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

A satellite is in a circular equatorial orbit of radius $7000\,km$ around the Earth. If it is transferred to a circular orbit of double the radius then its angular momentum will be

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

During motion of a planet from perihelion to aphelion the work done by gravitational force of sun on it is ...........

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 in an elliptic orbit around the earth with aphelion of $6R$ and perihelion of $2R$ where $R = 6400 \,km$ is the radius of the earth. Find eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius $6R$ ? $($ $G = 6.67 \times 10^{-11}\,SI$ $\rm {unit}$ and $M = 6 \times 10^{24}\,kg$$)$