The time period of a satellite of Earth is $24 \text{ hours}$. If the separation between the Earth and the satellite is decreased to one-fourth of the previous value, then its new time period will become: (in $\text{ hours}$)

The time period of a geostationary satellite is $24 \; h$,at a height $6 R_{E}$ ($R_{E}$ is the radius of the Earth) from the surface of the Earth. The time period of another satellite whose height is $2.5 R_{E}$ from the surface will be:

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

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

$A$ planet of mass $m$ is in an elliptical orbit about the sun $(m \ll M_{sun})$ with an orbital period $T$. If $A$ is the area of the orbit,then its angular momentum is:

Let the speed of the planet at the perihelion $P$ in the figure be $v_{P}$ and the Sun-planet distance $SP$ be $r_{P}$. Relate $\{r_{P}, v_{P}\}$ to the corresponding quantities at the aphelion $\{r_{A}, v_{A}\}$. Will the planet take equal times to traverse $BAC$ and $CPB$?