In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius $R$ is proportional to :

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

Assertion $(A)$: Angular speed,linear speed,and kinetic energy change with time,but angular momentum remains constant for a planet orbiting the sun.
Reason $(R)$: Angular momentum is constant as no external torque acts on the planet.

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

$A$ star of mass $M$ (equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a circular orbit. The velocity of the star with respect to the centre of mass of the star-planet system is shown below. The radius of the planet's orbit is closest to .......... $AU$ ($1 \, AU =$ Earth-Sun distance).

The time period of a satellite revolving around earth in a given orbit is $7 \, hours$. If the radius of orbit is increased to three times its previous value,then the approximate new time period of the satellite will be ...... $hours$.