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

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 $\mathrm{R}$; the maximum distance between the spaceship and the planet is $2\mathrm{R}$. 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 $2\mathrm{R}$. What is his new speed?

Assuming potential energy '$U$' at ground level to be zero.

All objects are made up of same material:-

$U_P=$Potential energy of solid sphere

$U_Q=$Potential energy of solid cube

$U_R=$Potential energy of solid cone

$U_S=$Potential energy of solid cylinder