Question

Show that period of a satellite revolving around the Earth depends upon mass of the Earth.

Answer 1

a.   Let,
M = mass of earth
m = mass of satellite
R = radius of earth
vc = critical velocity
b.   In one revolution, distance covered by satellite is equal to circumference of its circular
orbit. 
c.   If T is the time period of satellite, then

` T="Circumference of the orbit"/"Critical Velocity"`

`therefore T=(2pir)/v_c` ....................(1)

But `v_c=sqrt((GM)/r)` ......................(2)

d.  Substituting equation (2) in (1),

`  T=(2pir)/sqrt((GM)/r)`

`=2pisqrt(r^2xxr/(GM))`

`T=2pisqrt(r^3/(GM))`...............(3)

Thus, period of a satellite revolving around the Earth depends upon mass of the Earth.