A satellite has a mass of 5900 kg and is in a circular orbit 4.50X10^5 m above t

Question

A satellite has a mass of 5900 kg and is in a circular orbit 4.50X10^5 m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is 4.20X10^6 m. What is the true weight of the satellite when it is at rest on the planet's surface?
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Explanation / Answer

Radius of satellites orbit = 4.5*10^5 + 4.2*10^6 = 46.5 * 10^5 m Circumference = 292.168 * 10^5 m => orbital speed = Circumference/period = 4057.89 m/s => centripetal acceleration = V^2 / r = 3.541 m/s^2 This is acceleration due to gravity at 46.5*10^5 m distance from centre of planet. => acceleration due to gravity at the surface of planet = 3.541 * (46.5 * 10^5 /4.2 * 10^6 )^2 = 4.3404 m/s^2 => True weight of satellite on planet's surface = 5900 * 4.3404 = 25608.5662 N

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