Gravity of Earth

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]

The gravity of Earth, denoted by g, is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation).[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. This quantity is sometimes referred to informally as little g (in contrast, the gravitational constant G is referred to as big G).

The precise strength of Earth's gravity varies with location. The agreed upon value for standard gravity is 9.80665 m/s2 (32.1740 ft/s2) by definition.[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).

The weight of an object on Earth's surface is the downwards force on that object, given by Newton's second law of motion, or F = m a (force = mass × acceleration). Gravitational acceleration contributes to the total gravity acceleration, but other factors, such as the rotation of Earth, also contribute, and, therefore, affect the weight of the object. Gravity does not normally include the gravitational pull of the Moon and Sun, which are accounted for in terms of tidal effects.

  1. ^ NASA/JPL/University of Texas Center for Space Research. "PIA12146: GRACE Global Gravity Animation". Photojournal. NASA Jet Propulsion Laboratory. Retrieved 30 December 2013.
  2. ^ Cite error: The named reference Boynton was invoked but never defined (see the help page).
  3. ^ Hofmann-Wellenhof, B.; Moritz, H. (2006). Physical Geodesy (2nd ed.). Springer. ISBN 978-3-211-33544-4. § 2.1: "The total force acting on a body at rest on the earth's surface is the resultant of gravitational force and the centrifugal force of the earth's rotation and is called gravity."
  4. ^ Bureau International des Poids et Mesures (1901). "Déclaration relative à l'unité de masse et à la définition du poids; valeur conventionnelle de gn". Comptes Rendus des Séances de la Troisième Conférence· Générale des Poids et Mesures (in French). Paris: Gauthier-Villars. p. 68. Le nombre adopté dans le Service international des Poids et Mesures pour la valeur de l'accélération normale de la pesanteur est 980,665 cm/sec², nombre sanctionné déjà par quelques législations. Déclaration relative à l'unité de masse et à la définition du poids; valeur conventionnelle de gn.
  5. ^ Moritz, Helmut (2000). "Geodetic Reference System 1980". Journal of Geodesy. 74 (1): 128–133. doi:10.1007/s001900050278. S2CID 195290884. Retrieved 2023-07-26. γe = 9.780 326 7715 m/s² normal gravity at equator

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