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#
