## Thursday, February 12, 2009

### U.S., Russian sattellites crash

Soyuz-Apollo, collider edition

It's been the first time when full-fledged satellites collided. Both were communication satellites - one ton (Kozmos 2251) against half a ton (Iridium LLC, both above Siberia). The Russian vehicle won, turning Iridium into smoke, but its own fate wasn't much better. ;-)

The debris may be a threat to ISS and other objects. When they determine the coordinates of the dangerous pieces, ISS may get ready for a slalom!
So far, the density of objects in the orbit has been low enough that no one has bothered to write down any traffic rules for the satellites. I am afraid that this will become necessary in the future.

An order-of-magnitude estimate follows. Feel free to fix it if it is unrealistic.

If you allow their average velocity differences to be 15,000 km/h (the actual relative speed in this case was 40,000 km/h), it takes one tenth of a day for a satellite to probe all longitudes. If you assume the cross section to be 3 squared meters and divide it by the total cross section of the space for orbits - say 10,000 km (latitude) times 1,000 km (vertical) which is 10^{13} squared meters, you deal with 3 x 10^{-13} of the space every tenth of a day.

Because there are 3,000 satellites or so, we deal with 5 million pairs or so. Multiply it by 3 x 10^{-13} to get 1.5 x 10^{-6} per tenth of a day or 50% per century (and I could have added the factor of two or four somewhere, too). So it shouldn't be too shocking that we have already seen a collision. ;-) The space people should celebrate that no one has been killed so far and work on the traffic rules and synchronization.

What I have in mind is a simple NASA program that will predict the trajectories of those 3,000 objects plus a few thousand of annoying pieces for a few orbits in advance and will recommend satellites to change the velocity so that they will be a few meters away from the other object at the time of the expected collision. ;-)