Manipal Entrance Test 2015 Physics Paper

Applying Newton’s second law to a circular orbit,
we have

mv2

r

=

4π2rm

T2

=

GMm

r2

where, m is the mass of satellite, and v is the orbital speed, T is the time period
∴T=

2πr3∕2

√GM

For r≈R
and
M=

4

3

πR3ρ (ρ = density of planet)
∵T=√

3π

ρG

i.e. T is independent of R