Answer
The radius of the orbit is $~~1.9\times 10^7~m$
Work Step by Step
We can find an expression for the speed:
$v = \frac{distance}{time} = \frac{2\pi~r}{T}$
The gravitational force provides the centripetal force to keep the satellite moving in a circle. We can find the radius $r$ of the orbit:
$F = \frac{mv^2}{r} = 80~N$
$\frac{m(\frac{2\pi~r}{T})^2}{r} = 80~N$
$\frac{4\pi^2 mr}{T^2} = 80~N$
$r = \frac{(80~N)~T^2}{4\pi^2 m}$
$r = \frac{(80~N)~(21,600~s)^2}{(4\pi^2)(50~kg)}$
$r = 1.9\times 10^7~m$
The radius of the orbit is $~~1.9\times 10^7~m$.
