$A$ planet of mass $m$ is moving around a star of mass $M$ and radius $R$ in a circular orbit of radius $r$. The star abruptly shrinks to half its radius without any loss of mass. What change will be there in the orbit of the planet?

$A$ small planet is revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force between the planet and the star were proportional to $R^{-5/2}$,then $T$ would be proportional to:

The periodic time of a communication satellite is ......... $hours$.

If $L$ is the angular momentum of a satellite revolving around the Earth in a circular orbit of radius $r$ with speed $v$,then .........

$A$ satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius $R_e$. By firing rockets attached to it,its speed is instantaneously increased in the direction of its motion so that it becomes $\sqrt{\frac{3}{2}}$ times larger. Due to this,the farthest distance from the centre of the earth that the satellite reaches is $R$. The value of $R$ is $....R_e$.

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. For a satellite orbiting at an altitude of half the earth's radius above the surface,the orbital velocity is: