Import Question JSON

$\text{Hint: According to Kepler's 2}^{\text{nd}} \text{ law, areal velocity is constant.}$ $\text{Explanation: Let's analyze each statement given about a planet revolving in an elliptical orbit:}$ $\text{(A) A constant velocity of revolution.}$ $\text{This is false. The velocity of a planet in an elliptical orbit varies. It moves faster when it is closer to the Sun (perihelion) and slower when it is farther from the Sun (aphelion) due to Kepler's second law.}$ $\text{(B) Has the least velocity when it is nearest to the Sun.}$ $\text{This is false. The planet has its greatest velocity when it is nearest to the Sun (perihelion) and its least velocity when it is farthest from the Sun (aphelion).}$ $\text{(C) Its areal velocity is directly proportional to its velocity.}$ $\text{This is false. The areal velocity is not directly proportional to the linear velocity; it depends on both the velocity and the distance from the Sun.}$ $\text{(D) Areal velocity is inversely proportional to its velocity.}$ $\text{This is false. The areal velocity is not inversely proportional to the linear velocity.}$ $\text{(E) To follow a trajectory such that the areal velocity is constant.}$ $\text{According to Kepler's second law, the areal velocity of a planet (the area swept out per unit time) remains constant. This law implies that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.}$ $\text{Hence, option (4) is the correct answer.}$