A geosynchronous orbit is a circular orbit such that the period of the orbiting

Question

A geosynchronous orbit is a circular orbit such that the period of the orbiting object exactly matches the rotational period of the planet below. In such a case, the orbiting object would appear to remain stationary above a fixed point on the planet's surface.
Suppose that Captain Omega of the Imperial Space Patrol wishes to place a spy satellite in geosynchronous orbit above the mysterious Planet X, which has a mass of 6.20 x1024 kg, and a rotational period of 26.6 hours. (a) What should be the radius of the satellite's orbit? (b) What would be the orbital speed of the satellite?

Explanation / Answer

a)

R = (sqrt(GM)*T/(2*3.14))^(2/3)

= (sqrt(6.67*10^-11*7*10^24)*27.8*3600/(2*3.14))^(2/3)

= 4.91*10^7 m <------answer

b)

orbital speed = 2*3.14*4.91*10^7/(27.8*3600) = 3081.02 m/s <-----answer

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