Gravity well

A gravity well or gravitational well is a conceptual model of the gravitational field surrounding a body in space – the more massive the body, the deeper and more extensive the gravity well associated with it. The Sun is very massive, relative to other bodies in the Solar System, so the corresponding gravity well that surrounds it appears "deep" and far-reaching. The gravity wells of asteroids and small moons, conversely, are often depicted as very shallow. Anything on the surface of a planet or moon is considered to be at the bottom of that celestial body's gravity well, and so escaping the effects of gravity from such a planet or moon (to enter outer space) is sometimes called "climbing out of the gravity well". The deeper a gravity well is, the more energy any space-bound "climber" must use to escape it.

In astrophysics, a gravity well is specifically the gravitational potential field around a massive body. Other types of potential wells include electrical and magnetic potential wells. Physical models of gravity wells are sometimes used to illustrate orbital mechanics. Gravity wells are frequently confused with embedding diagrams used in general relativity theory, but the two concepts are distinctly separate, and not directly related.

If G is the universal gravitational constant (G = 6.67×10⁻¹¹ m³ kg⁻¹ s⁻²), the external gravitational potential of a spherically symmetric body of mass M is given by the formula:

A plot of this function in two dimensions is shown in the figure. This plot has been completed with an interior potential proportional to |x|², corresponding to an object of uniform density, but this interior potential is generally irrelevant since the orbit of a test particle cannot intersect the body.

The potential function has a hyperbolic cross section; the sudden dip in the center is the origin of the name "gravity well". A black hole would not have this "closing" dip due to its size being only determined by its event horizon.

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