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

[Jaccobtw]

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 don't understand something fundamental. How can energy be negative? Thank you

 

[berkeman]

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

 

[doggydan42]

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.