Two planets revolve round the sun with frequencies ${N_1}$ and ${N_2}$ revolutions per year. If their average orbital radii be ${R_1}$ and ${R_2}$ respectively, then ${R_1}/{R_2}$ is equal to

Kepler's third law states that square of period of revolution $(T)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet i.e.

$\therefore \;{T^2} = k{r^3}$

here $K$ is constant.

If the masses of sun and planet are $M$ and $m$ respectively then as per Newton's law of gravitation force of attraction between them is $F = \frac{{GMm}}{{{r^2}}}$ , here $G$ gravitational constant . The relation between $G$ and $K$ is described as

If $L$ is the angular momentum of a satellite revolving around earth is a circular orbit of radius $r$ with speed $v$, then .........

India's Mangalyan was sent to the Mars by launching it into a transfer orbit $EOM$ around the sun . It leaves the earth at $E$ and meets Mars at $M$ . If the semi-major axis of Earth's orbit is $a_e = 1.5 \times 10^{11}\, m$, that of Mars orbit $a_m= 2.28 \times 10^{11}\, m$, taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to ........ $days$.

Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A}=2 T_{B}$. These planets are revolving in the circular orbits of radii $I_{A}$ and $I_{B}$ respectively. Which out of the following would be the correct relationship of their orbits?

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.

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