Satellites which give high value data for remote sensing,meteorology and environmental studies are

Express the constant $k$ of $T^{2}=k(R_{E}+h)^{3}$ in days and kilometres. Given $k = 10^{-13} \; s^{2} \; m^{-3}$. The moon is at a distance of $3.84 \times 10^{5} \; km$ from the earth. Obtain its time period of revolution in days.

Two planets,$A$ and $B$,orbit around a star such that the time period of $A$ is $8$ times the time period of $B$. The ratio of the orbital velocities of planets $A$ and $B$ is:

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

Consider a binary star system consisting of two stars of masses $M_1$ and $M_2$ separated by a distance of $30 \text{ AU}$ with a period of revolution equal to $30 \text{ years}$. If one of the two stars is $5$ times farther from the centre of mass than the other, find the masses of the two stars in terms of solar masses.

$A$ geostationary satellite is taken to a new orbit such that its distance from the centre of the earth is doubled. Find the time period of this satellite in the new orbit.