The maximum and minimum distances of a comet from the sun are $8 \times 10^{12} \, m$ and $1.6 \times 10^{12} \, m$. If its velocity when nearest to the sun is $60 \, m/s$,what will be its velocity in $m/s$ when it is farthest?

$A$ satellite of mass $m$ is moving in a circular orbit of radius $r$ around the earth. The angular momentum of the satellite about the center of orbit is ($M=$ mass of earth,$G=$ gravitational constant).

$A$ satellite of the earth is revolving in a circular orbit with a uniform speed $v$. If the gravitational force suddenly disappears,the satellite will

$A$ comet orbits the Sun in a highly elliptical orbit. Does the comet have a constant $(a)$ linear speed,$(b)$ angular speed,$(c)$ angular momentum,$(d)$ kinetic energy,$(e)$ potential energy,$(f)$ total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

$A$ planet revolves around the Sun in an elliptical orbit. When it is closest to the Sun,its distance from the Sun is $d_1$ and its velocity is $v_1$. When it is farthest from the Sun,its distance from the Sun is $d_2$. What is its velocity at that point?

An artificial satellite is revolving around a planet of radius $R$ in a circular orbit of radius $a$. If the time period of revolution of the satellite $T \propto a^{3/2} g^x R^y$,then the values of $x$ and $y$ are respectively. [Note: $g$ is the acceleration due to gravity at the surface of the planet.]