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Assume CR3BP (Circular Restricted 3-Body Problem) where a satellite occupies the Earth-Sun L1 point. The satellite dies, stops station-keeping, experiences a small perturbation (minimal effect on Jacobi), then decays for some arbitrary time t. What is the delta-v budget and travel time for Earth to rescue the satellite to L4? This can be split into two cases: sunward decay, and earthward decay.

(Most of the literature I've found discusses Earth-Lagrange transfers, not Lagrange-Lagrange, let alone after decay. I suspect the only solution is to simulate, sampling random t, but there may be more analytical insight I don't know.)

Curtis Klein
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  • I just wrote an answer to how to recover back to the original orbit then deleted it when I re-read the question. This is much more interesting! – uhoh Mar 11 '21 at 06:49
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    That could be a weak solution, just take the long route: decay->L1->LEO->L4. An upper bound on the problem, but I was hoping for the direct route. I didn't ask for the most minimal delta-v solution, since I'm sure chaos theorists could optimise the direct route and add a century or two to the travel time, but I would like a <10yr travel time. – Curtis Klein Mar 11 '21 at 17:35

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