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What is the easiest orbit or most most fuel efficient orbit to achieve around Mars? How difficult is it to go from one type of orbit to another? I want to see if it is more fuel efficient and less turbulent for a ship to be dropped fro geosynchronous orbit verses other methods.

related question: Could a blimp shed speed this way entering the atmosphere of Mars?

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    $\begingroup$ Why the heck are you so bound on synchronous orbits? Other than for observation or providing communication to fixed surface structures they are quite inconvenient, especially for 'transit' purposes like arrival from outside the system, reentry, departure etc. Circular and too high to provide Oberth effect benefits, no inclination to give maneuvrability across varied latitudes, no longitudal coverage, generally you have no business putting anything else than a comm or spy sat in a geosynchronous orbit. Absolutely useless in interplanetary travel. $\endgroup$
    – SF.
    Commented Dec 26, 2016 at 1:05
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    $\begingroup$ The easiest / most fuel efficient orbit would be highly eccentric, with periapsis skimming upper Mars atmosphere and apoapsis near its Hill sphere - attainable with the smallest, airbraking-augmented insertion burn. Inclination=plane of ecliptic, although cost of other inclinations would be minimal. $\endgroup$
    – SF.
    Commented Dec 26, 2016 at 1:16

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Space Flight 101: Do your burns as deep in a gravity well as you can to maximize the Oberth effect. That means your capture burn should be done as close to the planet as you dare no matter what your intended final orbit. Note that this very well might be in the outer fringes of the planet's atmosphere. While in theory there might be some scenario where you were approaching slowly and your objective was a high orbit where this isn't the right I do not believe any such cases exist within our solar system.

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You could, but it wouldn't make sense. The most fuel efficient way to enter an areosynchronous (same as geosynchronous, but Mars) would be to do a close pass of Mars to orbit, burning until the apoaerion is at the areosynchronous orbital height, and then burn again to have it be at a true areosynchronous orbital plane.

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