# 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.

## Answer and Explanation:

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}