Every planet revolves around the sun in an elliptical orbit :

$A.$ The force acting on a planet is inversely proportional to square of distance from sun.

$B.$ Force acting on planet is inversely proportional to product of the masses of the planet and the sun

$C.$ The centripetal force acting on the planet is directed away from the sun.

$D.$ The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.

Choose the correct answer from the options given below :

The planet Mars has two moons, phobos and delmos.

$(i)$ phobos has a period $7$ hours, $39$ minutes and an orbital radius of $9.4 \times 10^{3} \;km .$ Calculate the mass of mars.

$(ii)$ Assume that earth and mars move in circular orbits around the sun. with the martian orbit being $1.52$ times the orbital radius of the earth. What is the length of the martian year in days?

A planet is moving in an elliptical orbit around the sun. If $T, V, E$ and $L$ stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct ?

The time period of a satellite of earth is $24$ hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become $…….\,hours$

The relative uncertainty in the period of a sateilite 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