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?

The radius of the orbit of a geostationary satellite is (mean radius of the earth is $R$,angular velocity about its axis is $\omega$,and acceleration due to gravity on the earth's surface is $g$).

$A$ satellite is in an elliptic orbit around the Earth with an aphelion of $6R$ and a perihelion of $2R$,where $R = 6400 \, km$ is the radius of the Earth. Find the 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 $6R$? $(G = 6.67 \times 10^{-11} \, SI \text{ units and } M = 6 \times 10^{24} \, kg)$

$A$ ball is dropped from a spacecraft revolving around the earth at a height of $120 \ km$. What will happen to the ball?

The orbit of a geo-stationary satellite is circular. The time period of the satellite depends on:
$(i)$ mass of the satellite
(ii) mass of the earth
(iii) radius of the orbit
(iv) height of the satellite from the surface of the earth
Which of the following is correct?

The rotation period of an earth satellite close to the surface of the earth is $83$ minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be .......... $\min$