What is the ratio of the time periods of a sa | vedclass

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

Question

(D) According to Kepler's third law of planetary motion,the square of the time period $(T)$ is directly proportional to the cube of the orbital radius

Vedclass · Accepted Answer

$1 : 2\sqrt{2}$

Vedclass · Answer

(D) According to Kepler's third law of planetary motion,the square of the time period $(T)$ is directly proportional to the cube of the orbital radius $(r)$: $T^2 \propto r^3$.Therefore,the ratio of the time periods is given by $\frac{T_A}{T_B} = \left( \frac{r_A}{r_B} \right)^{3/2}$.Given $r_A = r$ and $r_B = 2r$,we substitute these values into the formula:$\frac{T_A}{T_B} = \left( \frac{r}{2r} \right)^{3/2} = \left( \frac{1}{2} \right)^{3/2} = \frac{1}{2^{3/2}} = \frac{1}{2\sqrt{2}}$.Thus,the ratio of the time periods is $1 : 2\sqrt{2}$.

What is the ratio of the time periods of a satellite $A$ of mass $m$ at a distance $r$ from the center of the Earth and a satellite $B$ of mass $2m$ at a distance $2r$ from the center of the Earth?

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.

Obtain an equation for the orbital time period of a satellite revolving around the Earth.

The period of a satellite in a circular orbit around a planet is independent of

The relay satellite transmits the television signals continuously from one part of the world to another because its

The distances of two planets $A$ and $B$ from the sun are $r_A$ and $r_B$ respectively. Given that $r_B = 100 r_A$. If the orbital speed of planet $A$ is $v$,then the orbital speed of planet $B$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module