Question

Two satellites of masses '3m' and 'm' orbit the earth in circular orbits of radii 'r' and '3r respectively. what is the ratio of their orbital velocities?
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Answer 1

Well, orbital velocity is the velocity with which a body or a satellite revolves along a circular orbit around the earth. The expression for orbital velocity is,

$v=\sqrt{\dfrac{GM}{r}}$

From the expression, since G, gravitational constant, and M, mass of the earth, are constants,

$v\propto\sqrt{\dfrac{1}{r}}$

This means the orbital velocity depends on the orbital radius of the satellite but not on the mass of the satellite. From the relation, we thus form an equation,

$\dfrac{v_1}{v_2}=\sqrt{\dfrac{r_2}{r_1}}$

In the question,

$\dfrac{r_1}{r_2}=\dfrac{1}{3}$

Then,

$\dfrac{v_1}{v_2}=\boxed{\mathbf{\sqrt{3}}}$