Gravitational potential energy

When dealing with potential energy changes involving a gravitational system, zero potential energy represents the state of the objects when they are infinitely far apart. All other values are negative. The two masses have fallen together into a well of their mutual binding energy.

As we discussed earlier within Newton's Laws, there are two main types of gravity problems, those in which the gravitational force is virtually constant over the distances involved and those in which the gravitational force changes with varying position within the system.

Each of these different models has a different approach to energy. The manner of describing changes in energy is different in a constant force system versus a system where force changes with position.

In both cases, however, as work is done against or by the field, as the object is changing position, its state of potential energy is changing. As two attracting objects are moved further apart, the potential energy of the system increases whether an object is being raised from the surface of the Earth or whether two objects are separating in outer space.

On the surface of the Earth, where the distances over which the object is going to move will be relatively small, it is more convenient to assign zero as the potential energy on the ground.

For situations in outer space, however, where the force can be seen to decrease the further apart the objects are moved, zero potential energy represents the state of the objects when they are infinitely far apart. All other values are negative. Think about this. Make sure you understand this.

In both cases, potential energy increases with increasing separation, and if you applied the outer space model to the object near the Earth's surface, you would compute the same change in energy. The outer space model is the more descriptive of reality, because it shows gravitational potential energy as a form of binding energy. Two objects under the influence of mutual gravitation have fallen into a potential energy well together. They have fallen together into the well of their mutual binding energy. The magnitude of negative potential energy shows how much energy would have to be imparted to the system to allow the objects to escape from each other.

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