In a satellite if the time of revolution is $T$, then $P E$ is proportional to ..........

A satellite of mass $m$ is at a distance $a$ from $a$ star of mass $M$. The speed of satellite is $u$. Suppose the law of universal gravity is $F =  - G\frac{{Mm}}{{{r^{2.1}}}}$  instead of $F =  - G\frac{{Mm}}{{{r^2}}}$, find the speed of the statellite when it is at $a$ distance $b$ from the star.

If the acceleration due to gravity at earth is $'g'$ and mass of earth is $80$ times that of moon and radius of earth is $4$ times that of moon, the value of acceleration due to gravity at the surface of moon will be

A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth

A satellite of mass $m$ is in a circular orbit of radius $2R_E$ about the earth. The energy required to transfer it to a circular orbit of radius $4R_E$ is (where $M_E$ and $R_E$ is the mass and radius of the earth respectively)

A body of mass $m$ is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is

where $g$ is acceleration due to gravity at the surface of earth.