[ben_w]

Yes there's no air resistance, but also most of the fragments aren't going your way.

If you have a 25 m^2 cross section in the direction of the explosion, at that distance you have a roughly 1 in 246 billion chance of any given bit of debris hitting you.

[anjel]

It might not place neighbors at appreciable risk but wouldn't debris still prevent replacing the failed satellite with another one at the same precious original address?

[ethbr1]

Wouldn't debris at the same address (after some time) therefore have zero relative motion?

[user32489318]

No, because the debris = tiny pieces of aluminum, will be pushed around by solar radiation. Also, there’re tiny meteorites, and other pieces of debris colliding with it, which adds energy to the system, if you like. TLEs are not maintained for small debris, so you can’t really predict conclusively. But my hunch is that eventually, the orbit will become a bit more parabolic, precession of which could put it into a trajectory of a S/C and cause a collision.

[verzali]

Things in geo orbit aren't perfectly stable, since the Earth's gravitational field is not perfectly uniform. Without active station keeping things tend to gather at two particular longitudes over the equator. So eventually that debris will probably end up at those points.

[throw4950sh06]

What is the chance of getting hit by further broken pieces of that satellite and other satellites?

When calculating risk, you have to take into account how many are there and what is the chance that any will be hit. Then you have to calculate what's the chance this will happen again, etc - and only then you can calculate the risk to your own satellite.

It's true that the chance of getting hit by one broken satellite is small. But that assumes there are exactly 2 things on the orbit.

[ethbr1]

Aka Kessler syndrome [0] or neutron flux / cross-section (and associated equations, if you want to model it that way) [1].

[0] https://en.m.wikipedia.org/wiki/Kessler_syndrome [1] https://en.m.wikipedia.org/wiki/Neutron_flux

[throw4950sh06]

That's if the risk comes out at 100%, but there's some space below that.

[randmeerkat]

> If you have a 25 m^2 cross section in the direction of the explosion, at that distance you have a roughly 1 in 246 billion chance of any given bit of debris hitting you.

Source?

[a1369209993]

  $ units
  You have: 25m2 / 2tau(700km)^2
  You want: /billion
    * 0.0040600751
    / 246.30086