Question

If identical spacecraft were orbiting Mars and Earth at identical radii (distances), which spacecraft would be moving faster

Answer 1

a = G M / R^2 gravitational acceleration

a = ω^2 R acceleration due to centripetal force

a2 / a1 = ω2^2 / ω1^2 the one with the greatest gravitational acceleration would require the greatest speed

a2 / a1 = M2 / M1 using the first equation - since M is greater for earth - then the spacecraft for earth would be moving faster - using the term radii as distance from center

Note that the acceleration of an object at the surface for Mars is less that on-half of that of earth - so at zero height above the surface the spacecraft on earth would still be moving faster