A 200 kg communications satellite is placed into a circularorbit around the Eart

Question

A 200 kg communications satellite is placed into a circularorbit around the Earth with a radius of 4.23 x 107m(26,000 miles). a) Find the gravitational force on the satellite. b) Use the equation for centripetal force to compute the speedof the satellite. c) show that the period of the satellite-the time it takes tocomplete one orbit-is 1 day. (The distance it travels duringone orbit is 2, or 6.28, times the radius.) This is ageosynchronous orbit: The satellite stays above a fixed pointon the Earth's equator. A 200 kg communications satellite is placed into a circularorbit around the Earth with a radius of 4.23 x 107m(26,000 miles). a) Find the gravitational force on the satellite. b) Use the equation for centripetal force to compute the speedof the satellite. c) show that the period of the satellite-the time it takes tocomplete one orbit-is 1 day. (The distance it travels duringone orbit is 2, or 6.28, times the radius.) This is ageosynchronous orbit: The satellite stays above a fixed pointon the Earth's equator.

Explanation / Answer

Given :          Mass of thesatellite (m) = 200 kg          Mass ofthe Earth (M) = 5.9 x 1024 kg          Radius of thesatellite (R) = 4.23 x 107 m (a)          Gravitationalforce is :                       F   = G ( M m / R2 )                            = 6.67 x 10-11 [ ( 5.9 x1024 * 200) / ( 4.23 x 107 )2 ]                            = 4.39 x 103 N (b)          Force   = m v2 / R                 v2 = F*R / m                      = ( 4.39 x 103 *  4.23 x 107 ) / 200                       = 9.28 x 108            velocity v = 3.05 x 104 m /s (c)         Time period ofrevolution of satellite is :                                 T = 2 Re / g         Where Re = Radius of the Earth. Plugg the values and solve. Hope this helps u!            velocity v = 3.05 x 104 m /s (c)         Time period ofrevolution of satellite is :                                 T = 2 Re / g         Where Re = Radius of the Earth. Plugg the values and solve. Hope this helps u!

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