The time period of a satellite in a circular | vedclass

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

Question

(B) According to Kepler's Third Law of Planetary Motion,the square of the time period $T$ is proportional to the cube of the orbital radius $R$,i.e.,$

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(B) According to Kepler's Third Law of Planetary Motion,the square of the time period $T$ is proportional to the cube of the orbital radius $R$,i.e.,$T^2 \propto R^3$.Let the time period of the first satellite be $T_1 = T$ with radius $R_1 = R$.Let the time period of the second satellite be $T_2$ with radius $R_2 = 9R$.Using the ratio formula:$\left(\frac{T_2}{T_1}\right)^2 = \left(\frac{R_2}{R_1}\right)^3$Substituting the given values:$\left(\frac{T_2}{T}\right)^2 = \left(\frac{9R}{R}\right)^3$$\left(\frac{T_2}{T}\right)^2 = (9)^3 = 729$Taking the square root on both sides:$\frac{T_2}{T} = \sqrt{729} = 27$Therefore,$T_2 = 27T$.

The time period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $9R$ is............ $T$.

Similar Questions

$A$ planet is revolving around the Sun in an elliptical orbit as shown in the figure. Which of the following is a correct statement?

An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to

Which of the following orbits is a possible orbit for a planet?

$A$ comet (assumed to be in an elliptical orbit around the sun) is at a distance of $0.4 \, AU$ from the sun at the perihelion. If the time period of the comet is $125 \, yr$,the aphelion distance is ........... $AU$ ($AU$: Astronomical Unit).

Consider a planet moving around a star in an elliptical orbit with period $T$. The area of the elliptical orbit is proportional to ...........

Vedclass Test Series

Exam Paper Generator

Online Exam Module