$A$ satellite of mass $m$ is circulating around the Earth with constant angular velocity. If the radius of the orbit is $R_0$ and the mass of the Earth is $M$,the angular momentum about the centre of the Earth is:

$A$ satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius $R_e$. By firing rockets attached to it,its speed is instantaneously increased in the direction of its motion so that it becomes $\sqrt{\frac{3}{2}}$ times larger. Due to this,the farthest distance from the centre of the earth that the satellite reaches is $R$. The value of $R$ is $....R_e$.

Two satellites $A$ and $B$ of masses $200 \, kg$ and $400 \, kg$ are revolving around the Earth at heights of $600 \, km$ and $1600 \, km$ respectively. If $T_{A}$ and $T_{B}$ are the time periods of $A$ and $B$ respectively,then find the value of $T_{B} - T_{A}$.
[Given: Radius of Earth $R = 6400 \, km$,Mass of Earth $M = 6 \times 10^{24} \, kg$,$G = 6.67 \times 10^{-11} \, Nm^{2}/kg^{2}$]

Three equal mass satellites $A, B,$ and $C$ are in coplanar orbits around a planet as shown in the figure. The magnitudes of the angular momenta of the satellites as measured about the planet are $L_A, L_B$,and $L_C$. Which of the following statements is correct?

$A$ satellite is to be placed in an equatorial geostationary orbit around the Earth for communication purposes. The height of such a satellite is $(M_{E} = 6 \times 10^{24} \,kg, R_{E} = 6400 \,km)$.

Two planets,$A$ and $B$,are orbiting a common star in circular orbits of radii $R_A$ and $R_B$,respectively,with $R_B = 2 R_A$. The planet $B$ is $4 \sqrt{2}$ times more massive than planet $A$. The ratio $\left(\frac{L_B}{L_A}\right)$ of angular momentum $(L_B)$ of planet $B$ to that of planet $A$ $(L_A)$ is closest to integer . . . . . . .