$A$ satellite is in a circular equatorial orbit of radius $r = 7000 \, km$ around the Earth. If it is transferred to a circular orbit of double the radius $(2r)$,then its angular momentum will:

$A$ double star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses $m$ and $2m$ and their separation be $l$. Their time period of rotation about their centre of mass will be proportional to:

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:

Which of the following is the evidence to show that there must be a force acting on the Earth and directed towards the Sun?

What is the period of revolution of an Earth satellite? Ignore the height of the satellite above the surface of the Earth.
Given:
$(1)$ The value of gravitational acceleration $g = 10 \ ms^{-2}$.
$(2)$ Radius of Earth $R_E = 6400 \ km$. Take $\pi = 3.14$.

$A$ 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).