Physical geodesy

Traditional geodetic instruments such as theodolites rely on the gravity field for orienting their vertical axis along the local plumb line or local vertical direction with the aid of a spirit level.

Levelling instruments again are used to obtain geopotential differences between points on the Earth's surface.

This also can be expressed (multiplying by the gravitational constant G in order to change units) as newtons per kilogram of attracted mass.

Travelling one metre in the direction of a gravity vector of strength 1 m·s−2 will increase your potential by 1 m2·s−2.

Again employing G as a multiplier, the units can be changed to joules per kilogram of attracted mass.

[2][3] It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude is given by the norm

In SI units, this acceleration is expressed in metres per second squared (in symbols, m/s2 or m·s−2) or equivalently in newtons per kilogram (N/kg or N·kg−1).

Near Earth's surface, the acceleration due to gravity, accurate to 2 significant figures, is 9.8 m/s2 (32 ft/s2).

This means that, ignoring the effects of air resistance, the speed of an object falling freely will increase by about 9.8 metres per second (32 ft/s) every second.

[4] This quantity is denoted variously as gn, ge (though this sometimes means the normal gravity at the equator, 9.7803267715 m/s2 (32.087686258 ft/s2)),[5] g0, or simply g (which is also used for the variable local value).

Technically, an equipotential surface of the true geopotential, chosen to coincide (on average) with mean sea level.

As mean sea level is physically realized by tide gauge bench marks on the coasts of different countries and continents, a number of slightly incompatible "near-geoids" will result, with differences of several decimetres to over one metre between them, due to the dynamic sea surface topography.

(This is an oversimplification; in practice the location in space at which γ is evaluated will differ slightly from that where g has been measured.)

Ocean basins mapped gravitationally. Seafloor features larger than 10 km are detected by resulting gravitational distortion of sea surface. (1995, NOAA )
Earth's gravity measured by NASA GRACE mission, showing deviations from the theoretical gravity of an idealized, smooth Earth, the so-called Earth ellipsoid . Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker ( Animated version ). [ 1 ]
Map of the undulation of the geoid in meters (based on the EGM96 )