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

In an elliptical orbit under gravitational force,in general

$A$ geostationary satellite is orbiting the earth at a height of $6R$ above the surface of the earth ($R$ is the radius of the earth). The time period of another satellite at a height of $2.5R$ from the surface of the earth is:

Earth's orbit is an ellipse with eccentricity $e = 0.0167$. Thus,the Earth's distance from the Sun and its speed as it moves around the Sun vary from day to day. This means that the length of the solar day is not constant throughout the year. Assume that the Earth's spin axis is normal to its orbital plane and find the length of the shortest and the longest day. $A$ day should be taken from noon to noon. Does this explain the variation in the length of the day during the year?

$A$ satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of the Earth in the new orbit is $2$ times that of the earlier orbit. The time period in the second orbit is:

$A$ planet of mass $m$ is moving in an elliptical orbit about the sun with time period $T$. If $A$ is the area of the orbit,then its angular momentum is: