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The solver of the Lambert's problem gives me a hyperbolic velocity to move to some position on orbit. But the spacecraft is moving on orbit and changing the velocity takes some time. So, when I achieve the needed velocity I will be in the another position and given orbit will lead me to the wrong place.

So, how to correctly change the velocity to achieve the predicted orbit?

I know, that you can turn on engine in half time of needed impulse before needed point and turn off in half time after. It works. But how to find this needed point? For i.e. I can assume that I need to turn on engine after 5s from current moment. But half of impulse time can be longer than 5s. So, I need to select farer point. But it will need different orbit with different transition impulse and current calculations became irrelevant.

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  • $\begingroup$ So your Lambert solver only works for impulse maneuvers? It would be better if you provided more information on what solver you are using. For finite duration burns there may not be simple solutions and you may need to implement some kind of trial-and-error. I think there are may be some related questions and answers here somewhere. $\endgroup$
    – uhoh
    Oct 26, 2021 at 13:31
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    $\begingroup$ From what I can remember, the Space Shuttle Orbiter's onboard computer used to solve Lambert burns iteratively. Since all real-world burns take time, I think that the actual TIG was planned such that the actual burn duration bracketed the ideal TIG, with half the burn occurring before said ideal TIG and half after... $\endgroup$
    – Digger
    Oct 26, 2021 at 16:36
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    $\begingroup$ Half time before half after is a good enough estimate for short burns. for longer burns you need to start to do more complicated stuff, because TWR is higher at the end. For really long burns, you will want to split them over multiple burns. I don't know any better method to calculate that than to iteratively search for a good solution with the ideal instant impulse as starting point of the search. $\endgroup$
    – Polygnome
    Apr 13, 2022 at 20:56

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