### surface gravity

(g)
(measure of gravity at the surface of a body)

An astronomical body's surface gravity (often indicated by the variable g) is the amount of gravity at the surface of the body, characterized by the resulting acceleration of an (unsupported) object at the surface, which is easily calculated from the body's mass and its radius, using the law of gravitation. (In effect, between mass, radius, and surface gravity, only two need be cited and all three are evident.) An averaged surface gravity might be cited for the body, or it may be cited as that of a particular point on the surface: differences can arise from rotation of the body as well as hills/valleys and density variations.

Surface gravity can be expressed in any units of acceleration and m/s² is common. It is also often expressed using a unit of acceleration termed a standard gravity (i.e., 9.80665 m/², a determination of the average surface gravity of Earth, also commonly abbreviated by g, which can confuse), so 274 m/s² could be expressed as "27.9 g". In astrophysics, it is also commonly expressed as the log base 10 of the acceleration in units of cm/s², indicated by log g, so 274 ms² could be cited as "log g = 2.44".

Surface gravity naturally requires a clear definition of the surface of the body, e.g., the outer surface of the photosphere of a star, and some kind of definition of the surface of any planet that is all gas, and some conventional definition for cases where the atmosphere is so deep, the depth reaching a hard surface is unknown. One convention is using the depth at which the atmospheric pressure is a bar. For black holes, an appropriate definition of acceleration within strong-field gravity also requires convention.

The law of gravitation provides a relation between the body's mass, radius and surface gravity, so determinations of any two reveal the third. For stars and extra-solar planets, determining a pair of these to any accuracy can be a substantial challenge. Accurate stellar mass determination is possible for some binary stars, after which case surface gravity determination is equivalent to stellar radius determination. The reverse, using determinations of radius and surface gravity to estimate the mass can assist in classifying objects as main sequence stars, versus brown dwarfs or planets. Spectral lines reveal information regarding surface gravity: pressure broadening is increased by the higher density at the surface of a star with high surface gravity, and spectral lines tend to be narrower for giant stars (low surface gravity) and wider for dwarf stars. Other spectral signatures assist, e.g., gravity-sensitive spectral lines. Stars (including brown dwarfs) change radius with age, so any means of determining surface gravity also assists in stellar age determination, another challenge.

(gravity,planets,stars,measure)