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

Which of the following quantities does not depend upon the orbital radius of the satellite

A satellite $S$ moves around a planet $P$ in an elliptical orbit as shown in figure. The ratio the speed of the satellite at point $a$ to that at point $b$ is

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

Two satellites $S_{1}$ and $S_{2}$ are revolving around a planet in the opposite sense in coplanar circular concentric orbits. At time $t=0$, the satellites are farthest apart. The periods of revolution of $S_{1}$ and $S_{2}$ are $3 \,h$ and $24 \,h$, respectively. The radius of the orbit of $S_{1}$ is $3 \times 10^{4} \,km$. Then, the orbital speed of $S_{2}$ as observed from