Question

What does negative sign in total energy of satellite signify ?

Answer 1

Dear Student

The reason is due to the potential energy term which is a negative one.
The general expression for gravitational potential energy arises from the law of gravity and is equal to the work done against gravity to bring a mass to a given point in space. The gravitational potential energy near a planet is then negative, since gravity does positive work as the mass approaches. This negative potential is indicative of a "bound state"; once a mass is near a large body, it is trapped until something can provide enough energy to allow it to escape.

Expression for kinetic energy and potential energy of satellite can be given as
$$\begin{gathered} K.E.=\frac{GmM}{2\left(R+h\right)} \\ P.E.=-\frac{GmM}{\left(R+h\right)} \\ Sototalenergy \\ T.E.=-\frac{GmM}{2\left(R+h\right)} \end{gathered}$$

As we know that the total energy of a body is positive or zero, when it is at infinity from the earth. Therefore, the satellite will escape to infinity if its total energy becomes zero or positive.
Since, the satellite is always at finite distance from the earth, its total energy can never be positive or zero.

Regards