## Basic measurement units

**Gravity, g**

g is the symbol for the average acceleration produced by gravity at the Earth's surface (sea level). The actual acceleration of gravity varies from place to place, depending on latitude, altitude, and local geology. The symbol g is often used informally as a unit of acceleration. By agreement among physicists, the standard acceleration of gravity g_{n} is defined to be exactly 9.80665 meters per second per second (m s^{-2)}, or about 32.174 05 feet per second per second. At latitude p, a conventional value of the acceleration of gravity at sea level is given by the **International Gravity Formula,** g = 978.0495 [1 + 0.0052892 sin^{2}*(p)* - 0.0000073 sin^{2} (2*p*)] centimetres per second per second (cm s^{-2}). The symbol g was used as a unit first in aeronautical and space engineering, where it is important to limit the accelerations experienced by the crew members of aircraft and spaceships: the "g forces," as they are called. This use became familiar through the space programs, and now a variety of accelerations are measured in g's. Note that g is also the symbol for the gram.

**Galileo (Gal or gal)**

The Gal unit is used in making measurements of local variations in the acceleration of gravity g. Variations in the acceleration of Earth’s gravity (i.e. *gravity anomalies*) are typically measured in milligals (mGal). One Gal is approximately 0.0010197g, so a milligal (or mGal) is a very small acceleration, of about 10^{-6} *g* (or 10^{–5} m s^{-2}). The mean Earth gravity is about 981 000 mGal (the well-known 9.81 *m/s ^{2}*), varies from 978,100 mGal to 983,200 mGal from Equator to pole due to the Earth's flattening and rotation. Variations, due to density inhomogeneities, mountain ridges, etc., range from

*tens to hundreds of milligals.*The unit is named after the Italian astronomer and natural philosopher Galileo Galilei, who lived from 1564 until 1642. Galileo proved that all objects at the Earth's surface experience the same gravitational acceleration.

(*Note: to avoid confusion with the symbol for the gallon, and to conform to the usual metric style, the symbol for this unit should be Gal rather than gal).

**Eötvös (E)**

The *Eötvös* unit is used in geophysics to measure the rate of change, or gradient in the acceleration of gravity with horizontal distance. One *Eötvös* equals 10^{-7} Gal per metre or 10^{-4} Gal per kilometer. In proper SI units, the *Eötvös* unit equals 10^{-9} per second squared (s^{-2}). The largest component is the vertical gravity gradient, being about 3000 *E* on Earth *(gravity changes by 3.10 ^{-6}m/s^{2} per metre of elevation)*. The horizontal components are approximately half this size; mixed gradients are below 100

*E*for the normal field. Gravity-gradient anomalies can be much larger and reach 1000

*E*in mountainous area. This unit is named after the Hungarian physicist Roland von Eötvös who lived from 1848 until 1919.

**Hertz (Hz)**

Hertz is the SI unit of frequency, equal to one cycle per second. The hertz is used to measure the rates of events that happen periodically in a fixed and definite cycle. Multiples of the hertz are common: the frequencies of radio and television waves are measured in kilohertz (kHz), megahertz (MHz), or even gigahertz (GHz), and the frequencies of light waves in terahertz (THz). The unit is named after the German physicist Heinrich Rudolf Hertz (1857-1894), who proved in 1887 that energy is transmitted through a vacuum by electromagnetic waves.

**Units Conversion**

g ≈ 9.8 m s^{-2}

1 Gal ≈ 0.001 g ≈ 10^{-2} m s^{-2}

1 mGal ≈ 10^{-6} g ≈ 10^{-5} m s^{-2}

1 E ≈ 10^{-10} g m^{-1} ≈ 10^{-7} Gal m^{-1} ≈ 10^{-9} s^{-2}

1 mE ≈ 10^{-12} s^{-2}

Last update: 26 May 2010

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