$A$ 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.

Two identical particles of mass $1 \, kg$ each go round a circle of radius $R$,under the action of their mutual gravitational attraction. The angular speed of each particle is:

Four identical particles of equal masses $m = 1 \, kg$ are made to move along the circumference of a circle of radius $R = 1 \, m$ under the action of their own mutual gravitational attraction. The speed of each particle will be

$(a)$ Earth can be thought of as a sphere of radius $6400 \, km$. Any object (or a person) is performing circular motion around the axis of the Earth due to the Earth's rotation (period $1 \, \text{day}$). What is the acceleration of an object on the surface of the Earth (at the equator) towards its centre? What is it at latitude $\theta$? How do these accelerations compare with $g = 9.8 \, m/s^2$?
$(b)$ The Earth also moves in a circular orbit around the Sun once every year with an orbital radius of $1.5 \times 10^{11} \, m$. What is the acceleration of the Earth (or any object on the surface of the Earth) towards the centre of the Sun? How does this acceleration compare with $g = 9.8 \, m/s^2$?

The ratio of the $K.E.$ required to be given to a satellite to escape Earth's gravitational field to the $K.E.$ required to be given so that the satellite moves in a circular orbit just above Earth's atmosphere is:

Which of the following symptoms is likely to afflict an astronaut in space? $(a)$ Swollen feet,$(b)$ Swollen face,$(c)$ Headache,$(d)$ Orientational problem.