The time period of a satellite of Earth is $5\, h$. If the separation between the centre of the Earth and the satellite is increased to $4$ times the previous value,the new time period will become ....... $h$.

$A$ satellite is launched into a circular orbit of radius $R$ around Earth,while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is:

$A$ 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:

According to Kepler, the period of revolution of a planet $(T)$ and its mean distance from the sun $(r)$ are related by the equation:

The Earth revolves around the Sun in an elliptical orbit with a mean radius of $9.3 \times 10^{10} \ m$ in a period of $1$ year. Assuming that there are no outside influences,which of the following statements is true?

Assume that the earth moves around the sun in a circular orbit of radius $R$ and there exists a planet which also moves around the sun in a circular orbit with an angular speed twice as large as that of the earth. The radius of the orbit of the planet is