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Encyclopedia > Earth's gravity
 Gravitation Portal

Earth's gravity, denoted by g, refers to the attractive force that the Earth exerts on objects on or near its surface (or, more generally, objects anywhere in the Earth's vicinity). Its strength is usually quoted as an acceleration, which in SI units is measured in m/s² (metres per second per second, equivalently written as m·s−2). It has an approximate value of 9.8 m/s², which means that, ignoring air resistance, the speed of an object falling freely near the Earth's surface increases by about 9.8 metres per second every second. Image File history File links Portal. ... This article is about Earth as a planet. ... â€œSIâ€ redirects here. ...

There is a direct relationship between gravitational acceleration and the downwards weight force experienced by objects on Earth. This is explained at weight; see also apparent weight. For other uses, see Weight (disambiguation). ... An objects weight, henceforth called actual weight, is the downward force exerted upon it by the earths gravity. ...

The precise strength of the Earth's gravity varies depending on location. The nominal "average" value at the Earth's surface, known as standard gravity is, by definition, 9.80665 m/s² (32.1740 ft/s²). This quantity is denoted variously as gn, ge (though this sometimes means the normal equatorial value on Earth, 9.78033 m/s²), g0, gee, or simply g (which is also used for the variable local value). The symbol g should not be confused with G, the gravitational constant, or g, the abbreviation for gram (which is not italicized). g (also gee, g-force or g-load) is a non-SI unit of acceleration defined as exactly 9. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

The change in gravitational strength per unit distance (in a given direction) is known as the gravitational gradient. In the SI system this is measured in m/s² (strength) per metre (distance), which resolves to simply s−2 (inverse seconds squared). In the cgs system, gravitational gradient is measured in eotvoses. For other uses, see Gradient (disambiguation). ... CGS is an acronym for centimetre-gram-second. ... The eotvos is a unit of acceleration divided by distance in the older Centimeter-gram-second system of units. ...

The strength (or apparent strength) of Earth's gravity varies with latitude, altitude, and local topography and geology. For most purposes the gravitational force is assumed to act in a line directly towards a point at the centre of the Earth, but for very precise work the direction can also vary slightly because the Earth is not a perfectly uniform sphere. This article is about the geographical term. ... For discussion of land surfaces themselves, see Terrain. ... This article includes a list of works cited but its sources remain unclear because it lacks in-text citations. ...

### Latitude

The second reason is that the Earth's equatorial bulge (itself also caused by centrifugal force), causes objects at the equator to be farther from the planet's centre than objects at the poles. Because the force due to gravitational attraction between two bodies (the Earth and the object being weighed) varies inversely with the square of the distance between them, objects at the equator experience a weaker gravitational pull than objects at the poles. An equatorial bulge is a planetological term which describes a bulge which a planet may have around its equator, distorting it into an oblate spheroid. ...

In combination, the equatorial bulge and the effects of centrifugal force mean that sea-level gravitational acceleration increases from about 9.780 m/s² at the equator to about 9.832 m/s² at the poles, so an object will weigh about 0.5% more at the poles than at the equator.

### Altitude

Gravity decreases with altitude, since greater altitude means greater distance from the Earth's centre. All other things being equal, an increase in altitude from sea level to the top of Mount Everest (8,850 metres) causes a weight decrease of about 0.28%. (An additional factor affecting apparent weight is the decrease in air density at altitude, which lessens an object's buoyancy.) It is a common misconception that astronauts in orbit are weightless because they have flown high enough to "escape" the Earth's gravity. In fact, at an altitude of 400 kilometres (250 miles), equivilant to a typical orbit of the Space Shuttle, gravity is still nearly 90% as strong as at the Earth's surface, and weightlessness actually occurs because orbiting objects are in free-fall. This article is about the space vehicle. ... Free Fall opens with one of the most stunning first paragraphs I have ever, or am ever likely to, read. ...

### Local topography and geology

Local variations in topography (such as the presence of mountains) and geology (such as the density of rocks in the vicinity) cause fluctuations in the Earth's gravitational field, known as gravitational anomalies. Some of these anomalies can be very extensive, resulting in bulges in sea level of up to 200 metres in the Pacific ocean, and throwing pendulum clocks out of synchronisation. Definition Physical geodesy is the study of the physical properties of the gravity field of the Earth, the geopotential, with a view to their application in geodesy. ... For discussion of land surfaces themselves, see Terrain. ... This article includes a list of works cited but its sources remain unclear because it lacks in-text citations. ... Gravity anomalies are widely used in geodesy and geophysics. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ... For other uses, see Pendulum (disambiguation). ...

### Other factors

In air, objects experience a supporting buoyancy force which reduces the apparent strength of gravity (as measured by an object's weight). The magnitude of the effect depends on air density (and hence air pressure); see Apparent weight for details. In physics, buoyancy is the upward force on an object produced by the surrounding fluid (i. ... An objects weight, henceforth called actual weight, is the downward force exerted upon it by the earths gravity. ...

### Comparative gravities in various cities around the world

The table below shows the gravitational acceleration in various cities around the world.

 Amsterdam 9.813 m/s² Istanbul 9.808 m/s² Paris 9.809 m/s² Athens 9.807 m/s² Havana 9.788 m/s² Rio de Janeiro 9.788 m/s² Auckland, NZ 9.799 m/s² Helsinki 9.819 m/s² Rome 9.803 m/s² Bangkok 9.783 m/s² Kuwait 9.793 m/s² San Francisco 9.800 m/s² Brussels 9.811 m/s² Lisbon 9.801 m/s² Singapore 9.781 m/s² Buenos Aires 9.797 m/s² London 9.812 m/s² Stockholm 9.818 m/s² Calcutta 9.788 m/s² Los Angeles 9.796 m/s² Sydney 9.797 m/s² Cape Town 9.796 m/s² Madrid 9.800 m/s² Taipei 9.790 m/s² Chicago 9.803 m/s² Manila 9.784 m/s² Tokyo 9.798 m/s² Copenhagen 9.815 m/s² Mexico City 9.779 m/s² Vancouver, BC 9.809 m/s² Nicosia 9.797 m/s² New York 9.802 m/s² Washington, DC 9.801 m/s² Jakarta 9.781 m/s² Oslo 9.819 m/s² Wellington, NZ 9.803 m/s² Frankfurt 9.810 m/s² Ottawa 9.806 m/s² Zurich 9.807 m/s²

### Mathematical models The graph shows the difference of gravity relative to the height of an object

If the terrain is at sea level, we can estimate g: Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ...

where

gφ = acceleration in m·s−2 at latitude φ

This is the International Gravity Formula 1967, the 1967 Geodetic Reference System Formula, Helmert's equation or Clairault's formula.

The first correction to this formula is the free air correction (FAC), which accounts for heights above sea level. Gravity decreases with height, at a rate which near the surface of the Earth is such that linear extrapolation would give zero gravity at a height of one half the radius of the Earth, i.e. the rate is 9.8 m·s−2 per 3200 km. Thus:

where

h = height in meters above sea level

For flat terrain above sea level a second term is added, for the gravity due to the extra mass; for this purpose the extra mass can be approximated by an infinite horizontal slab, and we get 2πG times the mass per unit area, i.e. 4.2×10-10 m³·s−2·kg−1 (0.042 μGal·kg−1·m²)) (the Bouguer correction). For a mean rock density of 2.67 g·cm−3 this gives 1.1×10-6 s−2 (0.11 mGal·m−1). Combined with the free-air correction this means a reduction of gravity at the surface of ca. 2 µm·s−2 (0.20 mGal) for every meter of elevation of the terrain. (The two effects would cancel at a surface rock density of 4/3 times the average density of the whole Earth.)

For the gravity below the surface we have to apply the free-air correction as well as a double Bouguer correction. With the infinite slab model this is because moving the point of observation below the slab changes the gravity due to it to its opposite. Alternatively, we can consider a spherically symmetrical Earth and subtract from the mass of the Earth that of the shell outside the point of observation, because that does not cause gravity inside. This gives the same result. In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Gauss-Ostrogradsky theorem is a result that relates the flow (that is, flux) of a vector field through a surface to the behaviour of the vector field inside the surface. ...

Helmert's equation may be written equivalently to the version above as either:

gφ = 9.8061999 − 0.0259296cos(2φ) + 0.0000567cos2(2φ)

or

gφ = 9.780327 + 0.0516323sin2(φ) + 0.0002269sin4(φ)

An alternate formula for g as a function of latitude is the WGS (World Geodetic System) 84 Ellipsoidal Gravity Formula: The World Geodetic System defines a reference frame for the earth, for use in geodesy and navigation. ...

A spot check comparing results from the WGS-84 formula with those from Helmert's equation (using increments 10 degrees of latitude starting with zero) indicated that they produce values which differ by less than 1e-6 m/s².

## Estimating g from the law of universal gravitation

Given the law of universal gravitation, the acceleration due to gravity, g, is merely a collection of factors in that equation: It has been suggested that this article or section be merged into Gravity. ...

where g is the bracketed factor, and thus:

To find the acceleration due to gravity at sea level, substitute the values of the gravitational constant, G, the Earth's mass (in kilograms), m1, and the Earth's radius (in meters), r, to obtain the value of g: According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... For other uses, see Mass (disambiguation). ... This article is about an authentication, authorization, and accounting protocol. ...

Note that this formula only works because of the pleasant (but non-obvious) mathematical fact that the gravity of a uniform spherical body, as measured on or above its surface, is the same as if all its mass were concentrated at a point at its centre.

This agrees approximately with the measured value of g. The difference may be attributed to several factors, mentioned above under "Variations":

• The Earth is not homogeneous
• The Earth is not a perfect sphere, and an average value must be used for its radius
• This calculated value of g does not include the centrifugal force effects that are found in practice due to the rotation of the Earth

There are significant uncertainties in the values of r and m1 as used in this calculation, and the value of G is also rather difficult to measure precisely. Look up Homogeneous in Wiktionary, the free dictionary. ... Centrifugal force (from Latin centrum centre and fugere to flee) is a term which may refer to two different forces which are related to rotation. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

If G, g and r are known then a reverse calculation will give an estimate of the mass of the Earth. This method was used by Henry Cavendish. For other persons named Henry Cavendish, see Henry Cavendish (disambiguation). ...

## Comparative gravities of the Earth, Sun, Moon and planets

The table below shows gravitational accelerations (in multiples of g) at the surface of the Sun, the Earth's moon, each of the planets in the solar system, and Pluto. The "surface" is taken to mean the cloud tops of the gas giants (Jupiter, Saturn, Uranus and Neptune). It is usually specified as the location where the pressure is equal to a certain value (normally 75 kPa[citation needed]). For the Sun, the "surface" is taken to mean the photosphere. It is also normally specified at the equator, though the value given here for Earth is not the equatorial value. The term g force or gee force refers to the symbol g, the force of acceleration due to gravity at the earths surface. ... The photosphere of an astronomical object is the region at which the optical depth becomes one for a photon of wavelength equal to 5000 angstroms. ...

 Body Multiple of g m/s² Sun 27.935 273.95 Mercury 0.3774 3.701 Venus 0.904 8.87 Earth 1 (by definition) 9.80665 Moon 0.1654 1.622 Mars 0.376 3.69 Jupiter 2.528 24.79 Saturn 0.917 8.96 Uranus 0.886 8.69 Neptune 1.137 11.15 Pluto 0.059 0.58 Results from FactBites:

 Earth Dynamics: Gravity (245 words) The gravity method detects and measures lateral variations in the earth’s gravitational field that are associated with near-surface changes in density. Gravity surveys may be conducted on land, in the air or in water. Gravity data and computed models are typically presented as linear profiles or as contour maps.
 Tides at MROB (2955 words) Because the Lunar tidal force is 1/8,000,000 as strong as the Earth's gravity, we would expect the height of the ocean bulges to be about 1/8,000,000 their width (which is 1/4 of the circumference of the Earth). Gravity is an inverse-squared force, and as a result, the increase in the Moon's gravity on the closer side of the Earth is a little greater than the decrease on the farther side of the Earth. In 3 dimensions, the Earth is a sphere.
More results at FactBites »

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