The relative uncertainty in the period of a satellite orbiting around the Earth is $10^{-2}$. If the relative uncertainty in the radius of the orbit is negligible,the relative uncertainty in the mass of the Earth is:

Two satellites $s_1$ and $s_2$ of equal masses revolve in the same sense around a heavy planet in coplanar circular orbits of radii $R$ and $4R$. Which of the following statements is correct?

$A$ particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a.$ The magnitude of the gravitational potential at a point situated at $a/2$ distance from the centre,will be

Four particles,each of mass $M$ and equidistant from each other,move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is

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

$A$ body of mass $m$ is moving in a circular orbit of radius $R$ about a planet of mass $M$. At some instant,it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$,and the other mass moves in a circular orbit of radius $\frac{3R}{2}$. The difference between the final and initial total energies is