If the distance of the earth from the Sun is | vedclass

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

Question

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

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) According to Kepler's third law of planetary motion,the square of the time period of revolution $(T)$ is directly proportional to the cube of the semi-major axis $(R)$ of the orbit: $T^2 \propto R^3$.Given:For Earth: $T_1 = 1 \, 	ext{year}$,$R_1 = 1.5 	imes 10^8 \, 	ext{km}$.For the imaginary planet: $T_2 = 2.83 \, 	ext{years}$,$R_2 = ?$.Using the ratio formula:$\left(\frac{T_2}{T_1}ight)^2 = \left(\frac{R_2}{R_1}ight)^3$Substituting the values:$\left(\frac{2.83}{1}ight)^2 = \left(\frac{R_2}{1.5 	imes 10^8}ight)^3$Since $2.83 \approx \sqrt{8}$,then $(2.83)^2 \approx 8$:$8 = \left(\frac{R_2}{1.5 	imes 10^8}ight)^3$Taking the cube root on both sides:$2 = \frac{R_2}{1.5 	imes 10^8}$$R_2 = 2 	imes 1.5 	imes 10^8 = 3 	imes 10^8 \, 	ext{km}$.Thus,the distance is $3 	imes 10^8 \, 	ext{km}$.

If the distance of the earth from the Sun is $1.5 \times 10^8 \, km$. Then the distance of an imaginary planet from the Sun,if its period of revolution is $2.83$ years,is $............. \times 10^8 \, km$.

Similar Questions

For proposing the universal law of gravitation,which laws were taken for help?

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:

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

An earth satellite $X$ is revolving around the earth in an orbit whose radius is one-fourth of the radius of the orbit of a communication satellite. The time period of revolution of $X$ is ..........

The ratio of the distances of two planets from the sun is $1.38$. The ratio of their period of revolution around the sun is

Vedclass Test Series

Exam Paper Generator

Online Exam Module