If the orbital period of a satellite becomes | 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 orbital period $T$ is directly proportional to the cube of the semi-major a

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) According to Kepler's Third Law of Planetary Motion, the square of the orbital period $T$ is directly proportional to the cube of the semi-major axis (orbital radius) $r$ of the orbit.$T^2 \propto r^3$This implies $T \propto r^{3/2}$ or $r \propto T^{2/3}$.Given that the new orbital period $T' = 8T$.Substituting this into the proportionality:$r' / r = (T' / T)^{2/3}$$r' / r = (8T / T)^{2/3} = (8)^{2/3}$$r' / r = (2^3)^{2/3} = 2^2 = 4$.Therefore, the orbital radius becomes $4$ times the original radius.

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

Similar Questions

The distance between the Sun and the Earth is $R$. What will be the duration of the year if the distance between the Sun and the Earth becomes $3R$?

$A$ planet is revolving around the sun in an elliptical path as shown. The orbital velocity of the planet will be minimum at:

The period of revolution of planet $A$ around the sun is $8$ times that of $B$. The distance of $A$ from the sun is how many times greater than that of $B$ from the sun?

$A$ satellite moves in a circle around the earth. The radius of this circle is equal to one half of the radius of the moon's orbit. The satellite completes one revolution in

$A$ planet of mass $m$ is moving in an elliptical orbit about the sun with time period $T$. If $A$ is the area of the orbit,then its angular momentum is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module