# Transfer between circular orbits in up to 5 maneuvers

There are 2 circular orbits with different inclination and RAAN. I have to transfer from a specific point (true anomaly given) of one orbit to a given point of another in 1 month. The period of the orbits is 1 year.

Currently, I'm solving Lambert problem, using 2 maneuvers and it works. However, it may be more optimal to use up to 5 maneuvers. Thats's to say, changing the velocity in flight, not only in the beginning and at the end.

I would appreciate for explanation.

• Period of orbits is 1 year, but your transfer must take 1 month and you're forced to get one specific departure burn point? That's gonna be brutal. If they intersect 90 degrees from the initial burn point it's 3 months worth of free flight until you arrive at the plane of the target orbit. You'll need to accelerate to at least 3x the initial orbital speed just to arrive there on time, completely regardless of all the plane change maneuvers. With this time budget the transfer would resemble change in course in free space with no central body more than orbital mechanics maneuvers. – SF. Jun 13 at 5:19
• In what delta-V comparing to initial and final velocity? Seriously, try it in two burns, inclination 45 degrees for both, RAAN 0 and 180 degrees respectively, true anomaly of first burn 90 degrees. Try that in 2 burns and compare the delta-V to initial/final orbital velocity. zusually most pessimistic scenarios for orbital transfers involve up to 2v of the initial (e.g. turn back 180 degrees in place). I'd be surprised if you manage it under 4v with the 1 month constraint. – SF. Jun 13 at 17:13
• @SF. I have a correct solution using two maneuvers. Do you need the total dV? Well, it's 100km/s. Is it possible to decrease it using more than 2 impulses and the same transfer time? – Leeloo Jun 13 at 17:30
• 100km/s with orbital (initial/final) velocity of...? I don't think more maneuvers would help because the costliest part is accelerating violently towards the target orbital plane in a mad dash (through a fragment of escape trajectory) to reach in a month the same point you'd reach in 3 months by doing nothing. – SF. Jun 13 at 21:55