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There is always a benefit to entering a planet's atmosphere with matching rotation. In the case of Earth, the difference is a rather huge 920m/s effective airspeed between reentering prograde or retrograde. With Mars the effect is smaller but still strong, at some 485m/s difference. Even on the Moon it makes a difference, but so small as to be almost ignored....


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Space craft will tend to enter orbit counter clockwise as viewed from the northern hemisphere. This is due to the fact that most objects in the solar system orbit and rotate this way with the exceptions of Venus, Uranus and a few asteroids. Moving in the direction of rotation will therefore reduce the required velocity loss where as entering orbit clockwise ...


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See also answers to How much does the rotation of the Earth affect re-entry and could we go against it? When things land on Mars what fraction of their velocity do they remove propulsively? Difference in atmospheric entry for Earth and Mars Any attempted Mars landings without an ablative-type heat shield? (asked just now) Answers to What aspects of reentry ...


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Let's try to work out what a slow reentry would be. A spacecraft on orbit balances the Earth's gravity with the centrifugal force in the oribital reference frame to keep altitude. This orbital lift is proportional to $v^2/r$, where $v$ is the spacecraft's speed r is the radius of the orbit. Once the spacecraft slows down below the orbital speed it will need ...


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