The time period T of a satellite is related t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For a satellite orbiting close to the surface of a planet of radius $R$ and density $\rho$,the time period $T$ is given by $T = 2\pi \sqrt{\frac{R

Vedclass · Accepted Answer

$T \propto \rho^{-1/2}$

Vedclass · Answer

(D) For a satellite orbiting close to the surface of a planet of radius $R$ and density $\rho$,the time period $T$ is given by $T = 2\pi \sqrt{\frac{R}{g}}$.Since $g = \frac{GM}{R^2}$ and $M = \rho \cdot \frac{4}{3} \pi R^3$,we have $g = \frac{G \cdot \rho \cdot \frac{4}{3} \pi R^3}{R^2} = \frac{4}{3} G \pi \rho R$.Substituting $g$ into the time period formula: $T = 2\pi \sqrt{\frac{R}{\frac{4}{3} G \pi \rho R}} = 2\pi \sqrt{\frac{3}{4 G \pi \rho}}$.Thus,$T \propto \rho^{-1/2}$.

The time period $T$ of a satellite is related to the density $(\rho)$ of the planet around which it is orbiting close to the surface as:

Similar Questions

$A$ satellite $S$ is moving in an elliptical orbit around the Earth. The mass of the satellite is very small compared to the mass of the Earth.

The orbital speed of Jupiter is

Why does a satellite not have an escape velocity?

The distance of a geostationary satellite from the surface of the Earth (radius $R_e = 6400 \ km$) in terms of $R_e$ is ....... (in $R_e$)

What is the time period of a satellite orbiting at a height $R$ above the Earth's surface?

Vedclass Test Series

Exam Paper Generator

Online Exam Module