# Two satellites A and B of the same mass are orbiting Earth in concentric orbits. The distance of...

## Question:

Two satellites A and B of the same mass are orbiting Earth in concentric orbits. The distance of satellite B from Earth's center is twice that of satellite A. What is the ratio of the tangential speed of B to that of A?

## The orbital velocity:

If an object is placed in an orbit around the planet, then it behaves as a satellite of the planet.

The object moves in the circular orbit with a tangential speed.

This speed is called the orbital speed of the object.

The orbital speed is the ratio of the total distance covered by the object to its time period.

The mass of both satellites is the same.

The distance of satellite B from Earth's center is twice that of satellite A.

{eq}r_b = 2\ r_a {/eq}

We know that orbital speed is given as,

{eq}v = \sqrt{\dfrac {G\ M}{r}} {/eq}

Hence,

{eq}\begin{align} v&\propto \sqrt{\dfrac{1}{r}}\\ \implies \dfrac{v_b}{v_a}& =\sqrt{ \dfrac{r_a}{r_b}}\\ \dfrac{v_b}{v_a} &= \sqrt{\dfrac{r_a}{2\ r_a}}\\ \dfrac{v_b}{v_a} &= 0.707\\ \end{align} {/eq} 