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I'm starting to investigate the danger of orbital debris on the ISS (international space station). One could assume that due to the orbital velocity vector, that any debris that the ISS encounter, would be more frequent and more dangerous for debris coming from a certain solid angle (Ω).

Q: What is the debris impact bias for ISS?

I suspect this is a somewhat complicated question that would involve many parts, such as:

  • What is the general statistical (and observed) debris velocity vector bias (relative earth)?

  • What is the most dangerous solid angle for debris attack (for the ISS)?

  • Does the debris velocity distribution field, depend on the size of the debris? (How so?)

  • The original Kessler paper (1978)


References:

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I guess I'm more or less the right person to answer this.

The orbital debris threat to ISS is heavily concentrated into two lobes in the local horizontal plane, somewhere between 20 and 30 degrees to the left and right of the velocity vector.

NASA operates an orbital debris threat model called ORDEM, which provides data on the environment in terms of velocity, directionality, particle size, and particle density.

Below is a sample debris flux plot for a vehicle in an ISS-ish orbit extracted from the page linked above. The center of the plot is directly ahead along the earth-relative velocity vector. The left and right edges of the plot correspond to directly behind the vehicle. The two threat lobes I described are plainly visible as the red patches to the left and right of the center of the plot. Orbital debris flux plot

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    $\begingroup$ I was hoping you'd weigh in on this. $\endgroup$ Sep 15, 2023 at 14:05
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    $\begingroup$ @tristan Very nice, but it seems like the plot it is L-R symmetric, so how does that account for the "against-rotational direction" debris (launch) bias? I guess I'm reading it wrong. If so how to see the launch directional bias? $\endgroup$
    – not2qubit
    Sep 18, 2023 at 11:57
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    $\begingroup$ @not2qubit For every intersection between orbital planes, you cross it twice per orbit, once where the other plane meets you on the left, and once where it meets you on the right. The only place you really run into any asymmetry is some special cases where you and/or the debris you're intersecting are on pretty elliptical orbits. For the ISS orbit case, that's not really much of a factor. $\endgroup$
    – Tristan
    Sep 18, 2023 at 15:47
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Since there are no other answers (and because I am unable to comment), I will try to give some information.

Most rockets and therefore satellites launch in the direction of Earth's motion, that is, eastward, and so move in that direction. This is because when launching eastward, extra velocity is imparted by the rotation of Earth.

But let's do some rough data analysis. Space-Track states the ISS's orbit has an apoapsis of 422.750 km and a periapsis of 415.008 km. I'll limit the band to debris objects who's apoapsis is within 30 km of that of the ISS (massive caveats apply, orbits are complex).

Out of 56,440 objects tracked by Space-Track, 33,367 are classified as "DEBRIS". Of these, 1,754 debris objects are within the bounds described above.

10 have inclinations >= 0 and < 15

22 have inclinations >= 15 and < 30

93 have inclinations >= 30 and < 45

93 have inclinations >= 45 and < 60

497 have inclination >= 60 and < 75

418 have inclination >= 75 and < 90

580 have inclination >= 90

The more polar an orbit is, the more northerly/southerly their velocity direction will be. From here we can start making estimations about the direction bias of debris in the neighborhood of the ISS.

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