As per Law of Universal Gravitation the force of attraction F_G between two bodies of masses M_1 and M_2 is directly proportional to the product of masses of the two bodies. it is also inversely proportional to the square of the distance r between the two. That is the force of gravity follows inverse square law.
Combining the two we obtain the proportionality expression
F_G prop (M_1.M_2)/r^2
Follows that
F_G =G (M_1.M_2)/r^2 .......(1)
Where G is the proportionality constant.
It has the value 6.67408 xx 10^-11 m^3 kg^-1 s^-2
If one of the bodies is earth of mass M_e and radius being R_e then for a object of m equation (1) becomes
F =G (M_e m)/R_e^2
Comparing with equation
F=mg, we get for earth
Acceleration due to gravity g=G (M_e )/R_e^2=9.81ms^-2 .....(2)
For a given satellite we get its
Acceleration due to gravity g_s=G (M_e/2 )/(R_e/2)^2
=>g_s=cancel4^2/cancel2(G (M_e )/R_e^2)
Using (2) to insert value of g we get
=>g_s=2xx9.81=19.62ms^-2
