with larger objects. In LEO, the probability of collision with debris in each size range is believed typically to increase by more than a factor of 100 for every factor of 10 decrease in size over most of the medium to small debris size ranges. (For example, LEO spacecraft are probably at least 100 times more likely to be struck by 1-mm-diameter objects than by 1-cm-diameter objects.) In the orbital altitude most densely populated with debris (between 900 and 1,000 km), models suggest that a typical spacecraft (10-square-meter cross-sectional area) has only about one chance in 1,000 of colliding with a large debris object over the spacecraft's 10-year functional lifetime. The chance of colliding with 1 to 10 cm debris over the same period, however, is estimated to be about 1 in 100, a collision with 1 mm to 1 cm diameter debris is believed to be likely, and frequent collisions with debris smaller than 1 mm will occur.

The chance of colliding with debris varies greatly with orbital altitude and, to a lesser extent, with orbital inclination. Based on the best available data, the probability of colliding with large or medium-sized debris in LEO is at least 100 times greater than the average probability in GEO and is likely to be 1,000 times greater than the probability in less used orbital regions. Even within LEO, the collision probability varies greatly with altitude; for example, the chance of collision with medium-sized or large debris is probably higher by a factor of 50 at 900 km altitude than at 250 km. Measurements of small debris are so limited that it is unclear whether this population follows a similar altitude distribution.

The damage that a collision with debris can cause to a spacecraft depends on the kinetic energy released in the collision, the design of the spacecraft, and the geometry of the collision. Due to the typically high relative velocities of the objects involved, collisions in orbit can be highly energetic. For example, a 1-kg object involved in a (typical for LEO) 10 km/s collision will impact with the same relative kinetic energy (about 100 MJ) as a fully loaded 35,000-kg truck moving at 190 km/h. If the kinetic energy released in a collision is large enough compared to the mass of the objects involved, a catastrophic breakup will occur. In such a breakup, numerous fragments capable of causing further catastrophic breakups could be produced. A 1-kg object impacting at 10 km/s, for example, is probably capable of catastrophically breaking up a 1,000-kg spacecraft if it strikes a high-density element in the spacecraft. In such a breakup, numerous fragments larger than 1 kg would be created.

Even if a collision does not fragment a spacecraft, the impact may generate a variety of other damage modes (e.g., spallation, rupturing, leakage, and deformation) possibly degrading spacecraft performance or causing spacecraft failure. In LEO, debris as small as a few millimeters in diameter can puncture unprotected fuel lines and damage other sensitive components, and debris smaller than 1 mm in diameter can erode ther-



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