Two satellites $A$ and $B$ rotate around a planet in orbits having radii $4R$ and $R$ respectively. If the speed of satellite $A$ is $3V$,then the speed of satellite $B$ is: (in $V$)

Spaceman Fred's spaceship (which has negligible mass) is in an elliptical orbit about Planet Bob. The minimum distance between the spaceship and the planet is $R$; the maximum distance between the spaceship and the planet is $2R$. At the point of maximum distance,Spaceman Fred is traveling at speed $v_0$. He then fires his thrusters so that he enters a circular orbit of radius $2R$. What is his new speed?

The radius of a planet is $R$. $A$ satellite revolves around it in a circle of radius $r$ with angular velocity $\omega_0$. The acceleration due to gravity on the planet's surface is

$A$ body $A$ of mass $m$ is moving in a circular orbit of radius $R$ about a planet. Another body $B$ of mass $\frac{m}{2}$ collides with $A$ with a velocity which is half $\left(\frac{\overrightarrow{v}}{2}\right)$ the instantaneous velocity $\overrightarrow{v}$ of $A$. The collision is completely inelastic. Then,the combined body

Write the equation for the orbital velocity of a satellite revolving very close to the surface of the Earth.

The distance between two stars of masses $3 M_S$ and $6 M_S$ is $9 R$. Here $R$ is the mean distance between the centers of the Earth and the Sun,and $M_S$ is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period $n T$,where $T$ is the period of Earth's revolution around the Sun. The value of $n$ is. . . . .