[swyx]

almost guaranteed that this problem is already solved by the rocket scientists out there. hopefully someone on HN can point us to the relevant algorithm. this seems like a closed system at least in newtonian physics that should be easily solvable.

chatgpt pointed me to the Gravity Turn altho it refused to give me a formula for it https://en.wikipedia.org/wiki/Gravity_turn#Deorbit_and_entry

[antoinealb]

This is typically solved using a class of control algorithm called Model Predictive Control which are capable of optimizing for a given cost function (such as using minimal fuel).

Search for "fuel optimal rocket landing algorithm" for good starting points.