When a satellite in a circular orbit around the earth enters the atmospheric region,it encounters small air resistance to its motion. Then

Three particles,each of mass $M$,are situated at the vertices of an equilateral triangle of side length $L$. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation $L$. The initial speed that should be given to each particle is

$A$ satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then

If the distance of Mercury from the Sun is $0.4$ times the distance of the Earth from the Sun,find the solar constant of Mercury in $cal/min \cdot cm^2$. The solar constant of the Earth is $2 \, cal/min \cdot cm^2$.

$A$ star of mass $M$ and radius $R$ is made up of gases. The average gravitational pressure compressing the star due to the gravitational pull of the gases making up the star depends on $R$ as

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
$Assertion$ $(A)$: The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
$Reason$ $(R)$: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements,choose the most appropriate answer from the options given below: