Question

Two satellites, X and Y orbit at the same altitude above Earth's surface. Satellite X has twice the mass of satellite Y. What is the ratio of the period of X to the period of Y?

Answer 1

Answer:

$\text{Time period of a satellite is given by the formula:}\\\\\\\implies \boxed{ \bf{ T = \dfrac{2\pi \sqrt{r^3}}{\sqrt{GM_e}}}}$

where, 'r' is the distance of the satellite from Earth (also known as the radius of the orbit) and M(e) refers to the Mass of the planet Earth.

Hence Time period of a satellite depends on:

• Distance of satellite from the planet (or) orbit radius
• Mass of the planet

According to the question, satellite 'X' has twice the mass of satellite 'Y'. But since Time period is independent of the mass of the satellite,

The ratio of the time period of satellite X to that of satellite Y is 1 : 1.