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 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?

The period of revolution of planet $A$ around the sun is $8$ times that of $B$. The distance of $A$ from the sun is how many times greater than that of $B$ from the sun?

The average distance of the Earth from the Sun is $L_{1}$. If one year of the Earth is $D$ days, then one year of another planet whose average distance from the Sun is $L_{2}$ will be:

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).