If $g \propto \frac{1}{R^3}$ (instead of $\frac{1}{R^2}$),then the relation between the time period $T$ of a satellite near the Earth's surface and the radius $R$ will be:

The orbital velocity of an artificial satellite in a circular orbit very close to the Earth is $v$. The velocity of a geostationary satellite orbiting in a circular orbit at an altitude of $3R$ from the Earth's surface will be

The International Space Station is maintained in a nearly circular orbit with a mean altitude of $330 \, km$ and a maximum of $410 \, km$. An astronaut is floating in the space station's cabin. The acceleration of the astronaut as measured from the Earth is:

$A$ satellite of mass $m$ is revolving around the Earth of mass $M$ in an orbit of radius $r$ with constant angular velocity $\omega$. The angular momentum of the satellite is ($G$ = gravitational constant).

The weight of an astronaut,in an artificial satellite revolving around the earth,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?