Question

The workdone to increase the radius of orbit of satellite of mass m reoling around a planet of mass m from orbit of radius r in to another orbit of radius 3r

Answer 1

Answer:

The gravitational force 'F' on satellite of mass 'm' revolving around the planet in the orbit of radius 'R' is

F=−

R

2

GMm

Where

G is gravitational constant

M is Mass of the planet.

The work done in increasing the radius of orbit of the satellite through 'dr' is

W=Fdr

but work done is equal to change in gravitational potential '−dV'

therefore

−dV=Fdr

V=−∫

R

3R

Fdr

V=−

R

2

GMm

∫

R

3R

−(Fdr)

V=GMm∫

R

3R

R

2

1

dr

V=

R

GMm

−

3R

GMm

V=

3R

2GMm

Thus work done to increase the radius of orbit of satellite is

3R

2GMm