Question

The time period of a satellite is independent of the mass of the satellite.

(a) True

(b) False

I had been asked this question by my college director while I was bunking the class.

My doubt is from Gravitation topic in chapter Gravitation of Physics – Class 11

Answer 1

The correct answer is (a) True.

Explanation:

The time period of a satellite in orbit around a planet (like Earth) is independent of the mass of the satellite. This can be understood from Kepler's Third Law and the gravitational formula for orbital motion.

The orbital time period $T$ of a satellite is given by the formula:

T=2πr3GMT = 2\pi \sqrt{\frac{r^3}{GM}}T=2πGMr3​​

where:

• $r$ is the radius of the orbit (distance from the center of the planet to the satellite),
• $G$ is the gravitational constant,
• $M$ is the mass of the central body (e.g., the Earth),
• $T$ is the orbital period.

Notice that the mass of the satellite does not appear in this formula. The time period depends on the radius of the orbit and the mass of the planet around which the satellite orbits, but not the mass of the satellite itself.

Thus, regardless of whether the satellite is large or small, the time period for completing one orbit remains the same for a given orbital radius. This is why the time period of a satellite is independent of the satellite's mass.