$A$ 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).

Two satellites $S_{1}$ and $S_{2}$ are revolving around a planet in the opposite sense in coplanar circular concentric orbits. At time $t=0$,the satellites are farthest apart. The periods of revolution of $S_{1}$ and $S_{2}$ are $3 \,h$ and $24 \,h$,respectively. The radius of the orbit of $S_{1}$ is $3 \times 10^{4} \,km$. Then,the orbital speed of $S_{2}$ as observed from

$A$ 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 the star is proportional to $r^{-3/2}$,then the square of the time period is proportional to

$A$ planet of mass $m$ moves in an ellipse around the sun of mass $M_S$ such that its maximum and minimum distances are $r_1$ and $r_2$ respectively. The angular momentum of the planet relative to the center of the sun is

Describe the method for drawing an ellipse and explain the foci of an ellipse,midpoint,and semi-major axis.

$A$ satellite of mass $\frac{M}{2}$ is revolving around the Earth in a circular orbit at a height of $\frac{R}{3}$ from the Earth's surface. The angular momentum of the satellite is $M \sqrt{\frac{GMR}{x}}$. The value of $x$ is . . . . . . ,where $M$ and $R$ are the mass and radius of the Earth,respectively. ($G$ is the gravitational constant)