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

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

Describe the model and theory of planetary motions presented in the earliest of times.

$A$ planet of mass $m$ is in an elliptical orbit about the sun $(m \ll M_{sun})$ with an orbital period $T$. If $A$ is the area of the orbit,then its angular momentum is:

The time period of a satellite of the Earth is $5$ hours. If the separation between the Earth and the satellite is increased to four times the previous value,the new time period will become ......... $hours$.

Which of the following quantities does not depend upon the orbital radius of the satellite?

Vedclass Test Series

Exam Paper Generator

Online Exam Module