Gravity well......The path of light
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.
Both the rigid gravity well and the rubber-sheet model are frequently misidentified as models of general relativity, due to an accidental resemblance to general relativistic embedding diagrams,[citation needed] and perhaps Einstein's employment of gravitational "curvature" bending the path of light, which he described as a prediction of general relativity. In particular, the embedding diagram most commonly found in textbooks (an isometric embedding of a constant-time equatorial slice of the Schwarzschild metric in Euclidean 3-dimensional space) superficially resembles a gravity well.
Embedding diagrams are, however, fundamentally different from gravity wells in a number of ways. Most importantly, an embedding is merely a shape, while a potential plot has a distinguished "downward" direction; thus turning a gravity well "upside down" (by negating the potential) turns the attractive force into a repulsive force, while turning a Schwarzschild embedding upside down (by rotating it) has no effect, since it leaves its intrinsic geometry unchanged. Geodesics following across the Schwarzschild surface would bend toward the central mass like a ball rolling in a gravity well, but for entirely different reasons. There is no analogue of the Schwarzschild embedding for a repulsive field: while such a field can be modeled in general relativity, the spatial geometry cannot be embedded in three dimensions.[citation needed]
The Schwarzschild embedding is commonly drawn with a hyperbolic cross section like the potential well, but in fact it has a parabolic cross section which, unlike the gravity well, does not approach a planar asymptote. See Flamm's paraboloid
Gravity well......The path of light
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.
Both the rigid gravity well and the rubber-sheet model are frequently misidentified as models of general relativity, due to an accidental resemblance to general relativistic embedding diagrams,[citation needed] and perhaps Einstein's employment of gravitational "curvature" bending the path of light, which he described as a prediction of general relativity. In particular, the embedding diagram most commonly found in textbooks (an isometric embedding of a constant-time equatorial slice of the Schwarzschild metric in Euclidean 3-dimensional space) superficially resembles a gravity well.
Embedding diagrams are, however, fundamentally different from gravity wells in a number of ways. Most importantly, an embedding is merely a shape, while a potential plot has a distinguished "downward" direction; thus turning a gravity well "upside down" (by negating the potential) turns the attractive force into a repulsive force, while turning a Schwarzschild embedding upside down (by rotating it) has no effect, since it leaves its intrinsic geometry unchanged. Geodesics following across the Schwarzschild surface would bend toward the central mass like a ball rolling in a gravity well, but for entirely different reasons. There is no analogue of the Schwarzschild embedding for a repulsive field: while such a field can be modeled in general relativity, the spatial geometry cannot be embedded in three dimensions.[citation needed]
The Schwarzschild embedding is commonly drawn with a hyperbolic cross section like the potential well, but in fact it has a parabolic cross section which, unlike the gravity well, does not approach a planar asymptote. See Flamm's paraboloid