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The gravity of Earth, denoted by , is the net
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
that is imparted to objects due to the combined effect of
gravitation In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
(from mass distribution within
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
) and the
centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is paralle ...
(from the Earth's rotation). It is a vector quantity, whose direction coincides with a
plumb bob A plumb bob, plumb bob level, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical reference line, or plumb-line. It is a precursor to the spirit level and used to establish a verti ...
and strength or magnitude is given by the norm g=\, \mathit\, . 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 gravity acceleration is approximately , which means that, ignoring the effects of air resistance, the
speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quant ...
of an object falling freely will increase by about per second every second. This quantity is sometimes referred to informally as ''little '' (in contrast, the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
is referred to as ''big ''). The precise strength of Earth's gravity varies depending on location. The nominal "average" value at Earth's surface, known as is, by definition, . This quantity is denoted variously as , (though this sometimes means the normal equatorial value on Earth, ), , gee, or simply (which is also used for the variable local value). The
weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar qua ...
of an object on Earth's surface is the downwards force on that object, given by
Newton's second law of motion Newton's laws of motion are three basic Scientific law, laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at re ...
, or ().
Gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodie ...
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.


Variation in magnitude

A non-rotating perfect
sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the c ...
of uniform mass density, or whose density varies solely with distance from the centre ( spherical symmetry), would produce a
gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational pheno ...
of uniform magnitude at all points on its surface. The Earth is rotating and is also not spherically symmetric; rather, it is slightly flatter at the poles while bulging at the Equator: an oblate spheroid. There are consequently slight deviations in the magnitude of gravity across its surface. Gravity on the Earth's surface varies by around 0.7%, from 9.7639 m/s2 on the Nevado Huascarán mountain in Peru to 9.8337 m/s2 at the surface of the
Arctic Ocean The Arctic Ocean is the smallest and shallowest of the world's five major oceans. It spans an area of approximately and is known as the coldest of all the oceans. The International Hydrographic Organization (IHO) recognizes it as an ocean, a ...
. In large cities, it ranges from 9.7806"Wolfram, Alpha Gravity in Kuala Lumpur", Wolfram Alpha, accessed November 2020
/ref> in
Kuala Lumpur , anthem = ''Maju dan Sejahtera'' , image_map = , map_caption = , pushpin_map = Malaysia#Southeast Asia#Asia , pushpin_map_caption = , coordinates = , sub ...
,
Mexico City Mexico City ( es, link=no, Ciudad de México, ; abbr.: CDMX; Nahuatl: ''Altepetl Mexico'') is the capital and largest city of Mexico, and the most populous city in North America. One of the world's alpha cities, it is located in the Valley o ...
, and
Singapore Singapore (), officially the Republic of Singapore, is a sovereign island country and city-state in maritime Southeast Asia. It lies about one degree of latitude () north of the equator, off the southern tip of the Malay Peninsula, bor ...
to 9.825 in
Oslo Oslo ( , , or ; sma, Oslove) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population of ...
and
Helsinki Helsinki ( or ; ; sv, Helsingfors, ) is the Capital city, capital, primate city, primate, and List of cities and towns in Finland, most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of U ...
.


Conventional value

In 1901 the third General Conference on Weights and Measures defined a standard gravitational acceleration for the surface of the Earth: ''g''n = 9.80665 m/s2. It was based on measurements done at the Pavillon de Breteuil near Paris in 1888, with a theoretical correction applied in order to convert to a latitude of 45° at sea level. This definition is thus not a value of any particular place or carefully worked out average, but an agreement for a value to use if a better actual local value is not known or not important. It is also used to define the units kilogram force and pound force. Calculating the gravity at Earth's surface using the average radius of Earth (), the experimentally determined value of the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
, and the Earth mass of 5.9722 kg gives an acceleration of 9.8203 m/s2, slightly greater than the standard gravity of 9.80665 m/s2. The value of standard gravity corresponds to the gravity on Earth at a radius of .


Latitude

The surface of the Earth is rotating, so it is not an inertial frame of reference. At latitudes nearer the Equator, the outward
centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is paralle ...
produced by Earth's rotation is larger than at polar latitudes. This counteracts the Earth's gravity to a small degree – up to a maximum of 0.3% at the Equator – and reduces the apparent downward acceleration of falling objects. The second major reason for the difference in gravity at different latitudes is that the Earth's equatorial bulge (itself also caused by centrifugal force from rotation) causes objects at the Equator to be farther from the planet's center 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, an object at the Equator experiences a weaker gravitational pull than an object on the pole. In combination, the equatorial bulge and the effects of the surface centrifugal force due to rotation mean that sea-level gravity increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles, so an object will weigh approximately 0.5% more at the poles than at the Equator.


Altitude

Gravity decreases with altitude as one rises above the Earth's surface because greater altitude means greater distance from the Earth's centre. All other things being equal, an increase in altitude from sea level to causes a weight decrease of about 0.29%. (An additional factor affecting apparent weight is the decrease in air density at altitude, which lessens an object's buoyancy. This would increase a person's apparent weight at an altitude of 9,000 metres by about 0.08%) 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 , equivalent to a typical orbit of the ISS, gravity is still nearly 90% as strong as at the Earth's surface. Weightlessness actually occurs because orbiting objects are in free-fall. The effect of ground elevation depends on the density of the ground (see Slab correction section). A person flying at above sea level over mountains will feel more gravity than someone at the same elevation but over the sea. However, a person standing on the Earth's surface feels less gravity when the elevation is higher. The following formula approximates the Earth's gravity variation with altitude: :g_h=g_0\left(\frac\right)^2 Where * is the gravitational acceleration at height above sea level. * is the Earth's mean radius. * is the
standard gravitational acceleration The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. ...
. The formula treats the Earth as a perfect sphere with a radially symmetric distribution of mass; a more accurate mathematical treatment is discussed below.


Depth

An approximate value for gravity at a distance from the center of the Earth can be obtained by assuming that the Earth's density is spherically symmetric. The gravity depends only on the mass inside the sphere of radius . All the contributions from outside cancel out as a consequence of the inverse-square law of gravitation. Another consequence is that the gravity is the same as if all the mass were concentrated at the center. Thus, the gravitational acceleration at this radius is :g(r) = -\frac. where is the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
and is the total mass enclosed within radius . If the Earth had a constant density , the mass would be and the dependence of gravity on depth would be :g(r) = \frac G \rho r. The gravity at depth is given by where is acceleration due to gravity on the surface of the Earth, is depth and is the radius of the
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
. If the density decreased linearly with increasing radius from a density at the center to at the surface, then , and the dependence would be :g(r) = \frac G \rho_0 r - \pi G \left(\rho_0-\rho_1\right) \frac. The actual depth dependence of density and gravity, inferred from seismic travel times (see
Adams–Williamson equation The Adams–Williamson equation, named after Leason H. Adams and E. D. Williamson, is an equation used to determine density as a function of radius, more commonly used to determine the relation between the velocities of seismic waves and the den ...
), is shown in the graphs below.


Local topography and geology

Local differences in
topography Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps. Topography is a field of geoscience and planetary sc ...
(such as the presence of mountains),
geology Geology () is a branch of natural science concerned with Earth and other Astronomical object, astronomical objects, the features or rock (geology), rocks of which it is composed, and the processes by which they change over time. Modern geology ...
(such as the density of rocks in the vicinity), and deeper tectonic structure cause local and regional differences in the Earth's gravitational field, known as gravitational anomalies. Some of these anomalies can be very extensive, resulting in bulges in
sea level Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardis ...
, and throwing
pendulum A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward th ...
clocks out of synchronisation. The study of these anomalies forms the basis of gravitational
geophysics Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' so ...
. The fluctuations are measured with highly sensitive gravimeters, the effect of topography and other known factors is subtracted, and from the resulting data conclusions are drawn. Such techniques are now used by prospectors to find oil and mineral deposits. Denser rocks (often containing mineral ores) cause higher than normal local gravitational fields on the Earth's surface. Less dense
sedimentary rock Sedimentary rocks are types of rock that are formed by the accumulation or deposition of mineral or organic particles at Earth's surface, followed by cementation. Sedimentation is the collective name for processes that cause these particles ...
s cause the opposite. There is a strong correlation between the gravity derivation map of earth from NASA GRACE with positions of recent volcanic activity, ridge spreading and volcanos: these regions have a stronger gravitation than theoretical predictions.


Other factors

In air or water, objects experience a supporting
buoyancy Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the ...
force which reduces the apparent strength of gravity (as measured by an object's weight). The magnitude of the effect depends on the air density (and hence air pressure) or the water density respectively; see Apparent weight for details. The gravitational effects of the
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
and the Sun (also the cause of the
tide Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables ...
s) have a very small effect on the apparent strength of Earth's gravity, depending on their relative positions; typical variations are 2 µm/s2 (0.2 mGal) over the course of a day.


Direction

Gravity acceleration is a
vector quantity In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors ac ...
, with direction in addition to magnitude. In a spherically symmetric Earth, gravity would point directly towards the sphere's centre. As the Earth's figure is slightly flatter, there are consequently significant deviations in the direction of gravity: essentially the difference between
geodetic latitude Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a ''reference ellipsoid''. They include geodetic latitude (north/south) , '' longitude'' (east/west) , and ellipsoidal height (also known as g ...
and geocentric latitude. Smaller deviations, called vertical deflection, are caused by local mass anomalies, such as mountains.


Comparative values worldwide

Tools exist for calculating the strength of gravity at various cities around the world.Gravitational Fields Widget as of Oct 25th, 2012
WolframAlpha WolframAlpha ( ) is an answer engine developed by Wolfram Research. It answers factual queries by computing answers from externally sourced data. WolframAlpha was released on May 18, 2009 and is based on Wolfram's earlier product Wolfram Mathe ...
The effect of latitude can be clearly seen with gravity in high-latitude cities: Anchorage (9.826 m/s2), Helsinki (9.825 m/s2), being about 0.5% greater than that in cities near the equator: Kuala Lumpur (9.776 m/s2). The effect of altitude can be seen in Mexico City (9.776 m/s2; altitude ), and by comparing Denver (9.798 m/s2; ) with Washington, D.C. (9.801 m/s2; ), both of which are near 39° N. Measured values can be obtained from Physical and Mathematical Tables by T.M. Yarwood and F. Castle, Macmillan, revised edition 1970.


Mathematical models

If the terrain is at sea level, we can estimate, for the Geodetic Reference System 1980, g\, the acceleration at latitude \phi: :\begin g\ & = 9.780327\,\,\mathrm\cdot\mathrm^ \,\, \left(1 + 0.0053024\,\sin^2\phi - 0.0000058\,\sin^2 2\phi \right), \\ & = 9.780327\,\,\mathrm\cdot\mathrm^ \,\, \left(1 + 0.0052792\,\sin^2\phi + 0.0000232\,\sin^4 \phi \right), \\ & = 9.780327\,\,\mathrm\cdot\mathrm^ \,\, \left(1.0053024 - 0.0053256\,\cos^2\phi + 0.0000232\,\cos^4 \phi \right), \\ & = 9.780327\,\,\mathrm\cdot\mathrm^ \,\, \left(1.0026454 - 0.0026512\,\cos 2\phi + 0.0000058\,\cos^2 2\phi \right) \end This is the
International Gravity Formula In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of the true gravity on Earth's surface by means of a mathematical model representing Earth. The most common model of a smoothed Earth is a rotating Earth ellips ...
1967, the 1967 Geodetic Reference System Formula, Helmert's equation or Clairaut's formula.International Gravity formula
An alternative formula for ''g'' as a function of latitude is the WGS ( World Geodetic System) 84 Ellipsoidal
Gravity Formula In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of the true gravity on Earth's surface by means of a mathematical model representing Earth. The most common model of a smoothed Earth is a rotating Earth ellipsoid ...
: :g\= \mathbb_e\left frac\right\,\! where, *a,\,b are the equatorial and polar semi-axes, respectively; *e^2 = 1 - (b/a)^2 is the spheroid's eccentricity, squared; *\mathbb_e,\,\mathbb_p\, is the defined gravity at the equator and poles, respectively; *k = \frac (formula constant); then, where \mathbb_p = 9.8321849378 \,\,\mathrm\cdot\mathrm^, :g\= 9.7803253359\,\,\mathrm\cdot\mathrm^ \left frac\right/math>. where the semi-axes of the earth are: :a = 6378137.0 \,\,\mbox :b = 6356752.314245 \,\,\mbox The difference between the WGS-84 formula and Helmert's equation is less than 0.68 μm·s−2. Further reductions are applied to obtain gravity anomalies (see: Gravity anomaly#Computation).


Estimating ''g'' from the law of universal gravitation

From the law of universal gravitation, the force on a body acted upon by Earth's gravitational force is given by :F=G\frac = (G\frac)m where ''r'' is the distance between the centre of the Earth and the body (see below), and here we take M_\oplus to be the mass of the Earth and ''m'' to be the mass of the body. Additionally,
Newton's second law Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in mo ...
, ''F'' = ''ma'', where ''m'' is mass and ''a'' is acceleration, here tells us that :F=mg Comparing the two formulas it is seen that: :g=G\frac So, to find the acceleration due to gravity at sea level, substitute the values of the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
, ''G'', the Earth's
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
(in kilograms), ''m''1, and the Earth's
radius In classical geometry, a radius (plural, : radii) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', ...
(in metres), ''r'', to obtain the value of ''g'': :g=G\frac=6.67 \cdot 10^^3^^\times \frac = 9.77\cdot^ This formula only works because of the 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 is what allows us to use the Earth's radius for ''r''. The value obtained 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'' only includes true gravity. It does not include the reduction of constraint force that we perceive as a reduction of gravity due to the rotation of Earth, and some of gravity being counteracted by centrifugal force. There are significant uncertainties in the values of ''r'' and ''m''1 as used in this calculation, and the value of '' G'' is also rather difficult to measure precisely. 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.


Measurement

The measurement of Earth's gravity is called ''
gravimetry Gravimetry is the measurement of the strength of a gravitational field. Gravimetry may be used when either the magnitude of a gravitational field or the properties of matter responsible for its creation are of interest. Units of measurement G ...
''.


Satellite measurements


See also

* Escape velocity **
Atmospheric escape Atmospheric escape is the loss of planetary atmospheric gases to outer space. A number of different mechanisms can be responsible for atmospheric escape; these processes can be divided into thermal escape, non-thermal (or suprathermal) escape, and ...
*
Figure of the Earth Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approxim ...
* Geopotential ** Geopotential model *
Gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
(Gravitation) *
Gravity anomaly The gravity anomaly at a location on the Earth's surface is the difference between the observed value of gravity and the value predicted by a theoretical model. If the Earth were an ideal oblate spheroid of uniform density, then the gravity me ...
, Bouguer anomaly * Gravitation of the Moon *
Gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodie ...
* Gravity of Mars * Newton's law of universal gravitation * Vertical deflection


References


External links


Altitude gravity calculator

GRACE – Gravity Recovery and Climate Experiment

GGMplus high resolution data (2013)

Geoid 2011 model
Potsdam Gravity Potato {{Authority control Gravimetry of objects
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
Earth