### RULES OF THUMB AND DATA FOR SPACE DEBRIS STUDIES

#### Space Debris Velocities

Average orbital velocity in Low Earth Orbit (LEO) is 7 km/sec.

The average collisional velocity in LEO is 10 km/sec.

#### Debris Impact Craters

The diameter of an impact crater is typically from 10 to 20 times the diameter of the impactor.

Most hypervelocity impacts produce circular craters, irrespective of the angle at which the impactor strikes the target.

If an impactor penetrates a target, the egress hole will be irregular and considerably larger than the ingress hole.

#### Space Debris Density

Low Earth Orbit, spanning an altitude range of about 200 to 1500 km, has a total volume of around one trillion (1012) cubic kilometres.

As of early 2010 the current orbital space object density (>10cm in size) in LEO is approximately 10-8 per cubic kilometre.

#### Space Debris Collisions

Any impact with debris greater than 1cm in size has serious consequences.

The average debris impact produces approximately 100 pieces with sizes greater than 10 cm.

Catastrophic impact generally occurs when the mass of the impactor is greater than 1/1000 the mass of the target.

The average collision frequency with a piece of space debris may be calculated from the product of the target area, the debris density and the collisional velocity:

• freqcollision (s-1) = Atarget ρdebris vcollision
• the cross sectional target area is in square metres,
• the debris number density is number per cubic metre, and
• the average collisional velocity is in metres per second.

For the International Space Station in the early part of the year 2010, this works out at one collision with a 10 cm piece of debris every ten years.

#### Reentry Hazard

An orbiting spacecraft or piece of orbital space debris in general needs to have an initial mass greater than 1 ton to at least partially survive atmospheric reentry and deposit pieces on the Earth's surface.

In general bodies above 10 ton will definitely partially survive reentry whereas objects less than 1 ton will not.

However, some particular classes of objects of much lower mass do make it (partially) to the Earth's surface. These include objects made of high melting point materials (eg titanium spheres), and objects with a very high area to mass ratio (eg thermal blankets).

The reentry interface altitude, where significant ablation of a reentering orbital object occurs is generally around 75 km.

#### Debris Mass and Size Distributions

The number distribution of a debris population is given by:
• N(>m) = A m-a where m is the object mass, and
• N(>s) = B s-b where s is the object size.
• a,A,b,B are all constants specific to the given population.