Question

The orbit velocity of an artificial satellite in a circular orbit just above the earths surface is $v$. For a satellite orbiting at an altitude of half of the earths radius, the orbit velocity is

Answer 1

Orbital velocity of artifical satellite near eart surface is given by , $v=\sqrt{\frac{GM}{R}}$...1

And orbital velocity at a distance $r$, is given by $v^{\prime }=\sqrt{\frac{GM}{r}}$

so for $r-R/2$, orbital velocity is $v^{\prime }=\sqrt{\frac{2GM}{R}}$....2

Taking ratio of eq1 and eq 2 we get , $\frac{v^{\prime }}{v}=\sqrt{2}$

this gives , $v^{\prime }=\sqrt{2}v$