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For communications purposes, satellites are typically placed in a circular geosynchronous orbit. If the orbit is...

For communications purposes, satellites are typically placed in a circular geosynchronous orbit. If the orbit is in the equatorial plane of the Earth, it is called geostationary. A satellite’s orbital speed in a geostationary orbit is set to match the angular velocity Ωe of the rotating Earth (with mass M), so that as seen from the Earth the satellite is stationary above a fixed point on the Equator. For a satellite of mass m in a geostationary circular orbit then v = rΩe.

(a) Calculate the radius of a geosynchronous orbit.

(b) Calculate the orbital velocity of a geosynchronous orbit.

(c) Calculate the minimum amount of energy required to put a satellite in geosynchronous orbit, launched from the Earth’s equator.

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