The ratio of the distances of two planets fro | 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 of revolution $(T)$ is directly proportional to the cube of the

Vedclass · Accepted Answer

$1.38^{3/2}$

Vedclass · Answer

(B) 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 $(a)$ of the orbit: $T^2 \propto a^3$.Given the ratio of distances (semi-major axes) of two planets from the sun is $\frac{a_1}{a_2} = 1.38$.We need to find the ratio of their periods of revolution $\frac{T_1}{T_2}$.From Kepler's third law: $\left(\frac{T_1}{T_2}\right)^2 = \left(\frac{a_1}{a_2}\right)^3$.Taking the square root on both sides: $\frac{T_1}{T_2} = \left(\frac{a_1}{a_2}\right)^{3/2}$.Substituting the given value: $\frac{T_1}{T_2} = (1.38)^{3/2}$.

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

Similar Questions

$A$ planet of mass $m$ moves around the sun of mass $M$ in an elliptical orbit. The maximum and minimum distances of the planet from the sun are $r_1$ and $r_2$ respectively. The time period of the planet is proportional to ..........

If $r_p, v_p, L_p$ and $r_a, v_a, L_a$ are radii,velocities and angular momenta of a planet at perihelion and aphelion of its elliptical orbit around the Sun respectively,then

The distance of Venus from the sun is $0.72\, AU$. The orbital period of Venus is ............ days.

Draw the areal velocity versus time graph for Mars.

Choose the incorrect statement from the following.

Vedclass Test Series

Exam Paper Generator

Online Exam Module