Kessler Syndrome realistic assessment

[kahlzun]

Hi gang!

I was having a discussion with someone about Kessler syndrome, where someone was asking me about realistic impact velocities for the pieces.

I know that for objects already in orbit, you're not likely to get more than a few dozen ms, but what sort of impact velocity would debris impacting a suborbital flight have?

For the sake of argument, i'm talking about a standard satellite launch, apoapsis at, say, 450km (ISS altitude) just before they start circularising, right when they are at apoapsis.

I realised the difference in velocity would be roughly the same as the final circularisation burn, but i'm having a lot of trouble finding data on final burns.

tl;dr: What is the difference in velocity re: suborbital vs orbital at 450km

[R0cketC0der]

Real rockets generally don't do a circularization burn when launching to LEO, they are just doing a single burn from ground to orbit, only disrupted by staging events.

[Corax]

I know that for objects already in orbit, you're not likely to get more than a few dozen ms, but what sort of impact velocity would debris impacting a suborbital flight have?

Let's see... orbital velocity at 450 km as per your example, assumed circular orbit:

v_o=sqrt(G·M/r) = sqrt(µ/r) where r = r_Earth+450km = 6378km+450km=6828km

v_o=sqrt(398600/6828)=7.64km·s^-1

So in the worst case scenario of a head-on collision, the impact velocity would be twice that, or roughly 15km/s (note: kilometres per second, not metres). For a collision with a vessel that's still suborbital, anything less than that.

[theend3r]

Let's see... orbital velocity at 450 km as per your example, assumed circular orbit:

v_o=sqrt(G·M/r) = sqrt(µ/r) where r = r_Earth+450km = 6378km+450km=6828km

v_o=sqrt(398600/6828)=7.64km·s^-1

So in the worst case scenario of a head-on collision, the impact velocity would be twice that, or roughly 15km/s (note: kilometres per second, not metres). For a collision with a vessel that's still suborbital, anything less than that.

This. And assuming non circular orbits it's 2*10.8121 = 21.6242 km

Edited July 5, 2014 by theend3r

[Kryten]

Hi gang!

I know that for objects already in orbit, you're not likely to get more than a few dozen ms, but what sort of impact velocity would debris impacting a suborbital flight have?

IRL, very few objects are in the sort of low, perfectly equatorial orbits that are common in KSP. Even quite small differences in inclination can add hundreds of m/s to relative velocity.