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?

Answer 1

Answer:

ratio of tangential velocity of satellite b and a will be 0.707

Explanation:

We have given distance of satellite B from satellite A is twice

So $r_b=2r_a$

Tangential speed of the satellite is given by

$v=\sqrt{\frac{GM}{r}}$, G is gravitational constant. M is mass of satellite and r is distance from the earth

We have to find the ratio of tangential velocities of b and a

From the relation we can see that tangential velocity is inversely proportional to square root of distance from earth

So $\frac{v_b}{v_a}=\sqrt{\frac{r_a}{r_b}}$

$\frac{v_b}{v_a}=\sqrt{\frac{r_a}{2r_a}}$

$\frac{v_b}{v_a}=\sqrt{\frac{1}{2}}$

$\frac{v_b}{v_a}=0.707$

So ratio of tangential velocity of satellite b and a will be 0.707