# Can energy be negative or can just a change in energy be negative?

## Homework Statement:

I'm reading my text book about the gravitational potential energy of a satellite-star system. It says 'The mechanical energy of a star-satellite system can be negative because gpe is always negative when we let the gpe be zero at infinite separation.

## Relevant Equations:

None
It sounds like the book is contradicting itself or I just dont understand something fundamental. How can energy be negative? Thank you

berkeman
Mentor
Potential energy is relative to some datum, so it can be positive, negative or zero.

• Jaccobtw and DaveE
It says 'The mechanical energy of a star-satellite system can be negative because gpe is always negative when we let the gpe be zero at infinite separation.
Potential energy is defined based on a reference point. So you are really looking at a change in potential energy. For example, if you simply look at a potential energy like ##U(x) = mgx##. This comes from letting U(0)=0 be a reference point. If you let U(h) = 0, then ##U(x) = mg(x-h)##. But if you look at the change in potential energy from two points, the second definition will give ##U(h_2)-U(h_1)=mg(h_2-h)-mg(h_1-h)=mgh_2-mgh_1##, which is consistent with the change in potential energy of the first point.

For gravitational potential energy, it is easiest to let the reference point be at ##x\rightarrow \infty##, since it gives you an additional zero instead of a constant.

Last edited:
• Jaccobtw and DaveE