The solar constant on the surface of the earth is $S$. What will be its value on the surface of another planet which is about $5.3 \, AU$ away from the sun?

Three point masses,each of mass $m$,are kept at the corners of an equilateral triangle of side $L$. The system rotates about the center of the triangle. The period of rotation $T$ is directly proportional to:

$A$ satellite is revolving in a circular orbit at a height $h$ from the Earth's surface,such that $h \ll R$,where $R$ is the radius of the Earth. Assuming that the effect of the Earth's atmosphere can be neglected,the minimum increase in the speed required so that the satellite could escape from the gravitational field of the Earth is:

State whether the following statements are true or false:
$(a)$ The value of '$g$' is slightly less at the poles than at the equator.
$(b)$ The unit $\text{Newton/kilogram}$ $(N/kg)$ is also a unit of acceleration due to gravity.
$(c)$ The escape velocity $v_e$ for a stationary object on the surface of a planet is directly proportional to the mass and radius of the planet.

Answer the following:
$(a)$ You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
$(b)$ An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size,can he hope to detect gravity?
$(c)$ If you compare the gravitational force on the earth due to the sun to that due to the moon,you would find that the Sun's pull is greater than the moon's pull. However,the tidal effect of the moon's pull is greater than the tidal effect of the sun. Why?

$A$ planet is moving in an elliptical orbit around the sun. The work done on the planet by the gravitational force of the sun:
$(i)$ is zero in no part of the motion.
(ii) is zero in some parts of the orbit.
(iii) is zero in one complete revolution.
(iv) is zero in any small part of the orbit.
Which of the following is true?