An artificial satellite circles the Earth in a circular orbi

An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is 4.09 m/s2. Determine the orbital period of the satellite in minutes.

Solution

Gravitational force,

F = GmM/ d^2

According to Netwon second law,

F = m*g ( here g = gravitational acceleration)

So that,

g = G*M /d^2

5.95= G*M/ d^2

d^2= 6.67*10^-11*5.97*10^24*(1/4.09)

d = 9867074.98 = 9.86*10^6 m

For orbital period

T^2/d^3 = 4*pi^2/ G*M

T = sqrt [(9.86*10^6)^3*4*pi^2)/6.67*10^-11*5.97*10^24)]

= 9748.6652 s

= 162.477 minutes