A satellite moves around the Earth in a circu | 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 directly proportional to the cube of the orbital radius

Vedclass · Accepted Answer

$4R$

Vedclass · Answer

(B) 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 $(r)$: $T^2 \propto r^3$.Given for the first satellite: $T_1 = 1 	ext{ day}$,$r_1 = R$.Given for the second satellite: $T_2 = 8 	ext{ days}$,$r_2 = ?$.Using the ratio: $\left( \frac{T_2}{T_1} ight)^2 = \left( \frac{r_2}{r_1} ight)^3$.Substituting the values: $\left( \frac{8}{1} ight)^2 = \left( \frac{r_2}{R} ight)^3$.$64 = \left( \frac{r_2}{R} ight)^3$.Taking the cube root on both sides: $\sqrt[3]{64} = \frac{r_2}{R}$.$4 = \frac{r_2}{R}$,which implies $r_2 = 4R$.

$A$ satellite moves around the Earth in a circular orbit of radius $R$ making one revolution per day. $A$ second satellite moving in a circular orbit moves around the Earth once in $8$ days. The radius of the orbit of the second satellite is

Similar Questions

If $J$ is the angular momentum of a planet revolving around the Sun,what is the areal velocity of the planet?

Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?

$A$ 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 Earth is $5\, h$. If the separation between the centre of the Earth and the satellite is increased to $4$ times the previous value,the new time period will become ....... $h$.

If a planet revolves around the sun with an angular velocity $(\omega)$ and distance $(r)$,then the areal velocity of the planet is proportional to which of the following?

Vedclass Test Series

Exam Paper Generator

Online Exam Module