Two particles,each of mass $m$,are moving in a circle of radius $R$ under the influence of their mutual gravitational attraction. What is their speed?

If the height of a satellite from the surface of the Earth is increased,then its

$A$ solid sphere of radius $R$ gravitationally attracts a particle of mass $m$ placed at a distance of $3R$ from its centre with a force $F_{1}$. Now,a spherical cavity of radius $\frac{R}{2}$ is made in the sphere (as shown in the figure) such that the cavity is tangent to the centre of the sphere and the outer surface. The force on the particle becomes $F_{2}$. The value of $F_{1} : F_{2}$ is:

$A$ particle of mass $m$ moves in a circular orbit under the central potential field,$U(r) = -\frac{C}{r}$,where $C$ is a positive constant. The correct radius-velocity graph of the particle's motion is:

Inside a uniform spherical shell:
$(a)$ The gravitational field is zero.
$(b)$ The gravitational potential is zero.
$(c)$ The gravitational field is same everywhere.
$(d)$ The gravitational potential is same everywhere.
$(e)$ All of the above.
Choose the most appropriate answer from the options given below:

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