- Newton's Law of Gravity
- Gravitational Fields
- Gravitational Potential Energy
- Gravity, Quantum Physics, & General Relativity
We define the gravitational potential energy, U, such that W = U1 - U2. This yields the equation to the right, for the Earth (with mass mE. In some other gravitational field, mE would be replaced with the appropriate mass, of course.
Gravitational Potential Energy on EarthOn the Earth, since we know the quantities involved, the gravitational potential energy U can be reduced to an equation in terms of the mass m of an object, the acceleration of gravity (g = 9.8 m/s), and the distance y above the coordinate origin (generally the ground in a gravity problem). This simplified equations yields a gravitational potential energy of:
U = mgy
There are some other details of applying gravity on the Earth, but this is the relevant fact with regards to gravitational potential energy.
Notice that if r gets bigger (an object goes higher), the gravitational potential energy increases (or becomes less negative). If the object moves lower, it gets closer to the Earth, so the gravitational potential energy decreases (becomes more negative). At an infinite difference, the gravitational potential energy goes to zero. In general, we really only care about the difference in the potential energy when an object moves in the gravitational field, so this negative value isn't a concern.
This formula is applied in energy calculations within a gravitational field. As a form of energy, gravitational potential energy is subject to the law of conservation of energy.