The planet Mars has two moons, if one of them has a period $7\, hours,\, 30\, minutes$ and an orbital radius of $9.0 \times 10^{3}\, {km} .$ Find the mass of Mars.

$\left\{\operatorname{Given} \frac{4 \pi^{2}}{G}=6 \times 10^{11} {N}^{-1} {m}^{-2} {kg}^{2}\right\}$

The time period of an artificial satellite in a circular orbit of radius $R$ is $2\, days$ and its  orbital velocity is $v_0$. If time period of another satellite in a circular orbit is $16 \,days$ then

If the angular momentum of a planet of mass $m$, moving a round the Sun in a circular orbit its $L$, about the center of the Sun, its areal velocity is

The time period of a satellite of earth is $24$ hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become $.......\,hours$

Let the speed of the planet at the perihelion Pin Figure be $v_{p}$ and the Sun-planet distance $SP$ be $r_{ P }$ Relate $\left\{r_{P}, v_{P}\right\}$ to the corresponding quantities at the aphelion $\left\{r_{A}, v_{A}\right\} .$ Will the planet take equal times to traverse $B A C$ and $C P B ?$

A planet has orbital radius twice as the earth's orbital radius then the time period of planet is .......... $years$