A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is ${R_0}$ and mass of the earth M, the angular momentum about the centre of the earth is
$m\sqrt {GM{R_0}} $
$M\sqrt {Gm{R_0}} $
$m\sqrt {\frac{{GM}}{{{R_0}}}} $
$M\sqrt {\frac{{GM}}{{{R_0}}}} $
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?
During motion of a planet from perihelion to aphelion the work done by gravitational force of sun on it is ...........
If the earth is at one-fourth of its present distance from the sun, the duration of the year will be
Which of the following quantities does not depend upon the orbital radius of the satellite
If $r$ denotes the distance between the sun and the earth, then the angular momentum of the earth around the sun is proportional to