Question

It was stated that a satellite with negative total energy is in a bound orbit, whereas one with zero or positive total energy is in an unbounded orbit. Why is this true? What choice for gravitational potential energy was made such that this is true?

Answer 1

The statement is true because of the relationship between kinetic and gravitational potential energy. A negative total energy indicates a bound orbit, while zero or positive total energy indicates an unbounded orbit.

Step-by-step explanation:

The statement that a satellite with negative total energy is in a bound orbit, while one with zero or positive total energy is in an unbounded orbit, is true because of the relationship between kinetic and gravitational potential energy. In orbital motion, the total energy of a system is the sum of these two energies, and this total energy is conserved.

If the total energy is negative, it means the kinetic energy is greater than the gravitational potential energy, which indicates a bound orbit. On the other hand, if the total energy is zero or positive, it means the gravitational potential energy is equal to or greater than the kinetic energy, leading to an unbounded orbit.