Conventional value

In 1901, the third General Conference on Weights and Measures defined a standard gravitational acceleration for the Earth's surface: = 9.80665 m/s. It was based on measurements made at the Pavillon de Breteuil") near Paris in 1888, with a theoretical correction applied to convert to a latitude of 45° sea level.[6] This definition is therefore not a value from a particular location or a carefully constructed average, but rather an agreement for a value to be used if a better actual local value is not known or not important.[7] It is also used to define the units of kilogram-force and pound-force "Pound (unit of force)").

Latitude

The Earth's surface is rotating, so it is a non-inertial reference frame. At latitudes closer to the equator, the external centrifugal force produced by the Earth's rotation is greater than at polar latitudes. This counteracts 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 main reason for the difference in gravity at different latitudes is that the Earth's equatorial bulge (also caused by the centrifugal force of rotation) causes objects at the equator to be farther from the center of the planet 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 at the poles.

In combination, the equatorial bulge and the effects of surface centrifugal force due to rotation mean that gravity at sea level increases from about 9,780 m/s at the equator to about 9,832 m/s at the poles, so an object will weigh about 0.5% more at the poles than at the equator.[8][9]​.

Altitude

Gravity decreases with altitude as one rises above the Earth's surface because higher altitude means greater distance from the center of the Earth. All things being equal, an increase in altitude from sea level to 30,000 feet (9,144.0 m) causes a decrease in weight of approximately 0.29%. (An additional factor affecting apparent weight is the decrease in air density at altitude, which decreases the buoyancy of an object.[10] This would increase the apparent weight of a person at an altitude of 9,000 meters by approximately 0.08%).

It is a common misconception that astronauts in orbit are weightless because they have flown high enough to escape Earth's gravity. In fact, at an altitude of 400 kilometers (248.5 mi), equivalent to a typical ISS orbit, gravity is still almost 90% as strong as on Earth's surface. Weightlessness actually occurs because objects in orbit are in free fall.[11]​.

The effect of terrain elevation depends on the density of the terrain. A person flying at 9,100 m above sea level over the 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 variation of Earth's gravity with altitude:

Where.

The formula treats the Earth as a perfect sphere with a radially symmetric mass distribution; A more precise mathematical treatment is discussed below.

Depth

An approximate value of gravity at a distance from the center of the Earth can be obtained by assuming that the density of the Earth is spherically symmetric. Gravity depends only on the mass inside the radius sphere. All contributions from the outside cancel out as a consequence of the inverse square law of gravitation. Another consequence is that gravity is the same as if all the mass were concentrated in the center. Therefore, the gravitational acceleration at this radius is[13]​.

where is the gravitational constant and is the total mass enclosed within the radius. If the Earth had a constant density, the mass would be and the dependence of gravity on depth would be.

Depth is given by where is the acceleration due to gravity at the Earth's surface, is the depth, and is the radius of the Earth. If the density decreases linearly with increasing radius from a density at the center to at the surface, then.

and the dependency would be.

The actual depth dependence of density and gravity, inferred from seismic travel times (Adams-Williamson equation), is shown in the graphs below.

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 gravitational anomalies.[14] Some of these anomalies can be very extensive, resulting in bulges in sea level and throwing pendulum clocks out of synchronization.

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 conclusions are drawn from the resulting data. Such techniques are now used by prospectors to find oil and mineral deposits. Denser rocks (often containing mineral minerals "Ore (mining)") cause higher than normal local gravitational fields at the Earth's surface. Less dense sedimentary rocks cause the opposite.

Other factors

In air or water, objects experience a supportive buoyancy force that reduces the apparent force of gravity (measured by the weight of an object). The magnitude of the effect depends on the density of air (and therefore air pressure) or the density of water, respectively; See Apparent Weight for details.

The gravitational effects of the Moon and Sun (also the cause of tides) have very little effect on the apparent strength of Earth's gravity, depending on their relative positions; Typical variations are 2 µm/s (0.2 mGal "Gal (unit)")) over the course of a day.

Conventional value

In 1901, the third General Conference on Weights and Measures defined a standard gravitational acceleration for the Earth's surface: = 9.80665 m/s. It was based on measurements made at the Pavillon de Breteuil") near Paris in 1888, with a theoretical correction applied to convert to a latitude of 45° sea level.[6] This definition is therefore not a value from a particular location or a carefully constructed average, but rather an agreement for a value to be used if a better actual local value is not known or not important.[7] It is also used to define the units of kilogram-force and pound-force "Pound (unit of force)").

Latitude

The Earth's surface is rotating, so it is a non-inertial reference frame. At latitudes closer to the equator, the external centrifugal force produced by the Earth's rotation is greater than at polar latitudes. This counteracts 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 main reason for the difference in gravity at different latitudes is that the Earth's equatorial bulge (also caused by the centrifugal force of rotation) causes objects at the equator to be farther from the center of the planet 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 at the poles.

In combination, the equatorial bulge and the effects of surface centrifugal force due to rotation mean that gravity at sea level increases from about 9,780 m/s at the equator to about 9,832 m/s at the poles, so an object will weigh about 0.5% more at the poles than at the equator.[8][9]​.

Altitude

Gravity decreases with altitude as one rises above the Earth's surface because higher altitude means greater distance from the center of the Earth. All things being equal, an increase in altitude from sea level to 30,000 feet (9,144.0 m) causes a decrease in weight of approximately 0.29%. (An additional factor affecting apparent weight is the decrease in air density at altitude, which decreases the buoyancy of an object.[10] This would increase the apparent weight of a person at an altitude of 9,000 meters by approximately 0.08%).

It is a common misconception that astronauts in orbit are weightless because they have flown high enough to escape Earth's gravity. In fact, at an altitude of 400 kilometers (248.5 mi), equivalent to a typical ISS orbit, gravity is still almost 90% as strong as on Earth's surface. Weightlessness actually occurs because objects in orbit are in free fall.[11]​.

The effect of terrain elevation depends on the density of the terrain. A person flying at 9,100 m above sea level over the 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 variation of Earth's gravity with altitude:

Where.

The formula treats the Earth as a perfect sphere with a radially symmetric mass distribution; A more precise mathematical treatment is discussed below.

Depth

An approximate value of gravity at a distance from the center of the Earth can be obtained by assuming that the density of the Earth is spherically symmetric. Gravity depends only on the mass inside the radius sphere. All contributions from the outside cancel out as a consequence of the inverse square law of gravitation. Another consequence is that gravity is the same as if all the mass were concentrated in the center. Therefore, the gravitational acceleration at this radius is[13]​.

where is the gravitational constant and is the total mass enclosed within the radius. If the Earth had a constant density, the mass would be and the dependence of gravity on depth would be.

Depth is given by where is the acceleration due to gravity at the Earth's surface, is the depth, and is the radius of the Earth. If the density decreases linearly with increasing radius from a density at the center to at the surface, then.

and the dependency would be.

The actual depth dependence of density and gravity, inferred from seismic travel times (Adams-Williamson equation), is shown in the graphs below.

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 gravitational anomalies.[14] Some of these anomalies can be very extensive, resulting in bulges in sea level and throwing pendulum clocks out of synchronization.

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 conclusions are drawn from the resulting data. Such techniques are now used by prospectors to find oil and mineral deposits. Denser rocks (often containing mineral minerals "Ore (mining)") cause higher than normal local gravitational fields at the Earth's surface. Less dense sedimentary rocks cause the opposite.

Other factors

In air or water, objects experience a supportive buoyancy force that reduces the apparent force of gravity (measured by the weight of an object). The magnitude of the effect depends on the density of air (and therefore air pressure) or the density of water, respectively; See Apparent Weight for details.

The gravitational effects of the Moon and Sun (also the cause of tides) have very little effect on the apparent strength of Earth's gravity, depending on their relative positions; Typical variations are 2 µm/s (0.2 mGal "Gal (unit)")) over the course of a day.