Orbital Debris: An Energy Management Problem

Orbital Debris: An Energy Management Problem
by Don Kessler Retired NASA Senior Scientist for Orbital Debris Research Asheville NC

Summary Current spacecraft operations have created an unstable orbital debris environment in Earth orbit The instability in LEO will increasingly affect the design of spacecraft in LEO over a period of 10’s of years At higher altitudes, the instability only becomes important over a period of 100’s of years. Both the problem and the solution are related to how we manage the energy that is associated with objects in Earth orbit Unstable Unstable Environment…..LEO 10’s of years….GEO 100’s of years….Problem and Solution related to management of Energy

The Solar System: Circular Orbits confined to a plane (stable system)

…Except for Comets and Asteroids: Asteroid Inclinations up to 20o (unstable system)

Space Shuttle Launch: Fuel converted to Kinetic Energy
2,000,000 kg: Fuel 110,000 kg: Shuttle (including payload) Fuel / Shuttle mass ratio = 18 At 7.5 km/sec Shuttle kinetic energy = 14 times its mass in TNT

Orbital Debris in LEO: Inclinations up to 145o (very unstable system)

Iridium 33 - Cosmos 2251 Collision February 10, 2009 Altitude 790 km

Iridium-Cosmos Collision
One year after the Iridium/Cosmos collision, about 2000 fragments cataloged, as longitudes of nodes randomize Cosmos 2251 Debris Right ascension of ascending node randomize. Slower for near polar orbits. Iridium 33 Debris

Number of Cataloged Objects in Earth Orbit
Anti-satellite Test plus the Iridium/Cosmos Collision doubled fragment count Iridium/Cosmos China Anti-satellite 2 events doubled fragment count. Had remained nearly constant for 20 years following Ariane explosion in 1986 Year

Mass and Energy in Low Earth Orbit
2.5 Million kilograms of mass in LEO 5000 upper stage rockets and payloads in orbit ….mostly non-operational. Average collision velocity about 10 km/sec Collision kinetic energy = 25 X debris mass in TNT Total kinetic energy available in LEO = 60 kilotons of TNT Comparable to nuclear bomb Fraction released with every collision

Building an Earth Orbital Debris Model
Model sources of small particles -Collisional fragmentation between artificial Satellites -Release of small objects by artificial satellites Model orbit changes of small particles -Atmospheric drag -Solar radiation pressure -Collisions Convert orbital elements into flux via spatial density Test model with observations Input traffic model, then model sources…changes in orbits….convert to flux….test with obs

Number of Objects in Orbit
Rate of Debris Generation When will collisions become dominant debris source? Rate of Debris Generation Amount of small debris proportional to Number With no mitigation, the rate that small debris is released would proportional to the number of objects in orbit; however, the rate that objects collide with one another is proportional to the square of the number of objects in orbit. Consequently, it is inevitable that the small debris generated by an increasing population will eventually be dominated by collision fragments. The question in the late 70’s was when? Number of Objects in Orbit

Number of Objects in Orbit
Rate of Debris Generation When will collisions become dominant debris source? Rate of Debris Generation Amount of small debris proportional to Number With no mitigation, the rate that small debris is released would proportional to the number of objects in orbit; however, the rate that objects collide with one another is proportional to the square of the number of objects in orbit. Consequently, it is inevitable that the small debris generated by an increasing population will eventually be dominated by collision fragments. The question in the late 70’s was when? Rate of collision fragmentation varies as square of Number Number of Objects in Orbit

1978 Predicted Collision Rate Assuming various growth rates in the catalogue
The objective of the Kessler/Cour-Palais paper published in 1978 was to answer that question. During the late 70’s, NASA was fairly optimistic about the growth in the space program, so the growth rate in the catalogue might have been fairly high; however, the actual growth rate was close to the minimum assumed in the paper of 320 catalogued objects per year.

Predicted Number of Fragments from a Collision between Cataloged Objects
Sampled Population Experimental sampling began in 1984 Systematic sampling in 1990 Cataloged population (only data prior to 1983) 1978 model Current “breakup models” predict about the same number of small fragment, and a slightly larger number of large objects

Cataloged Objects DoD Goals for past 50 years:
Maintain a catalogue of man-made objects No independent requirement for orbit accuracy No requirement to increase sensor sensitivity No requirement to keep track of satellite fragmentation events Currently reevaluating requirements to meet need for collision avoidance warnings Eglin radar in Florida NORAD was successfully fulfilling its charter by only maintaining a catalogue, while the outside world thought of NORAD as the “tracking all man-made objects in space”. However, it should have been obvious that the 70 cm wavelength of their main radars were incapable of detecting objects smaller that 10 cm in LEO; their telescopes were operated to only used to detect objects at much higher altitudes. NASA later operated these telescope to sample LEO and measured an environment that was more than twice that in the catalogue. Later, NASA used the Haystack radar, with a 3 cm wavelength, to “sample” the environment to sizes less than 1 cm, and obtained a sampling rate that was more than 20 times the rate predicted by the catalogue. Telescopes in Maui

Sampling Returned Spacecraft Surfaces by counting objects hitting surface
Examples of impact craters found on the Shuttle. The window pit cause the window to be replaced to ensure that the window would not fracture under the pressures cause by the next launch. Had the impact shown on the right, which hit the radiator surface, actually hit a radiator tube which circulates the radiator fluid, the mission would have had to be terminated. STS-118 Radiator panel Puncture 2 mm titanium-rich debris Entry hole 7 mm Exit hole 14 mm Orbital Debris impacts on returned spacecraft surfaces exceed the number of meteoroid impacts. Materials melted into the craters include aluminum, titanium, paint, copper, silicone, circuit board, sodium-potassium

Sampling using Radars by counting objects passing thru beam
Radar pencil beams with smaller wave lengths : X-band Haystack 3 cm, Goldstone 3.5, Hax 1.8 cm MIT Haystack, HAX > 0.5 cm JPL Goldstone > 0.2 cm

Haystack Measurements
Iridium 33 Debris Haystack data Cumulative Number 1998 Model If used 1978 model, would have had better agreement. 1 sigma uncertainty on Haystack data shown Catalog data Debris Characteristic Length, meters

Haystack and Goldstone Measurements
Cosmos 2251Debris Goldstone data Cumulative Number Haystack data 1998 Model If used 1978 model, would have had better agreement. 1 sigma uncertainty on Haystack and Goldstone data shown Catalog data Debris Characteristic Length, meters

Orbital Debris Activities over the last 30 years
Obtained large amounts of new data Developed more complex models Operational support for NASA and other agencies Spacecraft design support Established international organization (IADC) UN acceptance of Debris Mitigation Guidelines Conclusion reached that current debris environment exceeds a “critical density” Current National Space Policy expands debris activities Over the last 30 years, the NASA program has matured significantly, with measurements of the space environment for debris sizes from microns to centimeters. Their models include new debris sources (NaK, aluminum oxide, paint), they provide operation support for NASA’s manned missions as well as some DoD operations. The program test various spacecraft shielding designs with hypervelocity test facilities. NASA was key in establishing the IADC (Inter Agency Space Debris Coordination Committee), and international organization. Through the IADC, the UN has accepted debris mitigation guidelines that were developed by NASA. IADC members have concluded we have likely reached a threshold where some debris must returned from orbit in prevent future debris growth. As a result, the current Nation Space Policy directs NASA and DoD to come up with techniques to remove on-orbit debris.

Orbital Debris Mitigation Strategy: Prevent Explosions in Orbit
Deplete the on-board energy source in spacecraft and upper stage rockets at end of operations Unused fuel Battery charge Began in US in 1981 with Delta 2nd stage Began in Europe after 1986 as a result of Ariane 3d stage explosion USSR, Japan, China discussions followed Deplete internal S/C energy sources

First Explosion in Orbit: Ablestar upper stage, June 29, 1961
Debris count when from 54…increased by nearly 300 in Note called “Omicron” explosion. Wasn’t until after1978 that such events were labled by what acutally exploded. Even desirers and builders of upper stage rockets were unaware their rockets were exploding in orbit. 2011: 50 yrs after explosion 1965: 3 yrs after explosion John Gabbard’s original plot

Orbital Debris Mitigation Strategy: Reduce Collision Frequency
Reduce orbital energy to decrease orbital decay time to less than 25 years Plan final propulsion burn to drop perigee Drag augmentation devices Dilute population density in popular orbits with lower density graveyard orbits Reduces collision rate Short-term solution May cause long-term problem Much more energy in collisions vs explosions…”25-yr rule initiated by NASA in 1995.

Critical Density Question asked by various researchers: At what threshold will the number of objects in Earth Orbit reach a “tipping point” so that debris is generated from collisions at a rate faster than natural forces can remove the debris? All have concluded using the most recent models that we have already exceeded that threshold. Assume that the intact population (payloads + rocket bodies) is held constant. What will the debris environment do?

Source vs. Sink Critical Density Analysis
Data from 1985 USAF P-78 Anti-Satellite & Transit laboratory hypervelocity tests Defined two levels of Critical Density for constant number of intact objects. -Unstable threshold: Number of fragments increases with time until an equilibrium is reached -Runaway threshold: Number of fragments continue to increase for as long as the population density of intact objects is maintained

P-78 Breakup Fragments January, 1986: 68 Fragments larger than 1/1250 the mass of P-78 (243 cataloged fragments) 10-8 10-9 10-10 10-11 Source: Total of 90 fragments per collision with mass large enough to catastrophically break up another intact object Sink: Speed these objects decay from orbit Spatial Density, No./km3 Anti-Satellite test conducted by US Sept 13, kg P-78 (Solwind) hit by 14 kg projectile at 7 km/sec Transit/OSCAR: 35 km hit by 150 g at 6km At least 20 fragments concluded to be too small to catalog, but have mass > 1/1250 the mass of P-78. Altitude, km

P-78 Breakup Fragments January, 1987: 66 Fragments larger than 1/1250 the mass of P-78 (189 cataloged fragments) 10-8 10-9 10-10 10-11 Spatial Density, No./km3 Altitude, km

P-78 Breakup Fragments January, 1998: 8 Fragments larger than 1/1250 the mass of P-78 (8 cataloged fragments) 10-8 10-9 10-10 10-11 Results can be scaled to other altitudes. Example: If P-78 test had occurred at 950 km, each frame would represent 100 years. This frame would represent the year 3285 with the concentration of fragments near 850 km. Spatial Density, No./km3 These results were scaled for varous altitudes. Example: 950 is 100 times slower to decay. Altitude, km

Intact Rocket Bodies and Payloads: Regions of Instability in 1999
10-7 10-8 10-9 10-10 Unstable Runaway Runaway 1999 Catalog of intact objects Spatial Density, Number/km3 Such a determination was made in 2000 using the 1999 catalogue. Two regions were concluded to be in a Runaway condition, and most of LEO was concluded to be Unstable. The condition between 700 km and 1000 km is what we are beginning to observe today, with collisions between catalogued objects becoming more frequent. However the Runaway just below 1500 km is very slow since most of the satellites at this altitude are smaller and less massive…and therefore not of immediate concern. However, without adherence to current mitigation guidelines, these region will expand, and the rate of collision will increase. 4 past collisions: 1991-Cosmos 1934/Cosmos 926 debris; 1996: Cerise-Ariane Debris; 2005 Thor-Burner rocket-China fragment; 2009 Iridium 33-Cosmos 2251. Altitude, Km Altitude, Km

Fragment Population between 900 and 1000 km
Assumes maintaining current intact population and eliminating explosions 2000 1000 Intact population =400 Initial fragments =200 Number of fragments capable of a catastrophic collision with an intact object Initially, intact-intact collision dominate. Later, intact-fragment collision provide positive feed-back, increasing collision rate. Fragment population increases for as long as intact population is 400. The region between 900 km and 1000 km dominates this collision process. Shown is a model predictions of the number of large fragments in orbit as a result of collisions within this band alone. Each increase is the result of a collision, followed by a slow decay in the number from atmospheric drag. However, more fragments are generated than removed by drag, and for this region, the number of fragments will continue to increase for infinity….as long as there are 400 intact objects within this altitude range….assuming future generations will be short-sighted enough to replace each object after each collision. This condition has been defined as a “Runaway” Environment. Time, years

Fragment Population between 900 and 1000 km
Assumes maintaining current intact population and eliminating explosions Runaway 2000 1000 Intact population =400 initial fragments =200 Number of fragments capable of a catastrophic collision with an intact object Unstable At lower altitudes atmospheric drag would remove fragments quickly enough that an equilibrium can be eventually reached. If fewer than 400 objects are maintained within this altitude range, the fragment population would eventually level-off, but at some higher level than now exists. This condition is referred to as an “Unstable” Environment. If the population is reduced by a sufficient number, the number of fragments would not increase, or even might decrease with time. This is referred to as a “Stable” Environment. By looking at the rate that fragments are generated and removed from orbit by atmospheric drag, one can determine the stability condition for objects in LEO. Stable Time, years

NASA’s LEO-to-GEO Environment Debris (LEGEND) Model
Area/Mass distribution from experimental data -Orbital decay of fragments -Hypervelocity tests Experiment-based breakup models Includes non-fragmentation sources Historical and future traffic models Monte Carlo approach to collisions & explosions Predicts future environment under various assumed conditions NASA’s latest long-term model

Thor-Burner upper stage
LEGEND Predicted Collisions in LEO Compared to observed collisions (Average of 100 MC runs) Historical Business as Usual Post-Mission Disposal No Future Launches Data (excludes Cerise) Past collisions: 1991-Cosmos 1934/Cosmos 926 debris; : Cerise-Ariane Debris; Thor-Burner rocket-China fragment; Iridium 33-Cosmos 2251. Iridium 33 & Cosmos 2251 Thor-Burner upper stage Cosmos 1934

Intacts + mission related
LEGEND Predicted Objects Between 900km and 1000 km Assuming no launches after 2005 Average of 100 MC runs 200 yr run shows do sign of environment stabilizing. Includes all cataloged fragments, not just those with mass sufficient to cause catastrophic collision Collision Fragments Intacts + mission related

Probability of collision x mass
LEGEND Predicted Objects in LEO With Post Mission Disposal (PMD) and Active Debris Removal (ADR) Average of 100 MC runs Removal Criteria: Probability of collision x mass Removal criteria: Ri(t) = Pi(t) mi Requires at least 5 ADR/yr for 100 years. Another study could from 2 to 4 times that number due to climate change and lower solar cycles.

Active Collision Avoidance as a Debris Mitigation Technique
Collision avoidance has limitations -Existing debris cannot maneuver -Operational spacecraft may chose not to maneuver, given the uncertainty in collision predictions May be part of mitigation strategy -May reduce the number of required removals -Optimized to only prevent collisions of most likely and massive debris sources -Current population contains too few spacecraft with sufficient collision avoidance capability to be of benefit It is easy to think of collision avoidance maneuver from “ground controllers” as being the answer; however, only a small fraction of intact objects are active and have maneuver capabilities. In addition, because collision predictions are not accurate, some spacecraft choose to save their fuel, and not maneuver. But even if all spacecraft who could maneuver did maneuver, it would have only minor effects on the future environment.

Orbital Debris Remediation
2010 National Space Policy: Pursue research and development of technologies and techniques …. to mitigate and remove on-orbit debris… Search for the most energy efficient technique to remove on-orbit debris Energy to maneuver in orbit is the major cost driver.

Applying Past Technology for Remediation
NASA study concludes removing between 5 and 10 massive objects per year (for 100 years) is sufficient UK study predicts needing twice the NASA number Estimate 15% to 30% increase in cost to international space activities using past technology and robotics The only way to reduce or eliminate these regions of instability is to reduce the number of intact objects in orbit. NASA studies have concluded that if between 5 and 10 selective objects are removed per year (depending on the amount of adherence to mitigation guideline)….for the next 100 years… then the LEO would become stabilized. Since the current world launch rate is about 75 launcher per year and if only 5 or 10 additional launches per year are required to remove the 5 or 10 objects, then the cost to perform this remedial action would only increase the cost to space programs by about 15%. The current Space Policy asks NASA and DoD to develop techniques to remove debris, so as a result of new technologies, there may be techniques to that could remove debris more cheaply.

Applying Advanced Technology: Debris Sweeper
To eliminate debris that happens to pass within 20 km of a spot in Earth orbit -Nature’s technique: A 40 km diameter natural Earth moon to sweep debris -Technology: Space or ground based laser to reduce the orbital kinetic energy, increasing debris re-entry rate Negative issues: Lasers could be an unintended hazard to other spacecraft Reentry risk on the ground Fundamentally, there are two techniques to remove debris. The “sweeper” concept is based on the way nature would remove smaller objects from orbit. If the Earth had a natural moon that was about 40 km in diameter, in an orbit that passed through all of LEO, and has sufficient gravity to capture all the ejecta after each collision, then it could clear LEO in a few years of all debris. A large foam ball has been proposed to do the same thing, but that would require placing too much mass into orbit….plus it would also remove operational satellites. Using lasers to ‘slow down’ debris that passes within 20 km might become an option that is selective about which objects it captures. A ‘debris retriever’ matches the orbit of debris it expects to remove. It may be possible for a single grabber to retrieve several objects before it reenters….especially if the grabber is a tether. However, tethers have their own debris problems in that they can easily be severed by small debris.

Future Sources of Collision Generated Debris
= 180, max collision prob. Only 5 inclination regions (plus or minus 1 deg) included in top 500 Most significant: Altitudes between 600 km and 1000 km Inclinations near 82 deg and 98 deg

Applying Advanced Technology: Debris Collector
Spacecraft retrieves several intact objects per launch with similar inclinations Engineering issue of capturing spinning satellite Requires energy-efficient technique to change orbit: 100’s of km altitude change, 1 or 2 degrees inclination change over a period of years in orbit -Chemical propulsion: least efficient -Tethers: transfer energy using Earth’s magnetic field -Ion propulsion: solar energy Transfer of risk in space to risk on the ground .A ‘debris retriever’ matches the orbit of debris it expects to remove. It may be possible for a single grabber to retrieve several objects before it reenters….especially if the grabber is a tether. However, tethers have their own debris problems in that they can easily be severed by small debris.

Geosynchronous orbit Sun and Moon redefines “zero inclination”
A region of space that is both important, and growing rapidly, is geosynchronous orbit, at 36,000 km above the Earth’s surface. Because we place objects in GEO with a near circular orbit and zero inclination…just like the solar system… one might think that the debris environment in GEO would be stable. GEO debris is currently much less of a hazard than in LEO …. partly for the low inclination, and partly because the larger amount of space around the Earth at GEO altitude. Energy of orbit is exchanged with sun and moon to scatter the debris, increasing collision velocity. Collision in graveyard orbit would eventually scatter debris back through GEO Inclination increases to 15o without station keeping Long-term collision risk small Mitigation strategy: Graveyard orbit above GEO Long-term problem: Collisions in graveyard orbit

Geosynchronous Orbit: An Energy Efficient Long-term Solution
North Pole 0o inclination: North-South Station keeping required Abandoned S/C average collision velocity = 500 m/sec 7.3o Inclination, 0o RAAN: No North-South station keeping (10% fuel usage) Collision velocity are only a few meter/sec Ground track: “figure 8” Debris eventually collects at the stable points Ecliptic Plane inclined 23.5 deg. GEO Stable Plane inclined 7.3 deg. Equatorial Plane Earth At GEO altitudes, lunar & solar perturbations changes the plane of precession of the RAAN to one that is inclined 7.3 deg to the equatorial plane. GEO objects orbited in this “stable plane” maintain a near zero inclination relative to the plane. At GEO altitude, lunar & solar perturbations change the plane of precession for the Right Ascension of the Ascending Node from the Earth’s equatorial plane to a plane that in inclined 7.3 degree to the equator. The result is as if objects were placed in an 7.3 deg inclination near the Earth’s surface. Without North-South station keeping, the orbital inclination of objects placed in GEO changes over a 53 years cycle, going as high as 2 x 7.3 = 14.6 degrees. This results in average long-term average collision velocities of 500 meter/sec between abandoned satellites….not as bad as LEO, but not as good as it might be. Possible solution: Do what natures is trying to do-- Move the mass of objects in geosynchronous orbit to the “stable plane” via collisions. The effect of placing objects in the stable plane rather than equatorial plane would be that there would be no North-South station keeping for GEO satellites. North-South station keeping fuel is the major station-keeping fuel required for active satellites…a definite advantage for the spacecraft operator. The downside is for the ground customer: He would be required to have an antenna that tracked the small north-south motion that the GEO object would appear to follow from the ground. This may not be much of a problem for centralized business users, where the extra cost for the few receivers might be less than the savings from requiring less station-keeping fuel, or a longer-life satellite. However, for the larger number of individual homeowners, this might represent a significant increase in their costs.

Industrialization of Space: A Solution?
Mass and Energy in orbit: A natural resource? Minimum energy required to store mass in one location in GEO compared to LEO LEO would require multi-storage locations Trade-off between cost-benefit of recycling vs cost of returning objects to Earth Man has expended a lot of energy placing mass in oribt….it may someday become a “natural resouse” that would be more cost-effect to recycle.

Conclusions The lack of a long-term energy management strategy for objects placed in Earth orbit has created an orbital debris problem A solution will depend on both a change in past operations and development of new energy efficient techniques to maneuver in Earth orbit Large objects can and do make a lot of small objects. Colliding at 10 km/sec in LEO, they cause a lot of damage by these small objects. One must either get rid of the large objects, or make sure the large objects stay intact; however it is nearly impossible to keep spacecraft intact with the high inclination orbits that are necessary for certain operations. Without an effective strategy to manage the environment, the cost of space activities will increase….either from adding extra shielding to all spacecraft, or from removing massive objects from orbit.

Pre-Space Age Knowledge of Meteoroids
Potential Hazard to Spacecraft Earth-based observations -Comets -Asteroids -Meteors -Meteorites -Zodiacal Light Potential hazard for spacecraft -Measured Flux -Uncertainty in size -Flight experiments required -Hazard proved to be manageable Pre-space observations of comets, etc. lead to most NASA centers in the early 60’s to have a meteoroid research group in order to protect man in space. Initially, there was a large uncertain in the size distribution and velocity of meteoroids. Spacecraft and ground measurements resolved that uncertain, much more accurately defining the environment. However, this environment resulted in very little design changes to spacecraft (some extra shielding on the Apollo LEM, and lunar space suite…a meteoroid shield on Skylab, which fell off during launch), so nearly all that research ended around 1970. 1966 Leonid meteor shower

1978 JGR Predicted Collision Rate Compared to1991 to 2009 Observed Collision Rate
Observed collisions between catalogued objects: Cosmos 1934, Cerise, Thor-Burner, Iridium Catastrophic collision The actual collision rate observed between catalogued objects has been higher than predicted by the 320/yr curve….mostly because the actual sizes of spacecraft were larger than the RCS distribution used indicted. However, only 1 of the 4 observed collisions were catastrophic, producing a large number of catalogued objects. The Cerise collision only severed a boom; however, the 1st and 3d collisions may have produced a significant small debris population. Current NASA models are now predicting that about half of the collisions between catalogued objects would be catastrophic, but all collisions that impact the body of an intact object would likely produce a significant small debris population.

1978 JGR Predicted Debris Flux at 800 km Assumed no launches after 2020
The 78 paper also predicted what the future debris flux would look like relative to the meteoroid flux, assuming there were no other sources of small debris other than fragments from future collisions. The results not only concluded that the hazard would exceed the meteoroid hazard by 1990, even if all launch activity stopped after the year 2020, the environment would still increase slightly due to collision fragments being generated faster than they were removed by atmospheric drag. Added to the plot is the approximate diameter of the impacting particle. In general, the 1 mm to 1 cm size range has been the range that most spacecraft required some shielding to achieve their desired reliability, although debris and meteoroids as small as 0.1mm can easily sever a tether or a wire in an unshielded wiring bundle. Even smaller impacts may create a plasma that can create other electrical problems. During the 80’s NASA developed a debris measurements program that sampled the small debris environment using X-band radar, large telescopes, and examination of recovered spacecraft surfaces, and quickly found that there were many more sources of small debris….. 0.1mm 1mm cm

Model prediction for 2007 Based on measurements as of 2000 NASA used these measurements to refine their model predictions. Shown in green is the prediction of NASA’s ORDEM2000 model (based on up to the year 2000 data) of what the 2007 environment would look like at 800 km. While it pretty much agrees with the 78 prediction for sizes larger than 1 cm, for smaller sizes the flux is much higher. This is the result of many more debris sources being identified, such as paint coming off spacecraft, Al2O3 from solid rocket firing in orbit, NaK from USSR ROSATS, and on-orbit explosion….all generating these smaller particles faster than they can be removed from orbit by atmospheric drag. 0.1mm 1mm cm

Model prediction for 2007 Based on measurements as of 2000 Measured by Haystack in 2007 After 2007 China Asat-test However, ORDEM2000 already needs to be updated as a result of events in orbit. Shown in red is the results of Haystack measurements after the 2007 China Asat test. These flux curves indicate that all spacecraft will have visible impact craters on their surfaces….some that affect spacecraft operations and design. 0.1mm 1mm cm

Orbital Debris: An Energy Management Problem

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