Question

26. A satellite is revolving in a circular path. Its time period T depends on its mass M, velocity
v and radius of orbit R. Deduce the relationship among these quantities using the method of
dimension.​

Answer 1

Answer:

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Explanation:

Let the satellite of mass m

s

is revolving around the Earth of mass m

e

at a distance of r then the centripetal force will be given by:

F

c

=

r

m

s

v

2

where v is velocity of satellite. This force is equal to gravitational force between satellite and earth. Therefore

r

m

s

v

2

=G

r

2

m

s

m

e

v=

r

Gm

e

Now, period of the satellite is given by:

T=

v

2πr

=2π

Gm

e

r

3

Therefore time period of satellite(T) depends on the mass of earth(m