When a satellite going round the Earth in a circular orbit of radius $r$ and speed $v$ loses some of its energy,then $r$ and $v$ change as:

What is the binding energy of a satellite? Write its equation.

$A$ star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let $r$ be the distance of the body from the centre of the star and let its linear velocity be $v$,angular velocity $\omega$,kinetic energy $K$,gravitational potential energy $U$,total energy $E$ and angular momentum $l$. As the radius $r$ of the orbit increases,determine which of the above quantities increase and which ones decrease.

Obtain an expression for the total energy of a satellite revolving around the Earth.

$A$ launching vehicle carrying an artificial satellite of mass $m$ is set for launch on the surface of the earth of mass $M$ and radius $R$. If the satellite is intended to move in a circular orbit of radius $7R$,the minimum energy required to be spent by the launching vehicle on the satellite is ($G$ is the gravitational constant).

$A$ particle of mass $m$ moves in a horizontal circle of radius $r$ under the influence of a centripetal force given by $F = -k/r^2$,where $k$ is a constant. Calculate the total energy of the particle.