Why Is Gravitational Energy Considered Negative?

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

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.