Question

the time period of a satellite in orbit r and 4r is

Answer 1

f=ma
f=mv^2/r
GM/r=v^2
v=2πr/T
GM/r=4π^2r^2/T^2
T^2 =4π^2/GM a^3
T is inversly proportional to a^3/2
T^2 is inversly proportional to a^3
for a=r t=T
for a=4r t=?T^2/t^2=(R)^3/(4R)^3
T^2/t^2=R^3/256R^3
r cube and r cube will get cancel
t^2 =256
t=.
$\sqrt{256}$
t=16