Question

Two satellites are orbiting around the earth in circular orbits of the same radius. The mass of satellite A is five times greater than the mass of satellite B. Their periods of revolutions are in the ratio of

Answer 1

Their periods of revolutions are in the ratio of 1:1 as Time Period of a revolving object is independent of the mass of that object

Answer 2

The ratio of periods of revolutions of two satellites orbiting around the Earth in circular orbits of same radius and masses in the ratio 5:1 is 1:1

Time Period (T) = Distance/Orbital velocity

 $Time period(T) = \frac{2\pi r }{\sqrt{\frac{GM}{R} } }  = 2\pi r\sqrt{\frac{r}{GM} }  = 2\pi \sqrt{\frac{r^{3} }{GM} }$

r = radius of the satellite

G = universal gravitational constant

M = mass of Earth

Since time period is independent of mass of satellite, the time periods of both satellites will be equal.

Therefore, the ratio of Time periods will be 1:1