A planet is revolving around the sun in an el | vedclass

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

Question

(A) According to Kepler's second law of planetary motion,the radius vector joining the sun and the planet sweeps out equal areas in equal intervals of

Vedclass · Accepted Answer

The time taken in travelling $DAB$ is less than that for $BCD$.

Vedclass · Answer

(A) According to Kepler's second law of planetary motion,the radius vector joining the sun and the planet sweeps out equal areas in equal intervals of time.In the given figure,the sun $S$ is at one of the foci of the elliptical orbit.The area swept by the planet in path $DAB$ is less than the area swept in path $BCD$ because the sun is closer to the arc $DAB$.Since the area swept in path $DAB$ is smaller than the area swept in path $BCD$,the time taken to travel $DAB$ must be less than the time taken to travel $BCD$ to satisfy the condition of equal area in equal time.Alternatively,according to the law of conservation of angular momentum,the orbital velocity of the planet is higher when it is closer to the sun (near $A$) and lower when it is farther away (near $C$).Thus,the planet travels faster along the path $DAB$ and slower along the path $BCD$,confirming that the time taken for $DAB$ is less than that for $BCD$.

$A$ planet is revolving around the sun in an elliptical path as shown in the figure. Which of the following is the correct option?

Similar Questions

The average distance of the Earth from the Sun is $L_{1}$. If one year of the Earth is $D$ days, then one year of another planet whose average distance from the Sun is $L_{2}$ will be:

State and prove Kepler's second law (Law of Areas) of planetary motion.

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

Two planets $A$ and $B$ of equal mass have periods of revolution $T_{A}$ and $T_{B}$ such that $T_{A} = 2 T_{B}$. These planets are revolving in circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which of the following is the correct relationship between their orbital radii?

State Kepler's law of periods (Kepler's third law) for planetary motion.

Vedclass Test Series

Exam Paper Generator

Online Exam Module