A satellite is to be placed in an free - flight equatorial circular orbit around earth. The satellite remains stationary with respect to a point on earth. Determine the radius of the circular orbit.
( The universal gravitational constant ,
G = 66.73 ( 10 -12 ) and the mass of the earth is 5.976 ( 10 24 ) Kg . )

a ) 4.22 ( 10 4 ) Km
b ) 5.22 ( 10 4 ) Km

c ) 3.98 ( 10 4 ) Km
d ) 3.58 ( 10 4 ) Km

 

Let R be the radius of the circular orbit ; M e , the mass of the earth ; M s the mass of the satellite ; w , be the angular velocity of the satellite and G be the universal gravitational constant.

Since the satellite is in the free - flight equatorial circular orbit the net normal force on the satellite should be zero. Given that the satellite remains stationary with respect to a point on the earth , its time - period must be 24 hours = 86400 s. hence the angular acceleration of the satellite is given by ,

  w = ( 2 p ) / 86400 = 7.272 ( 10 - 5 )

Writing the equation of motion in the radial direction ,

The radius of the orbit is 4.22 ( 10 4 ) Km