A non-rotating perfect
sphere of uniform mass density, or whose density varies solely with distance from the centre (
spherical symmetry), would produce a
gravitational field 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.
In large cities, it ranges from 9.7806 m/s2 in
Kuala Lumpur,
Mexico City, and
Singapore to 9.825 m/s2 in
Oslo and
Helsinki.
Conventional value In 1901, the third
General Conference on Weights and Measures defined a standard gravitational acceleration for the surface of the Earth:
gn = 9.80665 m/s2. It was based on measurements 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.
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 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 further from the planet's center than objects at the poles. The force due to gravitational attraction between two masses (a piece of the Earth and the object being weighed) varies inversely with the square of the distance between them. The distribution of mass is also different below someone on the equator and below someone at a pole. The net result is that an object at the Equator experiences a weaker gravitational pull than an object on one of the poles. 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 vs
Mars vs
Moon gravity at
elevation 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%. The following formula approximates the Earth's gravity variation with altitude: : g_h=g_0\left(\frac{R_\mathrm{e}}{R_\mathrm{e}+h}\right)^2 where • is the gravitational acceleration at height above sea level. • is the
Earth's mean radius. • is the
standard gravitational acceleration. The formula treats the Earth as a perfect sphere with a radially symmetric distribution of mass. 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.
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 force of gravity at a radius depends only on the mass inside the sphere of that 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{GM}{r^2}. where is the
gravitational constant and is the total mass enclosed within radius . This result is known as the
Shell theorem; it took
Isaac Newton 20 years to prove this result, delaying his work on gravity. If the Earth had a constant density , the mass would be and the dependence of gravity on depth would be : g(r) = \frac{4\pi}{3} 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. 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{4\pi}{3} G \rho_0 r - \pi G \left(\rho_0-\rho_1\right) \frac{r^2}{R}. The actual depth dependence of density and gravity, inferred from seismic travel times (see
Adams–Williamson equation), is shown in the graphs below. {{Multiple image
Local topography and geology Local differences in
topography (such as the presence of mountains),
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
gravity anomalies. Some of these anomalies can be very extensive, resulting in bulges in
sea level, and throwing
pendulum clocks out of synchronisation. The study of these anomalies forms the basis of gravitational
geophysics. 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 rocks 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. == Atmosphere ==