Question

What is the meaning negative sign in the energy of an orbit equation indicates?

Answer 1

The significance of negative sign in the Total Energy of the electron in an atom or an object in a potential field like Gravitational Potential, means that it is Bounded.

For instance the total energy of an electron in a coulomb potential calculated by Bohr for the Hydrogen atom is E = -13.6/n>2 eV this is valid for any bound system if the potential energy taken to be zero atinfinity

Implies that the electron is bounded to the nucleus, we have to supply sufficient Energy in a particular orbit to free the electron from the potential field.

If a planet is orbiting around a star, will have a potential energy U = -GMm/r

and KE will be = 1/2 m v>2

and the total Energy will be = - GMm/2r

means that the planet is bounded to the star.

If we want to free the planet from star’s Gravitational field we have to supply the equal amount of energy.