In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, gravitational acceleration is the
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 t ...
of an object in
free fall
In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on ...
within a
vacuum (and thus without experiencing
drag). This is the steady gain in
speed
In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude
Magnitude may refer to:
Mathematics
*Euclidean vector, a quantity defined by both its magnitude and its direction
*Magnitude (ma ...
caused exclusively by the force of
gravitational attraction. All bodies accelerate in vacuum at the same rate, regardless of the
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 eleme ...
es or compositions of the bodies; the measurement and analysis of these rates is known as
gravimetry.
At a fixed point on the surface, the magnitude of
Earth's gravity results from combined effect of gravitation and the
centrifugal force from
Earth's rotation.
At different points on Earth's surface, the free fall acceleration ranges from ,
[
] depending on
altitude,
latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
, and
longitude
Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...
. A conventional
standard value is defined exactly as . Locations of significant variation from this value are known as
gravity anomalies. This does not take into account other effects, such as
buoyancy or drag.
Relation to the Universal Law
Newton's law of universal gravitation
Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distan ...
states that there is a gravitational force between any two masses that is equal in magnitude for each mass, and is aligned to draw the two masses toward each other. The formula is:
:
where
and
are any two masses,
is the
gravitational constant, and
is the distance between the two point-like masses.
Using the integral form of
Gauss's Law, this formula can be extended to any pair of objects of which one is far more massive than the other — like a planet relative to any man-scale artifact. The distances between planets and between the planets and the Sun are (by many orders of magnitude) larger than the sizes of the sun and the planets. In consequence both the sun and the planets can be considered as
point mass
A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up ...
es and the same formula applied to planetary motions. (As planets and
natural satellite
A natural satellite is, in the most common usage, an astronomical body that orbits a planet, dwarf planet, or small Solar System body (or sometimes another natural satellite). Natural satellites are often colloquially referred to as ''moons'' ...
s form pairs of comparable mass, the distance 'r' is measured from the common
centers of mass of each pair rather than the direct total distance between planet centers.)
If one mass is much larger than the other, it is convenient to take it as observational reference and define it as source of a gravitational field of magnitude and orientation given by:
[
]
:
where
is the mass of the field source (larger), and
is a
unit vector directed from the field source to the sample (smaller) mass. The negative sign indicates that the force is attractive (points backward, toward the source).
Then the attraction force
vector onto a sample mass
can be expressed as:
:
Here
is the
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of ...
less, free-fall acceleration sustained by the sampling mass
under the attraction of the gravitational source.
It is a vector oriented toward the field source, of magnitude measured in acceleration units. The gravitational acceleration vector depends ''only'' on how massive the field source
is and on the distance 'r' to the sample mass
. It does not depend on the magnitude of the small sample mass.
This model represents the "far-field" gravitational acceleration associated with a massive body. When the dimensions of a body are not trivial compared to the distances of interest, the
principle of superposition can be used for differential masses for an assumed
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
distribution throughout the body in order to get a more detailed model of the "near-field" gravitational acceleration. For satellites in orbit, the far-field model is sufficient for rough calculations of altitude versus
period
Period may refer to:
Common uses
* Era, a length or span of time
* Full stop (or period), a punctuation mark
Arts, entertainment, and media
* Period (music), a concept in musical composition
* Periodic sentence (or rhetorical period), a concept ...
, but not for precision estimation of future location after multiple orbits.
The more detailed models include (among other things) the
bulging at the equator for the Earth, and irregular mass concentrations (due to meteor impacts) for the Moon. The
Gravity Recovery and Climate Experiment (GRACE) mission launched in 2002 consists of two probes, nicknamed "Tom" and "Jerry", in polar orbit around the Earth measuring differences in the distance between the two probes in order to more precisely determine the gravitational field around the Earth, and to track changes that occur over time. Similarly, the
Gravity Recovery and Interior Laboratory
The Gravity Recovery and Interior Laboratory (GRAIL) was an American lunar science mission in NASA's Discovery Program which used high-quality gravitational field mapping of the Moon to determine its interior structure. The two small spacecraf ...
mission from 2011-2012 consisted of two probes ("Ebb" and "Flow") in polar orbit around the Moon to more precisely determine the gravitational field for future navigational purposes, and to infer information about the Moon's physical makeup.
Comparative gravities of the Earth, Sun, Moon, and planets
The table below shows comparative gravitational accelerations at the surface of the Sun, the Earth's moon, each of the planets in the Solar System and their major moons, Ceres, Pluto, and Eris. For gaseous bodies, the "surface" is taken to mean visible surface: the cloud tops of the
gas giants
A gas giant is a giant planet composed mainly of hydrogen and helium. Gas giants are also called failed stars because they contain the same basic elements as a star. Jupiter and Saturn are the gas giants of the Solar System. The term "gas giant" ...
(Jupiter, Saturn, Uranus and Neptune), and the Sun's
photosphere. The values in the table have not been de-rated for the centrifugal force effect of planet rotation (and cloud-top wind speeds for the gas giants) and therefore, generally speaking, are similar to the actual gravity that would be experienced near the poles. For reference the time it would take an object to fall 100 meters, the height of a skyscraper, is shown, along with the maximum speed reached. Air resistance is neglected.
General relativity
In Einstein's theory of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, gravitation is an attribute of curved
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
instead of being due to a force propagated between bodies. In Einstein's theory, masses distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. The gravitational force is a
fictitious force. There is no gravitational acceleration, in that the
proper acceleration and hence
four-acceleration of objects in
free fall
In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on ...
are zero. Rather than undergoing an acceleration, objects in free fall travel along straight lines (
geodesics
In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...
) on the curved spacetime.
See also
*
Air track
*
Gravimetry
*
Gravity of Earth
*
Gravitation of the Moon
*
Gravity of Mars
The gravity of Mars is a natural phenomenon, due to the law of gravity, or gravitation, by which all things with mass around the planet Mars are brought towards it. It is weaker than Earth's gravity due to the planet's smaller mass. The average ...
*
Newton's law of universal gravitation
Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distan ...
*
Standard gravity
Notes
References
{{DEFAULTSORT:Gravitational Acceleration
Gravimetry
Gravity
Acceleration
Temporal rates