Question

An artificial satellite is moving in a circular orbit around the earth with a speed of half the magnitude of escape velocity from the earth. The height of the satellite above the earth's surface is $nR(R$ is radius of earth$)$. Determine the value of $n$. ​​​​​​​

Answer 1

$v_0=\sqrt{\frac{GM}{R+h}}$
and $v_0=\frac{v_e}{2}=\frac{\sqrt{\frac{2GM}{R}}}{2}=\sqrt{\frac{GM}{2R}}$
$h=R$