Why Is Gravitational Energy Considered Negative?

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Discussion Overview

The discussion centers on the concept of gravitational energy being considered negative, particularly in relation to gravitational potential energy and its implications. Participants explore the theoretical underpinnings, mathematical formulations, and conventions surrounding gravitational energy, as well as potential analogies with other forces.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants clarify that gravitational potential energy is defined as negative, such as in the formula -GMm/r, and explain that this is due to the convention of setting the potential energy at an infinite distance to zero.
  • One participant argues that the absence of gravitational pull does not imply the absence of gravitational potential energy, suggesting that potential energy is relative to a reference point.
  • Another participant provides an analogy with magnets to illustrate the concept of negative potential energy, explaining that work done on a system is considered positive while work done by a system is negative.
  • A separate viewpoint introduces the idea of "antigravity" related to vacuum energy and its implications for cosmic phenomena, although this is questioned for its relevance to the main topic.
  • Some participants express confusion about the relevance of certain points to the original question regarding gravitational potential energy.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of gravitational potential energy and its conventions. There is no consensus on the implications of gravitational potential energy being negative, and some arguments remain contested.

Contextual Notes

Participants reference mathematical formulations and conventions that may depend on specific definitions and assumptions, which are not fully resolved in the discussion.

Jack
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What is meant by the theory/fact that gravitational energy is negative?

I would have thought that this would mean that gravity would cause objects to be repeled from each other
 
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Are you referring to the fact that gravitational potential energy is considered to thave a negative value, such as -GMm/r?

If so, the reasoning goes like this.

The total energy of a mass in a gravitational field is equal to the sum of its kinetic energy and its gravitaitonal energy with respect to the gravity field.

Any mass in free-fall has a constant total energy. (it just trades off kinetic energy for gravitational energy, or vice-versa)

An object moving at exactly escape velocity is considered to have zero total energy.(an object tossed up at escape velocity won't slow to a stop until it is an infinite distance away. conversely, escape velocity is equal to the velocity an object would hit the surface of a planet, if it were dropped from an infinite distance and at rest with respect to the planet.

If an object is at rest, it has zero kinetic energy. If it is an infinite disatnce away, it feels no gravitational pull from the planet, so it has zero gravitational potential with respect to the planet.
Zero + zero = zero total energy.

As the object moves towards the planet, it gains kinetic energy. in order for the total energy to remain constant, the Gravitational potential must decrease by the same amount. Since it starts at zero, it must go negative as you near the planet.

The mathematical reason is that to get gravitational potential, you integrate the formula for gravitational force (f= GMm/r²) with respect to r and get -GMm/r.
 
Just some comments
Originally posted by Janus
If an object is at rest, it has zero kinetic energy. If it is an infinite disatnce away, it feels no gravitational pull from the planet, so it has zero gravitational potential with respect to the planet.
Zero + zero = zero total energy.
I think that this is not quite right (the bolded text).
Please correct me if i am wrong, but the absense of gravitational pull does not mean the absense of gravitational potential energy.
Since the gravitational potential energy is compared to a refference point, it is likely to have an object that is not being affected by a gravitational energy, but still has gravitational potential energy.
But ...
It is conventional to take infinity as a refference point for gravitational potential energy, therefore we say that the object has Zero potential energy at infinity.

(so .. am i right ?)
 
Potential energy is negative by convention. We assume that gravitational potential of a body at infinite distance is zero.

You can think of this fairly easily with a couple of magnets -- for the purpose of this discussion the magnetic attraction is just like gravity.

When the magnets are far apart (in the ideal case, infinitely far apart), you declare that the potential energy between them is zero. (You're free to assign the zero anywhere you'd like.)

Now bring the magnets together. When you pull the magnets apart, you have to do work. Physicists, by convention, say that work done ON a system is positive, and work done BY a system is negative. In this case, to pull the magnets apart, you have to put in energy, so you have to do positive work.

Think about that for a second: when the magnets are separated, they have zero potential energy. If they are together, you have to add energy to get them back apart. If you have to add energy to get back to zero (separated), then the magnets must have negative potential energy when they're together.

- Warren
 
There is purported to be an "antigravity" propelled by the vacuum energy of space. This accounts for the accelerative repulsion between distant galaxies, and an eventual "heat death" of the universe. The "cosmological constant" introduced ~1920 by Einstein was more wonder than blunder, as it now suggests one possible mathematical model for this phenomenon.
 
Originally posted by Loren Booda
There is purported to be an "antigravity" propelled by the vacuum energy of space. This accounts for the accelerative repulsion between distant galaxies, and an eventual "heat death" of the universe. The "cosmological constant" introduced ~1920 by Einstein was more wonder than blunder, as it now suggests one possible mathematical model for this phenomenon.
What does this have to do with the definition of gravitational potential energy?

- Warren
 
The original post mentions nothing about gravitational potential energy.
 

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