Question

A satellite is put in an orbit just above the earth's surface with a velocity $\sqrt{1.5}$ times the velocity for a circular orbit on surface of earth. Assuming that path of satellite is elliptical in nature. The maximum distance of the satellite from the surface of the earth is $nR$ where R is radius of earth. Find $n$

Answer 1

At nearest point $P$ and farthest point $Q$.
Velocities are perpendicular to their $r_1$ and $r_2$
$\therefore$ Conservation of angular momentum, gives
$m_1{v}_1{r}_1=m_2{v}_2{r}_2$
Conservation of energy gives
$\frac{1}{2}m{v}_1^2-\frac{GMm}{r_1}=\frac{1}{2}m{v}_2^2-\frac{GMm}{r_2}$ ... (2)
Solving (1) and (2)
We get,
$r_2=3r_1$
So, maximum distance of satellite from the centre of earth is $3R$ (since $r_1\approx R)$
$\therefore$ Maximum distance of satellite from surface of earth will be $3R–R=2R$.