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

a. gravitationla force F = Gm1m2/r^2 = 6.67*10^-11* 200* 6*10^24/4.23^2*10^14

F = 44.7 N

b. F = mv^2/R

V^2 = 44.7 *4.23*10^7/200

v =3.06 km/s

C. T^2 = 2piR^3/GM

T^2 = 2*3.14*4.23^3*10^21/5.61 *10^-8* 6.67*10^-11* 6*10^24

T = 1 day

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