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Supposing you wanted to launch a spaceship from the surface of Mars into orbit around Mars. It would stay in orbit for up to one week while you prepared a second rocket that would dock with it to transfer fuel. After transferring fuel, the second rocket would land, and the first rocket would fly away from Mars.

In the absence of atmosphere, to have a circular orbit, you just need gravity = velocity^2/orbit_radius. So, in that case, radiuses all the way to the ground are valid solutions mathematically.

So, this questions probably comes down to atmospheric drag as the limiting factor.

  • The Martian atmosphere is like 2% as dense as Earth's at ground level, so one would expect that the lowest possible orbital height is much less than that of Earth.

  • Mars' gravity is only 3.71m/s^2 at ground level. So with less gravity the atmosphere spreads out more vertically, which would tend to increase the minimum required orbital height.

What is the lowest viable circular orbit around Mars that can last at least one week?

"Last one week" means that the ship doesn't fall to the ground, but its altitude may decrease a bit.

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