If the orbital period of a satellite becomes $8$ times, then by how many times does its orbital radius increase (in $times$)?

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 ....... $h$.

The ratio of the distances of two planets from the sun is $1.38$. The ratio of their period of revolution around the sun is

How will you 'weigh the sun',that is estimate its mass? The mean orbital radius of the earth around the sun is $1.5 \times 10^{8} \text{ km}$.

$A$ 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).

$A$ Saturn year is $29.5$ times the Earth year. How far is Saturn from the Sun if the Earth is $1.50 \times 10^{8} \; km$ away from the Sun?