An astronomical body's surface gravity 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. 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 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. Spectral lines reveal information regarding surface gravity: pressure broadening is pronounced by the higher density at the surface of a start with high surface gravity, and spectral lines tend to be narrower for giant stars and wider for dwarf stars. There are additional spectral signatures that can help, 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.