#### Question

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

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.

Is there an error in this question or solution?

#### APPEARS IN

Solution Show that Period of a Satellite Revolving Around the Earth Depends Upon Mass of the Earth. Concept: Projection of Satellite.