It is pointless to try to avoid two satellites coming within 10 metres of each other, if your tracking process cannot measure their positions better than to 100 metres (the green trace in my figure).
This seems straightforwardly false. If you can keep them from approaching within 100 metres of each other, then that necessarily also keeps them from approaching within 10 metres of each other.
It does, but very wastefully. Almost all of the avoidance manoeuvres you make will be unnecessary, and some will even cause a collision, but you will not know which ones. Further modelling (that I think would be belabouring the point to do) would allow a plot of how a decision rule for manoeuvring reduces the probability of collisions.
Let fm be the frequency of collisions given the tracking precision and some rule for manoeuvres. Let f0 be the frequency of collisions without manoeuvres. Define effectiveness to be 1−fmf0.
I would expect effectiveness to approach 1 for perfect tracking (and a sensible decision rule) and decline towards 0 as the precision gets worse.
Are you envisaging a system with 100m tracking resolution that aims to make satellites miss by exactly 10m if they appear to be on a collision course? Sure, some of those maneuvers will cause collisions. Which is why you make them all miss by 100m (or more as a safety margin) instead. This ensures, as a side effect, that they also avoid coming within 10m of each other.
This seems straightforwardly false. If you can keep them from approaching within 100 metres of each other, then that necessarily also keeps them from approaching within 10 metres of each other.
It does, but very wastefully. Almost all of the avoidance manoeuvres you make will be unnecessary, and some will even cause a collision, but you will not know which ones. Further modelling (that I think would be belabouring the point to do) would allow a plot of how a decision rule for manoeuvring reduces the probability of collisions.
Let fm be the frequency of collisions given the tracking precision and some rule for manoeuvres. Let f0 be the frequency of collisions without manoeuvres. Define effectiveness to be 1−fmf0.
I would expect effectiveness to approach 1 for perfect tracking (and a sensible decision rule) and decline towards 0 as the precision gets worse.
Are you envisaging a system with 100m tracking resolution that aims to make satellites miss by exactly 10m if they appear to be on a collision course? Sure, some of those maneuvers will cause collisions. Which is why you make them all miss by 100m (or more as a safety margin) instead. This ensures, as a side effect, that they also avoid coming within 10m of each other.