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 period of a planet around the sun is $8$ times that of earth. The ratio of the radius of the planet's orbit to the radius of the earth's orbit is:

Which of the following orbits is a possible orbit for a planet?

$A$ planet revolving in an elliptical orbit has:
$(A)$ a constant velocity of revolution.
$(B)$ 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.
$(E)$ a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below:

In planetary motion,the areal velocity of the position vector of a planet depends on the angular velocity $\omega$ and the distance of the planet from the sun $r$. The correct relation for areal velocity is:

The motion of satellites in the solar system is an example of which of the following?