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

• Jaccobtw
In summary, potential energy is measured relative to a reference point, which can be positive, negative, or zero. This means that the energy itself can also be negative, as in the case of a star-satellite system where the potential energy is defined based on a reference point at infinite separation. The concept of potential energy is based on changes between two points, and the choice of reference point does not change the overall energy.
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
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It sounds like the book is contradicting itself or I just don't understand something fundamental. How can energy be negative? Thank you

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

Jaccobtw and DaveE
Jaccobtw said:
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.

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Jaccobtw and DaveE

## 1. Can energy be negative?

No, energy cannot be negative. Energy is a measure of the ability to do work or cause change, and it is always positive. Negative energies do not exist in physics.

## 2. Can just a change in energy be negative?

Yes, a change in energy can be negative. According to the law of conservation of energy, energy can be transferred or transformed, but it cannot be created or destroyed. This means that the total amount of energy in a closed system remains constant, but the distribution of energy within the system can change, resulting in a negative change in energy for some components.

## 3. What does it mean for energy to be negative?

As previously mentioned, energy cannot be negative. However, in some mathematical equations, a negative sign is used to represent the direction of energy transfer. For example, if energy is being transferred out of a system, it is assigned a negative value, while energy being transferred into a system is assigned a positive value.

## 4. Can negative energy be used to do work?

No, negative energy cannot be used to do work. Negative energy is a mathematical concept used to represent the direction of energy transfer, but it does not have any physical meaning. In order for work to be done, energy must have a positive value.

## 5. Are there any examples of negative energy?

No, negative energy does not exist in the physical world. However, there are some theoretical concepts in physics, such as negative mass or negative pressure, which may be described using negative energy in equations. But these are still just mathematical concepts and do not have any physical manifestation.

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