A planet (P_1) is moving around a star of mas | vedclass

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

Question

(B) According to Kepler's Third Law, the time period $T$ of a planet orbiting a star of mass $M$ at a distance $R$ is given by $T^2 = \frac{4\pi^2 R^3

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) According to Kepler's Third Law, the time period $T$ of a planet orbiting a star of mass $M$ at a distance $R$ is given by $T^2 = \frac{4\pi^2 R^3}{GM}$.Thus, $T \propto \sqrt{\frac{R^3}{M}}$.For planet $P_1$: $T_1 \propto \sqrt{\frac{R^3}{2M}}$.For planet $P_2$: $T_2 \propto \sqrt{\frac{(2R)^3}{4M}} = \sqrt{\frac{8R^3}{4M}} = \sqrt{\frac{2R^3}{M}}$.Taking the ratio $\frac{T_2}{T_1}$:$\frac{T_2}{T_1} = \frac{\sqrt{2R^3/M}}{\sqrt{R^3/2M}} = \sqrt{\frac{2R^3}{M} \cdot \frac{2M}{R^3}} = \sqrt{4} = 2$.Therefore, the ratio of the time periods of revolution of $P_2$ and $P_1$ is $2$.

$A$ planet $(P_1)$ is moving around a star of mass $2M$ in an orbit of radius $R$. Another planet $(P_2)$ is moving around another star of mass $4M$ in an orbit of radius $2R$. The ratio of the time periods of revolution of $P_2$ and $P_1$ is . . . . . . .

Similar Questions

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 ......... $hours$.

The time period of a geostationary satellite is $24 \; h$,at a height $6 R_{E}$ ($R_{E}$ is the radius of the Earth) from the surface of the Earth. The time period of another satellite whose height is $2.5 R_{E}$ from the surface will be:

The figure shows the motion of a planet around the sun in an elliptical orbit with the sun at the focus. The shaded areas are equal. If $t_1$ and $t_2$ represent the time taken for the planet to move from $A$ to $B$ and $C$ to $D$ respectively,then:

$A$ satellite is launched into a circular orbit of radius $R$ around Earth,while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is:

If the orbital period of a satellite becomes $8$ times, then by how many times does its orbital radius increase (in $\times$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module