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 dont 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.