The Earth revolves around the Sun in one year. If the distance between them becomes double,the new period of revolution will be

$A$ 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).

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law,i.e.,$F \propto 1/r^3$,but still remains a central force. Then:

In planetary motion,the areal velocity of the position vector of a planet depends on the angular velocity $\omega$ and the distance of the planet from the sun $r$. The correct relation for areal velocity is:

$A$ 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 in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $9R$ is............ $T$.