Answer to Question #11506 in Mechanics | Relativity for Nero
a = GM/R²,
where R is the radius from the center of the Mars, M is the mass of the Mars and G is the Gravitational constant and also use the centripetal force equation:
a = W²R,
where W is the radians / second velocity and R is the radius from the center of the Mars. Using 1 revolution in 1.96 hours, you can compute the W as 2π/(3600*1.96).
Combining these equations and cancelling the a (acceleration) gives
GM/R² = W²R.
Solving for R we get
R³ = GM/W² ==> R = (CM/W²)^(1/3).
If you plug in all the numbers you will end up with a radius R which can then be subtracted from the Mars's radius to obtain the height above the Mars's surface.
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