The time period of a satellite of the Earth is $5 \text{ hours}$. If the separation between the Earth and the satellite is increased to four times the previous value, the new time period of the satellite will be: (in $\text{ hours}$)

$A$ satellite orbits the Earth in a circular orbit of radius $R$. Another satellite orbits in an orbit of radius $1.02 R$. What is the percentage increase in the time period of the second satellite compared to the first (in $\%$)?

$A$ 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:

Explain Kepler's first law (Law of Orbits) for planetary motion.

If the angular momentum of a planet of mass $m$,moving around the Sun in a circular orbit is $L$,about the center of the Sun,its areal velocity is

An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to