$A$ 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?

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 ......... $hours$.

If a satellite orbiting the Earth is $9$ times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $= 27 \text{ days}$ and gravitational attraction between the satellite and the moon is neglected.

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:

The figure shows the motion of a planet around the sun in an elliptical orbit with the sun at the focus. The shaded areas are equal. If $t_1$ and $t_2$ represent the time taken for the planet to move from $A$ to $B$ and $C$ to $D$ respectively,then:

$A$ planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at