Question

if ρ is the mean density of the earth and R is the radius then the time period of the satellite revolving close to the surface is

Answer 1

formula for time period=

2π(√(R+h)³/GM)

where,

R=radius of earth

h=height of settelite

G=universal gravitational constant

M=mass of earth

now;

if

h is very very less, for a satellite revolving close to earth,(negligible)

t=2π(√(R)³/GM)

we know;

density=mass/volume

ρ=M/4πR³                         volume=4πR³

M=ρ4πR³

substituting these values in the formula of time period, we get;

t=2π(√(R)³/Gρ4πR³)

t=2π(√1/Gρ4π)

t=√π/Gρ

answer:t=√π/Gρ