The period of a planet around the sun is $8$ times that of earth. The ratio of the radius of the planet's orbit to the radius of the earth's orbit is:

$A$ planet moving around the Sun sweeps out an area $A_{1}$ in $2$ days,$A_{2}$ in $3$ days,and $A_{3}$ in $6$ days. Then,the relation between $A_{1}, A_{2}$,and $A_{3}$ is

$A$ planet of mass $m$ moves around the sun of mass $M$ in an elliptical orbit. The maximum and minimum distances of the planet from the sun are $r_1$ and $r_2$ respectively. The time period of the planet is proportional to ..........

The figure shows the motion of a planet around the sun in an elliptical orbit with the sun at the focus. The shaded areas $A$ and $B$ are also shown in the figure,which can be assumed to be equal. If ${t_1}$ and ${t_2}$ represent the time taken for the planet to move from $a$ to $b$ and $d$ to $c$ respectively,then:

Io, one of the satellites of Jupiter, has an orbital period of $1.769$ days and the radius of the orbit is $4.22 \times 10^{8} \; m$. Show that the mass of Jupiter is about one-thousandth that of the Sun.

An earth satellite $S$ has an orbit radius which is $4$ times that of a communication satellite $C$. The period of revolution of $S$ is ........ $days$.