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

The correct graph representing the variation of total energy $(E_t)$,kinetic energy $(E_k)$,and potential energy $(U)$ of a satellite with its distance $(r)$ from the centre of the Earth is:

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)

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

The mass density of a spherical body is given by $\rho(r) = \frac{k}{r}$ for $r \leq R$ and $\rho(r) = 0$ for $r > R$,where $r$ is the distance from the centre. The correct graph that describes qualitatively the acceleration,$a$,of a test particle as a function of $r$ 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.