A geosynchronous satellite orbits Mars (mass = 6.42 x 1023 kg) once every Martian day, 88640 s. At what radius does it orbit?

angular speed ω = 2PI / T rad/sec  

ω^2*r = M*G/r^2

r = ³√ M*G/ω^2 = ³√6.42*10^23*6.67*10^-11*88640^2/39.5 = 2.04*10^7 m

Explanation:

no. dot product   =0 when vecs at right angles

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