During the motion of a planet from perihelion to aphelion,the work done by the gravitational force of the sun on it is ...........

Particles of masses $m, 2m, 3m$ and $4m$ are placed at the corners of a square of side $a$. What is the net gravitational force on a particle of mass $m$ placed at the center?

Which of the following astronomers first proposed that the Sun is static and the Earth revolves around the Sun?

$A$ satellite is orbiting the Earth at a height $h$ above the surface (where $R$ is the radius of the Earth and $h \ll R$). What is the minimum increase in the orbital velocity required for the satellite to escape the Earth's gravitational field? (Ignore the effect of the atmosphere.)

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:

Weighing the Earth: You are given the following data: $g = 9.81 \; m/s^2$, $R_E = 6.37 \times 10^6 \; m$, the distance to the moon $R = 3.84 \times 10^8 \; m$, and the time period of the moon's revolution is $27.3$ days. Obtain the mass of the Earth $M_E$ in two different ways.