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 5.90 x1024 kg, and a rotational period of 23.4 hours. (a) What should be the radius of the satellite's orbit? ___________ km (b) What would be the orbital speed of the satellite? _________ m/s

Explanation / Answer

a) since time period T = 2 pi square root of ( r^3 / GM) where 'r' is the radius of orbit so that r =( GMT^2/ 4pi^2)^1/3 =41363.445 km gravitational constant = 6.67300 × 10-11 m3 kg-1 s-2 b) orbital speed Vo = square root of (GM/r)=3085.16 m/s

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