A planet revolving in elliptical orbit has

$(A)$ a constant velocity of revolution.

$(B)$ has the least velocity when it is nearest to the sun.

$(C)$ its areal velocity is directly proportional to its velocity.

$(D)$ areal velocity is inversely proportional to its velocity.

$(E)$ to follow a trajectory such that the areal velocity is constant.

Choose the correct answer from the options given below

Which of the following statements is true for the planets orbiting around the sun ?

A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let $r$ be the distance of the body from the centre of the star and let its linear velocity be $v$, angular velocity  $\omega $, kinetic energy $K $, gravitational potential energy $U$, total energy $E$ and angular momentum $l$. As the radius $r$ of the orbit increases, determine which of the  abovequantities increase and which ones decrease.

The earth revolves round the sun in one year. If the distance between them becomes double, the new period of revolution will be

The motion of planets in the solar system is an example of the conservation of

The ratio of kinetic energy of a planet at perigee and apogee during its motion around the sun in elliptical orbit of eccentricity $e$ is ..........