Note that that's in the sense of angular separation, as viewed from the ground. They're physically hundreds of kilometers apart.
edit: (Geostationary orbits are ~42,000 km from the Earth center-of-mass; each degree of angle is an arc of ~700 km).
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.
It still is a 1/1,000,000,000 chance, maybe less.
But some debris (in particular slower pieces) will probably oscillate around the geostationary orbit giving it countless chances of hitting other satellites.
Has someone modelled this for example in Kerbal space program?
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.
[0] https://en.m.wikipedia.org/wiki/Kessler_syndrome [1] https://en.m.wikipedia.org/wiki/Neutron_flux
Almost all of the debris will have orbits which intersect their orbit of origin.
Source?
$ units
You have: 25m2 / 2tau(700km)^2
You want: /billion
* 0.0040600751
/ 246.30086
I assumed basic reading comprehension, my bad.
Also, I don't play by your rules but keep trying.
Personally I used basic high school geometry knowledge of "what's the area of a sphere", and you could also have just asked WolframAlpha, which also predates LLMs.
Might be a valuable lesson in "reading the question carefully" for them, though, as the scenario was: "That’s pretty close when your neighbor just exploded", which is why orbital mechanics can be disregarded in this instance.