In physics, and specifically with respect to the theory of general relativity, a gravity well is a distortion in space-time caused by a massive body such as a planet or star. The term is a reference to the 3-dimensional analogy of this phenomenon: an extrusion of an otherwise 2-dimensional sheet. An actual gravity well involves higher-dimensional bending.
The "depth" of a gravity well corresponds to the Δv required to leave -- also known as the escape velocity. Deeper wells require more Δv, and so it is harder for a rocket to escape from them (or to stop at the bottom). Deeper wells also tend to make for more efficient gravitational slingshots.
Because both space and time are altered in a gravity well, not only are objects attracted towards it, but time slows in its presence due to the effect of special relativity. This effect is more pronounced as the gravity well gets larger or one proceeds closer to its center.
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