The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in order not to disturb the system, has negligible mass.
Surface gravity is measured in units of acceleration, which, in the SI system, are meters per second squared.
The surface gravity of a white dwarf is very high, and of a neutron star even higher.
One measure of such immense gravity is that neutron stars have an escape velocity of around 100,000 km/s, about a third of the speed of light.
Generally speaking, this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space.
A large object, such as a planet or star, will usually be approximately round, approaching hydrostatic equilibrium (where all points on the surface have the same amount of gravitational potential energy).
On a large scale, the planet or star itself deforms until equilibrium is reached.
[4] For most celestial objects, the result is that the planet or star in question can be treated as a near-perfect sphere when the rotation rate is low.
Examples of such rapidly rotating stars include Achernar, Altair, Regulus A and Vega.
The fact that many large celestial objects are approximately spheres makes it easier to calculate their surface gravity.
According to the shell theorem, the gravitational force outside a spherically symmetric body is the same as if its entire mass were concentrated in the center, as was established by Sir Isaac Newton.
[5] Therefore, the surface gravity of a planet or star with a given mass will be approximately inversely proportional to the square of its radius, and the surface gravity of a planet or star with a given average density will be approximately proportional to its radius.
[7][8] Gravity on such a planet's surface would be approximately 2.2 times as strong as on Earth.
Without using the Earth as a reference body, the surface gravity may also be calculated directly from Newton's law of universal gravitation, which gives the formula
so that, for fixed mean density, the surface gravity g is proportional to the radius r. Solving for mass, this equation can be written as
But density is not constant, but increases as the planet grows in size, as they are not incompressible bodies.
For gas giant planets such as Jupiter, Saturn, Uranus, and Neptune, the surface gravity is given at the 1 bar pressure level in the atmosphere.
This causes stars and planets to be oblate, which means that their surface gravity is smaller at the equator than at the poles.
This fact has been put to practical use since 1915–1916, when Roland Eötvös's torsion balance was used to prospect for oil near the city of Egbell (now Gbely, Slovakia.
)[13]: 1663 [14]: 223 In 1924, the torsion balance was used to locate the Nash Dome oil fields in Texas.
[14]: 223 It is sometimes useful to calculate the surface gravity of simple hypothetical objects which are not found in nature.
In relativity, the Newtonian concept of acceleration turns out not to be clear cut.
For a black hole, which must be treated relativistically, one cannot define a surface gravity as the acceleration experienced by a test body at the object's surface because there is no surface, although the event horizon is a natural alternative candidate, but this still presents a problem because the acceleration of a test body at the event horizon of a black hole turns out to be infinite in relativity.
For the Schwarzschild case, this value is mathematically well behaved for all non-zero values of r and M. When one talks about the surface gravity of a black hole, one is defining a notion that behaves analogously to the Newtonian surface gravity, but is not the same thing.
In fact, the surface gravity of a general black hole is not well defined.
is a suitably normalized Killing vector, then the surface gravity is defined by
, the linear combination of the time translation and axisymmetry Killing vectors which is null at the horizon, where
[15] The surface gravity for the uncharged, rotating black hole is, simply
[17] Recently there has been a shift towards defining the surface gravity of dynamical black holes whose spacetime does not admit a timelike Killing vector (field).
[20] Semiclassical results indicate that the peeling surface gravity is ill-defined for transient objects formed in finite time of a distant observer.