop Solid Sate Prototype
For a laser with 100 kW output power, pulsing for 100 ns every 1 ms (this implies that Ed = 1000 J/pulse), and assuming no losses between the laser and the piece of debris, the total velocity and mass change over time can be computed utilizing Equation 2. The result is shown in Figure 5.
Figure 5. Ablative laser propulsion results for the total magnitude of the deltaV produced.
Over the course of approximately 4700 pulses (for 1 kg mass this equates to 47 seconds), the laser can exert a deltaV of approximately 115 m/s (0.115 km/s). Assuming that the deltaV is applied in the correct direction, this would push the debris out of a 500 km orbit to a 100 km orbit, well inside the atmosphere. Through this simple momentum-change analysis, the ablative laser propulsion proposal is a feasible method of space debris removal. In less than a minute, a deltaV large enough to push a small piece of debris into the atmosphere can be applied by a ground or space-based laser system.
Gabbard diagrams display a scatterplot of the orbital period of debris versus perigee altitude and apogee altitude for a set of space debris. It is used particularly in the cases of satellite collisions or fragmentation events, such as the COSMOS-Iridium collision or the Chinese A-SAT test to determine the location of the fragmentation event. Figure 6 shows the Gabbard diagram for the debris formed by the 2007 Chinese A-SAT weapons test, which resulted in the destruction of the Fengyun-1C weather satellite. Orbital elements for the debris were downloaded from the CelesTrak website.
Figure 6. Gabbard diagram for the orbital debris formed from the 2007 Chinese anti-satellite weapons test. There are 2700 debris pieces in this diagram.
Most of the debris from the Fengyun 1C satellite is concentrated near the 850 km altitude range (the convergence of periapse/apoapse altitudes). Returning to Figure 4, an 850 km orbit results in an orbital lifetime of over 30 years. During this timeframe, all satellites operating within the vicinity of the debris must perform maneuvers to avoid collision with any of the possible 2700 trackable debris pieces.
In order to use ablative laser propulsion to change the orbits of the satellite, several assumptions were made to simplify the analysis. First, the laser used to modify the orbits will have an output power of 100 kW, providing an instantaneous 1 pulse output. This results in the same deltaV produced in Figure 5, 0.115 km/s, but it will be provided as an impulsive deltaV rather than a continuous deltaV. Second, the laser will be assumed to be in the correct orientation to provide the deltaV tangentially to the debris orbit at apoapse to reduce the periapse altitude of the debris. Finally, the orbit will be analyzed using standard two-body equations of motion, with drag the only perturbation after the deltaV has been applied. Table 2 displays the average orbital elements for the A-SAT debris which will be used further in the analysis.
Table 2. Average orbital elements for the A-SAT debris.
Argument of Perigee
Right Ascension of the Ascending Node
Performing the analysis in the two-body perifocal frame of reference means that inclination, argument of perigee, and right ascension can be ignored. Under the assumptions stated above, the final orbit after an impulsive deltaV of 0.115 km/s provided by the ablative laser propulsion system yields a new set of semi-major axes and eccentricities. The deltaV was applied at apoapse in order to reduce the perigee altitude. A lower perigee altitude implies a higher drag force imposed on the satellite, which will in turn reduce the apogee altitude, circularizing the orbit around the perigee altitude.
The results of applying a deltaV onto each piece of debris shown in Figure 6 result in the histograms displayed in Figures 7 and 8.
Figure 7. Semi-major axis before and after the laser ablation procedure.
Figure 8. Eccentricity before and after the laser ablation procedure.
The results are not surprising. The semi-major axis of the debris decreases on average by 200 km. Eccentricity increases due to the deltaV being applied at apoapse to decrease the periapse altitude, causing a higher eccentricity.
Lifetime determination of objects in low earth orbit is a complex procedure, involving numerical integration of the equations of motion for the satellite including atmospheric drag. Due to the complexities of analyzing space debris, a rough order-of-magnitude estimate can be found using tabular lookups based on simulation data. STK 9.0 Lifetime calculator was used to solve for the lifetime of an average piece of space debris as a function of perigee altitude and eccentricity. The Lifetime calculator was setup to use the Jacchia-Roberts analytical atmospheric density model with J2 perturbations to speed up lifetime calculations. The burn-out decay height was set to 180 km, where the lifetime of a debris piece is less than one day. Solar radiation pressure was ignored as drag is the most dominate non-conservative force in LEO.
Table 3 displays the appropriate ballistic quantities used in the analysis. Orbital elements besides semi-major axis and eccentricity were held constant, using the average values for the A-SAT debris shown in Table 3. It should be noted that the quantities shown in Table 3 have large uncertainties associated with them, but are on the order of magnitude expected.
Table 3. Ballistic coefficients and quantities for A-SAT debris.
Coefficient of Drag
Cross-Sectional Area (constant)
Mass, post-Ablation (37% loss for 115 m/s)
Ballistic Coefficient, post-Ablation
In graphical form, the results from the lifetime simulations in STK 9.0 are shown in Figure 9.
Figure 9. 3D Surface of orbital lifetime as a function of both perigee altitude and eccentricity.
The obvious result from Figure 9 is that as perigee altitude increases, the lifetime of the orbit also increases. An increase in eccentricity implies that the apoapse altitude is higher; meaning that less drag force will be applied to the object as it approaches and descends from apoapse. If the object is in a circular orbit, it can be viewed in a 2D space, as shown in Figure 10.
Figure 10. Orbital lifetimes with eccentricities equal to zero (circular orbit).
Figure 10 can be directly compared to Figure 4. It can be seen that the lifetimes are similar and on the same order of magnitude, thus validating the lifetime results from STK. Deviations between the two lifetime graphs are due to additional perturbations such as solar radiation pressure and the differences in ballistic coefficients.
The lifetimes before and after the ablative laser propulsion procedure can be found using a basic linear interpolation between known data points evaluated in STK. Any debris outside the range of 0 ≤ e ≤ 0.1 and 200 km ≤ hp ≤ 800 km have been removed from the analysis. The results are shown in Figure 11.
Figure 11. Orbital lifetimes of the A-SAT debris before and after ablation.
After ablation occurs at apoapse, the lifetime of the debris drops significantly from an average of 103 years to only 1.67 years, with a majority of the debris decaying in less than a year. Ablation has a very large impact on the lifetime of the orbit. Table 4 highlights the statistical summary of the changes in orbital characteristics and lifetime of the A-SAT debris.
Table 4. Mean and standard deviation of orbital characteristics.
Not only has the mean orbital lifetime decreased after ablation by a factor of almost 100, but the standard deviation has decreased as well by a considerable margin. This result shows that a small deltaV applied via ablative laser propulsion at apoapse decreased the average orbital lifetime, but that all debris pieces in the simulation were effected in a manner that higher out debris came in closer than debris already close.
Although this analysis was performed under the context of ablative laser propulsion, the same analysis can be applied to any method of deorbit that provides a given deltaV at apoapse.
Orbital debris is a problem that will require an active solution. Aside from large orbital debris causing events such as the Chinese anti-satellite weapons test in 2007 and the Iridium-COSMOS collision, debris comes from additional sources such as defunct satellites, rocket bodies, and additional deployment equipment. Rendezvous solutions, such as the "trash-collector" conceptual design, are not practical due to the high cost of satellite launches and fuel requirements for rendezvous. However, new proposals, including electrodynamic tethering, ablative laser propulsion, and particle momentum transfer do not require rendezvous to deorbit debris, saving fuel and money. Ablative laser propulsion is a proposal that is feasible with today's high-powered laser technology. Utilizing a 120 kW solid-state laser, a deltaV of 0.115 km/s can be applied to a piece of debris, causing 37% of its mass to be used for the propellant.
For an average piece of debris, tabular lifetime studies were performed utilizing STK's Lifetime tool. After applying a deltaV of 0.115 km/s at apoapse, the periapse altitude of the debris was decreased enough for drag forces to dominate and cause deorbit of the debris much faster than normal. Under ideal conditions, statistical analysis on the debris created by the Chinese A-SAT weapons test shows that the debris would be deorbited 100 times faster than it would naturally due to drag, with an average lifetime post-ablation of 1.6 years.
Future analysis to understand the properties of ablative laser propulsion could include targeting the debris from the ground versus targeting the debris from a space-based satellite to analyze the dynamics that will occur upon ablation. However, the largest obstacle that faces ablative laser propulsion to become the frontrunner of orbital debris mitigation is political. Any laser system that has the capability to remove orbital debris also has the capability of being used in a military capacity to deorbit, disable, or even destroy other satellites in orbit. Mitigating other nation's concerns over ablative laser propulsion will be just as challenging as developing the technology required.