# Show that Period of a Satellite Revolving Around the Earth Depends Upon Mass of the Earth. - Physics

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

#### Solution

a.   Let,
M = mass of earth
m = mass of satellite
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.

Concept: Projection of Satellite
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