The motion of planets in the solar system is an example of the conservation of

If $\rho$ is the density of the planet,the time period of a nearby satellite is given by

$A$ satellite of mass $m$ revolves around the Earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the Earth,the orbital speed of the satellite is:

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?

$A$ planet moving along an elliptical orbit is closest to the sun at a distance $r_1$ and farthest away at a distance of $r_2$. If $v_1$ and $v_2$ are the linear velocities at these points respectively,then the ratio $\frac{v_1}{v_2}$ is

An artificial satellite revolves around a planet for which gravitational force $(F)$ varies with distance $r$ from its centre as $F \propto r^2$. If $v_0$ is its orbital speed,then