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.
a ) 4.22 ( 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