Two particles of equal mass $(m)$ each move in a circle of radius $(r)$ under the action of their mutual gravitational attraction. Find the speed of each particle.

Suppose the acceleration due to gravity at the earth's surface is $10 \, m/s^2$ and at the surface of Mars it is $4.0 \, m/s^2$. $A$ $60 \, kg$ passenger travels from the Earth to Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which curve in the figure best represents the weight (net gravitational force) of the passenger as a function of time?

$A$ satellite of mass $m$ is at a distance of $a$ from a star of mass $M$. The speed of the satellite is $u$. Suppose the law of universal gravity is $F = -G \frac{Mm}{r^{2.1}}$ instead of $F = -G \frac{Mm}{r^2}$. Find the speed of the satellite when it is at a distance $b$ from the star.

Suppose the acceleration due to gravity at the earth’s surface is $g \text{ m/s}^2$ and at the surface of the moon it is $g' \text{ m/s}^2$. An $M \text{ kg}$ passenger travels from the earth to the moon in a spaceship moving with a constant velocity. Neglecting all other celestial objects, which curve best represents the net gravitational force on the passenger as a function of time?

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)

Statement $(A)$ Two artificial satellites revolving in the same circular orbit have the same period of revolution.
Statement $(B)$ The orbital velocity is inversely proportional to the square root of the radius of the orbit.
Statement $(C)$ The escape velocity of a body is independent of the altitude of the point of projection.