A satellite is in a circular equatorial orbit of radius $7000\,km$ around the Earth. If it is transferred to a circular orbit of double the radius then its angular momentum will be

If the distance of the earth from Sun is $1.5 \times 10^6\,km$. Then the distance of an imaginary planet from Sun, if its period of revolution is $2.83$ years is $.............\times 10^6\,km$

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?

Kepler's third law states that square of period of revolution $(T)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet i.e.

$\therefore \;{T^2} = k{r^3}$

here $K$ is constant.

If the masses of sun and planet are $M$ and $m$ respectively then as per Newton's law of gravitation force of attraction between them is $F = \frac{{GMm}}{{{r^2}}}$ , here $G$ gravitational constant . The relation between $G$ and $K$ is described as

Kepler's second law (law of areas) is nothing but a statement of

A planet is revolving around the sun in a circular orbit with a radius $r$. The time period is $T$. If the force between the planet and star is proportional to $r^{-3 / 2}$, then the square of time period is proportional to