How strong is gravity on Earth?
Gravity of Earth
The precise strength of Earth's gravity varies depending on location. The nominal "average" value at Earth's surface, known as is, by definition, 9.80665 m/s. This quantity is denoted variously as , (though this sometimes means the normal equatorial value on Earth, 9.78033 m/s), , gee, or simply (which is also used for the variable local value).
Fundamental interaction
This force is larger than the planet Earth would weigh if weighed on another Earth. The atomic nuclei in one jug also repel those in the other with the same force. However, these repulsive forces are canceled by the attraction of the electrons in jug A with the nuclei in jug B and the attraction of the nuclei in jug A with the electrons in jug B, resulting in no net force. Electromagnetic forces are tremendously stronger than gravity but cancel out so that for large bodies gravity dominates.
Seconds pendulum
British physicist Isaac Newton, who used Picard's Earth measurement for establishing his law of universal gravity, explained this variation of the seconds pendulum's length in his "Principia Mathematica" (1687) in which he outlined his theory and calculations on the shape of the Earth. Newton theorized correctly that the Earth was not precisely a sphere but had an oblate ellipsoidal shape, slightly flattened at the poles due to the centrifugal force of its rotation. Since the surface of the Earth is closer to its center at the poles than at the equator, gravity is stronger there. Using geometric calculations, he gave a concrete argument as to the hypothetical ellipsoid shape of the Earth.
Gravity of Earth
At a height "h" above the nominal surface of the earth "g" is given by:
F(R) gravity
where
F(R) gravity
to
Gravitational binding energy
Assuming that the Earth is a uniform sphere (which is not correct, but is close enough to get an order-of-magnitude estimate) with "M" = 5.97 x 10 kg and "r" = 6.37 x 10 m, "U" is 2.24 x 10 J. This is roughly equal to one week of the Sun's total energy output. It is 37.5 MJ/kg, 60% of the absolute value of the potential energy per kilogram at the surface.
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 gravitational acceleration on Mars is 3.72076 ms (about 38% of that of Earth) and it varies laterally. In general, topography-controlled isostasy drives the short wavelength free-air gravity anomalies. At the same time, convective flow and finite strength of the mantle lead to long-wavelength planetary-scale free-air gravity anomalies over the entire planet. Variation in crustal thickness, magmatic and volcanic activities, impact-induced Moho-uplift, seasonal variation of polar ice caps, atmospheric mass variation and variation of porosity of the crust could also correlate to the lateral variations. Over the years models consisting of an increasing but limited number of spherical harmonics have been produced. Maps produced have included free-air gravity anomaly, Bouguer gravity anomaly, and crustal thickness. In some areas of Mars there is a correlation between gravity anomalies and topography. Given the known topography, higher resolution gravity field can be inferred. Tidal deformation of Mars by the Sun or Phobos can be measured by its gravity. This reveals how stiff the interior is, and shows that the core is partially liquid.
The study of surface gravity of Mars can therefore yield information about different features and provide beneficial information for future landing projects.
Gravity of Earth
Where
Spelljammer
All bodies of a sufficiently large size have gravity. This gravity usually (but not always) exerts a force equal to the standard gravitational attraction on the surface of an Earth-sized planetary body. Gravity in the "Spelljammer" universe is also an exceptionally convenient force, and almost always works such that "down" orients itself in a manner most humanoids would find sensible.
Gravity of Earth
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.
Gravitational wave
Gravitational waves are constantly passing Earth; however, even the strongest have a minuscule effect and their sources are generally at a great distance. For example, the waves given off by the cataclysmic final merger of GW150914 reached Earth after travelling over a billion light-years, as a ripple in spacetime that changed the length of a 4-km LIGO arm by a thousandth of the width of a proton, proportionally equivalent to changing the distance to the nearest star outside the Solar System by one hair's width. This tiny effect from even extreme gravitational waves makes them observable on Earth only with the most sophisticated detectors.
Meridian arc
Although it had been known since classical antiquity that the Earth was spherical, by the 17th century, evidence was accumulating that it was not a perfect sphere. In 1672, Jean Richer found the first evidence that gravity was not constant over the Earth (as it would be if the Earth were a sphere); he took a pendulum clock to Cayenne, French Guiana and found that it lost minutes per day compared to its rate at Paris. This indicated the acceleration of gravity was less at Cayenne than at Paris. Pendulum gravimeters began to be taken on voyages to remote parts of the world, and it was slowly discovered that gravity increases smoothly with increasing latitude, gravitational acceleration being about 0.5% greater at the geographical poles than at the Equator.
Gravity of Earth
From the law of universal gravitation, the force on a body acted upon by Earth's gravity is given by
Gravity of Earth
The actual depth dependence of density and gravity, inferred from seismic travel times (see Adams–Williamson equation), is shown in the graphs below.
Gravimeter
The current standard for sensitive gravimeters are the superconducting gravimeters, which operate by suspending a superconducting niobium sphere in an extremely stable magnetic field; the current required to generate the magnetic field that suspends the niobium sphere is proportional to the strength of the Earth's gravitational acceleration. The superconducting gravimeter achieves sensitivities of 10m·s (one nanogal), approximately one trillionth (10) of the Earth surface gravity. In a demonstration of the sensitivity of the superconducting gravimeter, Virtanen (2006), describes how an instrument at Metsähovi, Finland, detected the gradual increase in surface gravity as workmen cleared snow from its laboratory roof.
Earth
The Hill sphere, or the sphere of gravitational influence, of the Earth is about in radius. This is the maximum distance at which the Earth's gravitational influence is stronger than the more distant Sun and planets. Objects must orbit the Earth within this radius, or they can become unbound by the gravitational perturbation of the Sun.
Earth's magnetic field
The Earth's magnetic field strength was measured by Carl Friedrich Gauss in 1832 and has been repeatedly measured since then, showing a relative decay of about 10% over the last 150 years. The Magsat satellite and later satellites have used 3-axis vector magnetometers to probe the 3-D structure of the Earth's magnetic field. The later Ørsted satellite allowed a comparison indicating a dynamic geodynamo in action that appears to be giving rise to an alternate pole under the Atlantic Ocean west of South Africa.
Force
What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as formula_37 and has a magnitude of about 9.81 meters per second squared (this measurement is taken from sea level and may vary depending on location), and points toward the center of the Earth. This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of formula_21 will experience a force:
Graviton (comics)
With time and training, his powers further advanced, even to the extent of levitating an island miles above ground level, exerting his power even while sleeping, somewhat reshaping mountains on the Moon, and demonstrating the ability to lift a small stone in China while residing in L.A., then depositing it in Australia through a victim's head just to see if he could do so. By separating himself from Earth's gravitational field and instead attuning himself to the incredibly stronger gravitational field of the Sun, he was able to cross the distance from Earth to the Sun almost instantaneously, where his individual force field proved strong enough to withstand the forces of the Sun itself, effectively simulating long-range teleportation. To return from the Sun to Earth he utilized the Sun's gravitational field as a form of slingshot device and was able to cross the distance to Earth within minutes.
Mission of Gravity
The story is set on a highly oblate planet named Mesklin, which has surface gravity that varies between 700 "g" at the poles and 3 "g" at the equator. The story is told from the points of view of one of the local intelligent life forms and a human explorer. The locals are centipede-like, in order to withstand the enormous gravity, and terrified of even small heights (because in 700 "g" even a tiny fall is fatal). (See Mesklin for a more comprehensive description of the planet's characteristics.)
Earth mass
An expedition from 1737 to 1740 by Pierre Bouguer and Charles Marie de La Condamine attempted to determine the density of Earth by measuring the period of a pendulum (and therefore the strength of gravity) as a function of elevation. The experiments were carried out in Ecuador and Peru, on Pichincha Volcano and mount Chimborazo. Bouguer wrote in a 1749 paper that they had been able to detect a deflection of 8 seconds of arc, the accuracy was not enough for a definite estimate on the mean density of the Earth, but Bouguer stated that it was at least sufficient to prove that the Earth was not hollow.
Pendulum
During his expedition to Cayenne, French Guiana in 1671, Jean Richer found that a pendulum clock was minutes per day slower at Cayenne than at Paris. From this he deduced that the force of gravity was lower at Cayenne. In 1687, Isaac Newton in "Principia Mathematica" showed that this was because the Earth was not a true sphere but slightly oblate (flattened at the poles) from the effect of centrifugal force due to its rotation, causing gravity to increase with latitude. Portable pendulums began to be taken on voyages to distant lands, as precision gravimeters to measure the acceleration of gravity at different points on Earth, eventually resulting in accurate models of the shape of the Earth.
Weight
In a different gravitational field, for example, on the surface of the Moon, an object can have a significantly different weight than on Earth. The gravity on the surface of the Moon is only about one-sixth as strong as on the surface of the Earth. A one-kilogram mass is still a one-kilogram mass (as mass is an intrinsic property of the object) but the downward force due to gravity, and therefore its weight, is only one-sixth of what the object would have on Earth. So a man of mass 180 pounds weighs only about 30 pounds-force when visiting the Moon.
Gravity of Earth
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
where is the gravitational constant 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
If the density decreased linearly with increasing radius from a density at the center to at the surface, then , and the dependence would be
Standard gravity
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. It is defined by standard as (about ). This value was established by the 3rd CGPM (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration. The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration from the rotation of the Earth (but which is small enough to be neglected for most purposes); the total (the apparent gravity) is about 0.5% greater at the poles than at the Equator.
Gravity of Earth
Gravity acceleration is a vector quantity. In a spherically symmetric Earth, gravity would point directly towards the sphere's centre. As the Earth is slightly flatter, there are consequently slight deviations in the direction of gravity.
Newton (unit)
At average gravity on Earth (conventionally, ), a kilogram mass exerts a force of about 9.8 newtons. An average-sized apple exerts about one newton of force, which we measure as the apple's weight.
Equivalence principle
By contrast, in Newtonian mechanics, gravity is assumed to be a force. This force draws objects having mass towards the center of any massive body. At the Earth's surface, the force of gravity is counteracted by the mechanical (physical) resistance of the Earth's surface. So in Newtonian physics, a person at rest on the surface of a (non-rotating) massive object is in an inertial frame of reference. These considerations suggest the following corollary to the equivalence principle, which Einstein formulated precisely in 1911:
Mercury's magnetic field
The magnetic field is about 1.1% as strong as Earth's. At the Hermean equator, the relative strength of the magnetic field is around 300 nT, which is weaker than that of Jupiter's moon Ganymede. Mercury's magnetic field is weaker than Earth's because its core had cooled and solidified more quickly than Earth's. Although Mercury's magnetic field is much weaker than Earth's magnetic field, it is still strong enough to deflect the solar wind, inducing a magnetosphere. Because Mercury's magnetic field is weak while the interplanetary magnetic field it interacts with in its orbit is relatively strong, the solar wind dynamic pressure at Mercury′s orbit is also three times larger than at Earth.
Wonders of the Universe
This episode documents how gravity has a profound effect across the universe, and Cox seeks out a non-space zero-gravity experience to highlight his point. From the formation of galaxies and stars to the patterns of uplift and erosion seen on Earth, gravity is centrally important. Examples are given, such as the tidal force that captured and locked our moon over time, or more massively in the projected collision between the Andromeda and Milky Way Galaxies. Cox then enters a high-G training centrifuge to show how on Earth, gravity is a relatively weak force, but elsewhere in the Universe it is significantly stronger. In Chaco Culture National Historical Park he refers to Carl Sagan's Cosmos, and its link to a 3-week long supernova in 1054. The almost unimaginable crushing gravitational power of the Crab Pulsar is then contrasted to the distance of an atom's nucleus to its orbiting electrons. Finally, there is a look back at how Einstein's research on gravity has enabled us to better understand how gravity actually works within both "the falling valley" of spacetime and the "event horizon" of black holes.
Gravity
According to Newton's 3rd Law, the Earth itself experiences a force equal in magnitude and opposite in direction to that which it exerts on a falling object. This means that the Earth also accelerates towards the object until they collide. Because the mass of the Earth is huge, however, the acceleration imparted to the Earth by this opposite force is negligible in comparison to the object's. If the object does not bounce after it has collided with the Earth, each of them then exerts a repulsive contact force on the other which effectively balances the attractive force of gravity and prevents further acceleration.
Tide
Whereas the gravitational force subjected by a celestial body on Earth varies inversely as the square of its distance to the Earth, the maximal tidal force varies inversely as, approximately, the cube of this distance. If the tidal force caused by each body were instead equal to its full gravitational force (which is not the case due to the free fall of the whole Earth, not only the oceans, towards these bodies) a different pattern of tidal forces would be observed, e.g. with a much stronger influence from the Sun than from the Moon: The solar gravitational force on the Earth is on average 179 times stronger than the lunar, but because the Sun is on average 389 times farther from the Earth, its field gradient is weaker. The solar tidal force is 46% as large as the lunar. More precisely, the lunar tidal acceleration (along the Moon–Earth axis, at the Earth's surface) is about 1.1 × 10 "g", while the solar tidal acceleration (along the Sun–Earth axis, at the Earth's surface) is about 0.52 × 10 "g", where "g" is the gravitational acceleration at the Earth's surface. Venus has the largest effect of the other planets, at 0.000113 times the solar effect. The system of the Earth, the Moon and the Sun is an example of a three-body problem, and there is no exact mathematical closed-form expression of their interdependence.
Gravity tractor
To get a feel for the magnitude of these issues, let us suppose that a NEO of size around 100 m, and mass of one million metric tons, threatened to impact Earth. Suppose also thatWith these parameters, the required impulse would be: "V" × "M"  = 0.01 [m/s]×10 [kg] = 10 [N-s], so that the average tractor force on the asteroid for 10 years (which is 3.156×10 seconds), would need to be about 0.032 newtons.
An ion-electric spacecraft with a specific impulse of 10,000 N-s per kg, corresponding to an ion beam velocity of 10 kilometres per second (about 20 times that obtained with the best chemical rockets), would require 1,000 kg of reaction mass (xenon is currently favored) to provide the impulse.
The kinetic power of the ion beam would then be approximately 158 watts; the input electric power to the power converter and ion drive would of course be substantially higher.
The spacecraft would need to have enough mass and remain sufficiently close to the asteroid that the component of the average gravitational force on the asteroid in the desired direction would equal or exceed the required 0.032 newtons.
Assuming the spacecraft is hovering over the asteroid at a distance of 200 m to its centre of mass, that would
require it to have a mass of about 20 metric tonnes, because due to the gravitational force we
have
Orders of magnitude (force)
Since weight under gravity is a force, several of these examples refer to the weight of various objects. Unless otherwise stated, these are weights under average Earth gravity at sea level.
Standard gravity
The value of defined above is a nominal midrange value on Earth, originally based on the acceleration of a body in free fall at sea level at a geodetic latitude of 45°. Although the actual acceleration of free fall on Earth varies according to location, the above standard figure is always used for metrological purposes. In particular, it gives the conversion factor between newton and kilogram-force, two units of force.
Absolute rotation
Isaac Newton explained this in his "Principia Mathematica" (1687) in which he outlined his theory and calculations on the shape of the Earth. Newton theorized correctly that the Earth was not precisely a sphere but had an oblate ellipsoidal shape, slightly flattened at the poles due to the centrifugal force of its rotation. Since the surface of the Earth is closer to its center at the poles than at the equator, gravity is stronger there. Using geometric calculations, he gave a concrete argument as to the hypothetical ellipsoid shape of the Earth.
A modern measurement of the Earth's oblateness leads to an equatorial radius of 6378.14 km and a polar radius of 6356.77 km, about 0.1% less oblate than Newton's estimate. A theoretical determination of the precise extent of oblateness in response to a centrifugal force requires an understanding of the make-up of the planet, not only today but during its formation.
Colonization of Titan
Titan has a surface gravity of 0.138 "g", slightly less than the Moon. Managing long-term effects of low gravity on human health would therefore be a significant issue for long-term occupation of Titan, more so than on Mars. These effects are still an active field of study. They can include symptoms such as loss of bone density, loss of muscle density, and a weakened immune system. Astronauts in Earth orbit have remained in microgravity for up to a year or more at a time. Effective countermeasures for the negative effects of low gravity are well-established, particularly an aggressive regime of daily physical exercise or weighted clothing. The variation in the negative effects of low gravity as a function of different levels of low gravity are not known, since all research in this area is restricted to humans in zero gravity. The same goes for the potential effects of low gravity on fetal and pediatric development. It has been hypothesized that children born and raised in low gravity such as on Titan would not be well adapted for life under the higher gravity of Earth.
Geopotential
For geophysical applications, gravity is distinguished from gravitation. Gravity is defined as the resultant of gravitation and the centrifugal force caused by the Earth's rotation. The global mean sea surface is close to one of the equipotential surfaces of the geopotential of gravity formula_1. This equipotential surface, or surface of constant geopotential, is called the geoid.. How the gravitational force and the centrifugal force add up to a force orthogonal to the geoid is illustrated in the figure (not to scale). At latitude 50 deg the off-set between the gravitational force (red line in the figure) and the local vertical (green line in the figure) is in fact 0.098 deg. For a mass point (atmosphere) in motion the centrifugal force no more matches the gravitational and the vector sum is not exactly orthogonal to the Earth surface. This is the cause of the coriolis effect for atmospheric motion. .
Cavendish experiment
The Cavendish experiment, performed in 1797–1798 by British scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate values for the gravitational constant. Because of the unit conventions then in use, the gravitational constant does not appear explicitly in Cavendish's work. Instead, the result was originally expressed as the specific gravity of the Earth, or equivalently the mass of the Earth. His experiment gave the first accurate values for these geophysical constants.
Gravity of Earth
The gravitational effects of the Moon and the Sun (also the cause of the tides) have a very small effect on the apparent strength of Earth's gravity, depending on their relative positions; typical variations are 2 µm/s (0.2 mGal) over the course of a day.
Universe
Of the four fundamental interactions, gravitation is the dominant at astronomical length scales. Gravity's effects are cumulative; by contrast, the effects of positive and negative charges tend to cancel one another, making electromagnetism relatively insignificant on astronomical length scales. The remaining two interactions, the weak and strong nuclear forces, decline very rapidly with distance; their effects are confined mainly to sub-atomic length scales.
Verticity
In his acclaimed 1600 treatise "On the Magnet and Magnetick Bodies, and on That Great Magnet the Earth", William Gilbert distinguished two species of verticity. "Surface verticity", he said, is a tendency to point north found in ordinary "loadstones" and magnetised iron. This verticity was the weaker expression of a more powerful verticity—"deep verticity"—intrinsic to the Earth's core. Gilbert was among the first to believe that the Earth spins, and attributed this spinning to Earth's deep verticity. In his judgement, deep verticity also explained surface verticity: over time, bits and pieces of matter escaped from Earth's core, their verticity having been corrupted and weakened by exposure to the degraded matter of Earth's crust. These bits of matter became the variety of weak magnets found nearer the Earth's surface.
Eugene Gendlin
For example, when a pen falls off a desk, that seems to be proof that gravity exists, because gravity made it fall. But what is "gravity"? In 1500, "gravity" was the pen's desire to go to the center of the earth; in 1700 "gravity" was a force that acted at a distance according to mathematical laws; in the 1900s "gravity" was an effect of curved space-time; and today physicists theorize that "gravity" may be a force carried by subatomic particles called "gravitons". Gendlin views "gravity" as a concept and points out that concepts can't make anything fall. Instead of saying that gravity causes things to fall, it would be more accurate to say that things falling cause [the different concepts of] gravity. Interaction with the world is prior to concepts about the world.
Earth
The gravity of Earth is the acceleration that is imparted to objects due to the distribution of mass within the Earth. Near the Earth's surface, gravitational acceleration is approximately . Local differences in topography, geology, and deeper tectonic structure cause local and broad, regional differences in the Earth's gravitational field, known as gravity anomalies.
Gravitational constant
The existence of the constant is implied in Newton's law of universal gravitation as published in the 1680s (although its notation as dates to the 1890s), but is not calculated in his "Philosophiæ Naturalis Principia Mathematica" where it postulates the inverse-square law of gravitation. In the "Principia", Newton considered the possibility of measuring gravity's strength by measuring the deflection of a pendulum in the vicinity of a large hill, but thought that the effect would be too small to be measurable. 
Nevertheless, he estimated the order of magnitude of the constant when he surmised that "the mean density of the earth might be five or six times as great as the density of water", which is equivalent to a gravitational constant of the order:
Gravimeter
The first gravimeters were vertical accelerometers, specialized for measuring the constant downward acceleration of gravity on the earth's surface. The earth's vertical gravity varies from place to place over the surface of the Earth by about +/- 0.5%. It varies by about +/- 1000 nm/s^2 ("nanometers per second squared") at any location because of the changing positions of the sun and moon relative to the earth.
Gravitation of the Moon
The acceleration due to gravity on the surface of the Moon is about 1.625 m/s, about 16.6% that on Earth's surface or 0.166 . Over the entire surface, the variation in gravitational acceleration is about 0.0253 m/s (1.6% of the acceleration due to gravity). Because weight is directly dependent upon gravitational acceleration, things on the Moon will weigh only 16.6 % (≈ 1/6) of what they weigh on the Earth.
Kilogram-force
The kilogram-force (kgf or kg), or kilopond (kp, from Latin "pondus" meaning "weight"), is a gravitational metric unit of force. It is equal to the magnitude of the force exerted on one kilogram of mass in a gravitational field (standard gravity, a conventional value approximating the average magnitude of gravity on Earth). Therefore, one kilogram-force is by definition equal to . Similarly, a gram-force is , and a milligram-force is . One kilogram-force is approximately 2.204622 pound-force.
Weight
The distinction between mass and weight is unimportant for many practical purposes because the strength of gravity does not vary too much on the surface of the Earth. In a uniform gravitational field, the gravitational force exerted on an object (its weight) is directly proportional to its mass. For example, object A weighs 10 times as much as object B, so therefore the mass of object A is 10 times greater than that of object B. This means that an object's mass can be measured indirectly by its weight, and so, for everyday purposes, weighing (using a weighing scale) is an entirely acceptable way of measuring mass. Similarly, a balance measures mass indirectly by comparing the weight of the measured item to that of an object(s) of known mass. Since the measured item and the comparison mass are in virtually the same location, so experiencing the same gravitational field, the effect of varying gravity does not affect the comparison or the resulting measurement.
Entropic gravity
Entropic gravity provides the underlying framework to explain Modified Newtonian Dynamics, or MOND, which holds that at a gravitational acceleration threshold of approximately m/s², gravitational strength begins to vary "inversely" (linearly) with distance from a mass rather than the normal inverse-square law of the distance. This is an exceedingly low threshold, measuring only 12 trillionths gravity’s strength at earth’s surface; an object dropped from a height of one meter would fall for 36 hours were earth’s gravity this weak. It is also 3,000 times less than exists at the point where crossed our solar system’s heliopause and entered interstellar space.
Gravity of Earth
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 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, an object at the Equator experiences a weaker gravitational pull than an object at the poles.
Centrifugal force
The Earth constitutes a rotating reference frame because it rotates once a day on its axis. Because the rotation is slow, the fictitious forces it produces are small, and in everyday situations can generally be neglected. Even in calculations requiring high precision, the centrifugal force is generally not explicitly included, but rather lumped in with the gravitational force: the strength and direction of the local "gravity" at any point on the Earth's surface is actually a combination of gravitational and centrifugal forces.
Weighing scale
Because gravity varies by over 0.5% over the surface of the earth, the distinction between force due to gravity and mass is relevant for accurate calibration of scales for commercial purposes. Usually the goal is to measure the mass of the sample rather than its force due to gravity at that particular location.
List of unmanned NASA missions
The Gravity Recovery and Climate Experiment (GRACE), a joint mission of NASA and the German Aerospace Center, made detailed measurements of Earth's gravity field from its launch in March 2002 until October 2017. The satellites were launched from Plesetsk Cosmodrome, Russia on a Rockot launch vehicle. By measuring gravity, GRACE showed how mass is distributed around the planet and how it varies over time. Data from the GRACE satellites is an important tool for studying Earth's ocean, geology, and climate.
Fifth force
One way to search for a fifth force is with tests of the strong equivalence principle: this is one of the most powerful tests of Einstein's theory of gravity: general relativity. Alternative theories of gravity, such as Brans–Dicke theory, have a fifth force—possibly with infinite range. This is because gravitational interactions, in theories other than general relativity, have degrees of freedom other than the "metric", which dictates the curvature of space, and different kinds of degrees of freedom produce different effects. For example, a scalar field cannot produce the bending of light rays. The fifth force would manifest itself in an effect on solar system orbits, called the Nordtvedt effect. This is tested with Lunar Laser Ranging Experiment and very long baseline interferometry.
Gravitational acceleration
The "Earth Gravitational Model 1996" (EGM96) contains 130,676 coefficients that refine the model of the Earth's gravitational field ( p. 40). The most significant correction term is about two orders of magnitude more significant than the next largest term ( p. 40). That coefficient is referred to as the formula_21 term, and accounts for the flattening of the poles, or the oblateness, of the Earth. (A shape elongated on its axis of symmetry, like an American football, would be called prolate.) A gravitational potential function can be written for the change in potential energy for a unit mass that is brought from infinity into proximity to the Earth. Taking partial derivatives of that function with respect to a coordinate system will then resolve the directional components of the gravitational acceleration vector, as a function of location. The component due to the Earth's rotation can then be included, if appropriate, based on a sidereal day relative to the stars (≈366.24 days/year) rather than on a solar day (≈365.24 days/year). That component is perpendicular to the axis of rotation rather than to the surface of the Earth.
Astronomia nova
"Gravity is a mutual corporeal disposition among kindred bodies to unite or join together; thus the earth attracts a stone much more than the stone seeks the earth. (The magnetic faculty is another example of this sort)... If two stones were set near one another in some place in the world outside the sphere of influence of a third kindred body, these stones, like two magnetic bodies, would come together in an intermediate place, each approaching the other by a space proportional to the bulk ["moles"] of the other... For it follows that if the earth's power of attraction will be much more likely to extend to the moon and far beyond, and accordingly, that nothing that consists to any extent whatever of terrestrial material, carried up on high, ever escapes the grasp of this mighty power of attraction.”
Gravity of Earth
Tools exist for calculating the strength of gravity at various cities around the world. The effect of latitude can be clearly seen with gravity in high-latitude cities: Anchorage (9.826 m/s), Helsinki (9.825 m/s), being about 0.5% greater than that in cities near the equator: Kuala Lumpur (9.776 m/s), Manila (9.780 m/s). The effect of altitude can be seen in Mexico City (9.776 m/s; altitude ), and by comparing Denver (9.798 m/s; ) with Washington, D.C. (9.801 m/s; ), 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.
Jean Richer
While there he also measured the length of a seconds pendulum, that is a pendulum with a half-swing of one second, and found it to be 1.25 "lignes" (2.8 millimeters*) shorter than at Paris. Isaac Newton later commented that if, as he had proposed, the force of gravity decreases with the inverse square of the distance between objects, the obvious conclusion to be drawn from Richer's work is that near-equatorial Cayenne is further from the center of the earth than Paris, where the first such measurements had been taken. Thus the earth could not be spherical, as had earlier been presumed, but rather bulges at and near the equator. It could be said that Richer was the first person to observe a change in gravitational force over the surface of the earth, beginning the science of gravimetry.
Raft (novel)
The novel is an elaborated version of his 1989 short story of the same title. The story follows a group of humans who have accidentally entered an alternate universe where the gravitational force is far stronger than our own, a "billion" times as strong. Planets do not exist, as they would immediately collapse under their own gravity; stars are only a mile across and have extremely brief life-spans, becoming cooled kernels a hundred yards wide with a surface gravity of five "g". Human bodies possess a "respectable" gravity field in and of themselves. "Gravitic chemistry" also exists, where gravity is the dominant force on an atomic scale.
Eötvös experiment
As seen from the Earth's frame of reference (or "lab frame", which is not an inertial frame of reference), the primary forces acting on the balanced masses are the string tension, gravity, and the centrifugal force due to the rotation of the Earth. Gravity is calculated by Newton's law of universal gravitation, which depends on gravitational mass. The centrifugal force is calculated by Newton's laws of motion and depends on inertial mass.
Axial precession
The tidal force on Earth due to a perturbing body (Sun, Moon or planet) is expressed by Newton's law of universal gravitation, whereby the gravitational force of the perturbing body on the side of Earth nearest is said to be greater than the gravitational force on the far side by an amount proportional to the difference in the cubes of the distances between the near and far sides. If the gravitational force of the perturbing body acting on the mass of the Earth as a point mass at the center of Earth ( which provides the centripetal force causing the orbital motion ) is subtracted from the gravitational force of the perturbing body everywhere on the surface of Earth, what remains may be regarded as the tidal force. This gives the paradoxical notion of a force acting away from the satellite but in reality it is simply a lesser force towards that body due to the gradient in the gravitational field. For precession, this tidal force can be grouped into two forces which only act on the equatorial bulge outside of a mean spherical radius. This couple can be decomposed into two pairs of components, one pair parallel to Earth's equatorial plane toward and away from the perturbing body which cancel each other out, and another pair parallel to Earth's rotational axis, both toward the ecliptic plane. The latter pair of forces creates the following torque vector on Earth's equatorial bulge:
Micro-g environment
A "stationary" micro-g environment would require travelling far enough into deep space so as to reduce the effect of gravity by attenuation to almost zero. This is the simplest in conception, but requires traveling an enormous distance, rendering it most impractical. For example, to reduce the gravity of the Earth by a factor of one million, one needs to be at a distance of 6 million kilometers from the Earth, but to reduce the gravity of the Sun to this amount one has to be at a distance of 3.7 billion kilometers. (On Earth the gravity due to the rest of the Milky Way is already attenuated by a factor greater than one million, so we do not need to move away further from its center). Thus it is not impossible, but it has only been achieved so far by four interstellar probes (Voyager 1 and 2 of the Voyager program, and Pioneer 10 and 11 of the Pioneer program) and they did not return to Earth. To reduce the gravity to one thousandth of that on Earth's surface, one needs to be at a distance of 200,000 km.
F(R) gravity
with
Kilogram
Gravity and the nature of the Kibble balance, which oscillates test masses up and down against the local gravitational acceleration "g", are exploited so that mechanical power is compared against electrical power, which is the square of voltage divided by electrical resistance. However, "g" varies significantly—by nearly 1%—depending on where on the Earth's surface the measurement is made (see "Earth's gravity"). There are also slight seasonal variations in "g" at a location due to changes in underground water tables, and larger semimonthly and diurnal changes due to tidal distortions in the Earth's shape caused by the Moon and the Sun. Although "g" would not be a term in the "definition" of the kilogram, it would be crucial in the process of measurement of the kilogram when relating energy to power. Accordingly, "g" must be measured with at least as much precision and accuracy as are the other terms, so measurements of "g" must also be traceable to fundamental constants of nature. For the most precise work in mass metrology, "g" is measured using dropping-mass absolute gravimeters that contain an iodine-stabilized helium–neon laser interferometer. The fringe-signal, frequency-sweep output from the interferometer is measured with a rubidium atomic clock. Since this type of dropping-mass gravimeter derives its accuracy and stability from the constancy of the speed of light as well as the innate properties of helium, neon, and rubidium atoms, the 'gravity' term in the delineation of an all-electronic kilogram is also measured in terms of invariants of nature—and with very high precision. For instance, in the basement of the NIST's Gaithersburg facility in 2009, when measuring the gravity acting upon Pt10Ir test masses (which are denser, smaller, and have a slightly lower center of gravity inside the Kibble balance than stainless steel masses), the measured value was typically within 8 ppb of .
Earth's magnetic field
The average magnetic field in the Earth's outer core was calculated to be 25 gausses, 50 times stronger than the field at the surface.
Geophysics
Gravity measurements became part of geodesy because they were needed to related measurements at the surface of the Earth to the reference coordinate system. Gravity measurements on land can be made using gravimeters deployed either on the surface or in helicopter flyovers. Since the 1960s, the Earth's gravity field has been measured by analyzing the motion of satellites. Sea level can also be measured by satellites using radar altimetry, contributing to a more accurate geoid. In 2002, NASA launched the Gravity Recovery and Climate Experiment (GRACE), wherein two twin satellites map variations in Earth's gravity field by making measurements of the distance between the two satellites using GPS and a microwave ranging system. Gravity variations detected by GRACE include those caused by changes in ocean currents; runoff and ground water depletion; melting ice sheets and glaciers.
Earth mass
Precise measurement of the Earth mass is difficult, as it is equivalent to measuring the gravitational constant, which is the fundamental physical constant known with least accuracy, due to the relative weakness of the gravitational force.
The mass of the Earth was first measured with any accuracy (within about 20% of the correct value) in the Schiehallion experiment in the 1770s, and within 1% of the modern value in the Cavendish experiment of 1798.
Potential energy
In classical physics, gravity exerts a constant downward force F=(0, 0, "F") on the center of mass of a body moving near the surface of the Earth. The work of gravity on a body moving along a trajectory r(t) = ("x"(t), "y"(t), "z"(t)), such as the track of a roller coaster is calculated using its velocity, v=("v", "v", "v"), to obtain
where the integral of the vertical component of velocity is the vertical distance. Notice that the work of gravity depends only on the vertical movement of the curve r(t).
Clairaut's theorem
Although it had been known since antiquity that the Earth was spherical, by the 17th century evidence was accumulating that it was not a perfect sphere. In 1672 Jean Richer found the first evidence that gravity was not constant over the Earth (as it would be if the Earth were a sphere); he took a pendulum clock to Cayenne, French Guiana and found that it lost minutes per day compared to its rate at Paris. This indicated the acceleration of gravity was less at Cayenne than at Paris. Pendulum gravimeters began to be taken on voyages to remote parts of the world, and it was slowly discovered that gravity increases smoothly with increasing latitude, gravitational acceleration being about 0.5% greater at the poles than at the equator.
Saiyan (Dragon Ball)
Saiyans are incredibly strong, even at young age, easily lifting objects in the hundreds and thousands of kilos. Their strength is explained by their physiology and the gravity on Planet Vegeta, ten times the Earth's normal gravity, thus granting them correspondingly greater strength in Earth gravity and similar environments.
Gravity
Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915) which describes gravity not as a force, but as a consequence of the curvature of spacetime caused by the uneven distribution of mass. The most extreme example of this curvature of spacetime is a black hole, from which nothing—not even light—can escape once past the black hole's event horizon. However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force which causes any two bodies to be attracted to each other, with the force proportional to the product of their masses and inversely proportional to the square of the distance between them.
Gravitoelectromagnetism
From this calculation it follows that Earth's equatorial gravitomagnetic field is about  Hz, or in units of standard gravity (9.81 m/s) divided by the speed of light. Such a field is extremely weak and requires extremely sensitive measurements to be detected. One experiment to measure such field was the Gravity Probe B mission.
Gravity of Earth
Using the mass and radius of the Earth:
Weight
The kilogram-force is a non-SI unit of force, defined as the force exerted by a one kilogram mass in standard Earth gravity (equal to 9.80665 newtons exactly). The dyne is the cgs unit of force and is not a part of SI, while weights measured in the cgs unit of mass, the gram, remain a part of SI.
Equivalence principle
The strong equivalence principle suggests that gravity is entirely geometrical by nature (that is, the metric alone determines the effect of gravity) and does not have any extra fields associated with it. If an observer measures a patch of space to be flat, then the strong equivalence principle suggests that it is absolutely equivalent to any other patch of flat space elsewhere in the universe. Einstein's theory of general relativity (including the cosmological constant) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number of alternative theories, such as Brans–Dicke theory, satisfy only the Einstein equivalence principle.
Gravity of Earth
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.
Earth mass
The uncertainty in the modern value for the Earth's mass has been entirely due to the uncertainty in the gravitational constant "G" since at least the 1960s.
"G" is notoriously difficult to measure, and some high-precision measurements during the 1980s to 2010s have yielded mutually exclusive results.
Sagitov (1969) based on the measurement of "G" by Heyl and Chrzanowski (1942) cited a value of (relative uncertainty ).
Reaction (physics)
Any mass on earth is pulled down by the gravitational force of the earth; this force is also called its weight. The corresponding 'reaction' is the gravitational force that mass exerts on the planet.
Potential energy
The factors that affect an object's gravitational potential energy are its height relative to some reference point, its mass, and the strength of the gravitational field it is in. Thus, a book lying on a table has less gravitational potential energy than the same book on top of a taller cupboard and less gravitational potential energy than a heavier book lying on the same table. An object at a certain height above the Moon's surface has less gravitational potential energy than at the same height above the Earth's surface because the Moon's gravity is weaker. Note that "height" in the common sense of the term cannot be used for gravitational potential energy calculations when gravity is not assumed to be a constant. The following sections provide more detail.
Surface gravity
where "g" is the surface gravity of an object, expressed as a multiple of the Earth's, "m" is its mass, expressed as a multiple of the Earth's mass (5.976·10 kg) and "r" its radius, expressed as a multiple of the Earth's (mean) radius (6,371 km). For instance, Mars has a mass of 6.4185·10 kg = 0.107 Earth masses and a mean radius of 3,390 km = 0.532 Earth radii. The surface gravity of Mars is therefore approximately
Fundamental interaction
"Gravitation" is by far the weakest of the four interactions at the atomic scale, where electromagnetic interactions dominate. But the idea that the weakness of gravity can easily be demonstrated by suspending a pin using a simple magnet (such as a refrigerator magnet) is fundamentally flawed. The only reason the magnet is able to hold the pin against the gravitational pull of the entire Earth is due to its relative proximity. There is clearly a short distance of separation between magnet and pin where a breaking point is reached, and due to the large mass of Earth this distance is disappointingly small.
Gravimetry
Gravity is usually measured in units of acceleration. In the SI system of units, the standard unit of acceleration is 1 metre per second squared (abbreviated as m/s). Other units include the gal (sometimes known as a "galileo", in either case with symbol Gal), which equals 1 centimetre per second squared, and the "g" ("g"), equal to 9.80665 m/s. The value of the "g" approximately equals the acceleration due to gravity at the Earth's surface (although the value of "g" varies by location).
Admittance (geophysics)
In geophysics, admittance describes the small effects of atmospheric pressure on earth gravity. Studies have also been carried out regarding the gravity of Venus.
Admittance in geophysics takes atmospheric pressure as the input and measures small changes in the gravitational field as the output. Geophysics admittance is commonly measured in μGal/mbar. These units convert according to 1 Gal = 0.01 m/s and 1 bar = 100 kPa, so in SI units the measurement would be in units of;
The New Adventures of Flash Gordon
Mongo's surface gravity appears to be a bit less than that of Earth, or at least there are comments on occasion that Terrans are stronger on Mongo than they are on Earth. The difference in surface gravity can not be too great, because Mongo is so Earth-like, and Terrans on Mongo are by no means superhuman.
Colonization of Venus
At present it has not been established whether the gravity of Mars, 0.38 times that of the Earth, would be sufficient to avoid bone decalcification and loss of muscle tone experienced by astronauts living in an environment of microgravity. In contrast, Venus is close in size and mass to the Earth, resulting in a similar surface gravity (0.904 "g") that would likely be sufficient to prevent the health problems associated with weightlessness. Most other space exploration and colonization plans face concerns about the damaging effect of long-term exposure to fractional "g" or zero gravity on the human musculoskeletal system.
Gravity
Gravity (), or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or "gravitate" toward) one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing, forming starsand for the stars to group together into galaxiesso gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become increasingly weaker on farther objects.
Gravity of Earth
So, to find the acceleration due to gravity at sea level, substitute the values of the gravitational constant, "G", the Earth's mass (in kilograms), "m", and the Earth's radius (in metres), "r", to obtain the value of "g":
Gravity of Earth
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.
Gravity
The earliest instance of gravity in the Universe, possibly in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch (up to 10 seconds after the birth of the Universe), possibly from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a currently unknown manner. Attempts to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory, which would allow gravity to be united in a common mathematical framework (a theory of everything) with the other three forces of physics, are a current area of research.
Mass versus weight
When an object's weight (its gravitational force) is expressed in "kilograms", this actually refers to the kilogram-force (kgf or kg-f), also known as the "kilopond" (kp), which is a non-SI unit of force. All objects on the Earth's surface are subject to a gravitational acceleration of approximately 9.8 m/s. The General Conference on Weights and Measures fixed the value of standard gravity at precisely 9.80665 m/s so that disciplines such as metrology would have a standard value for converting units of defined mass into defined forces and pressures. Thus the kilogram-force is defined as precisely 9.80665 newtons. In reality, gravitational acceleration (symbol: "g") varies slightly with latitude, elevation and subsurface density; these variations are typically only a few tenths of a percent. See also "Gravimetry".
Artificial gravity in fiction
In the anime "Dragon Ball Z", gravity simulation plays a key part in various characters' training regime. It is also used to demonstrate the characters' increasing strength. For example, when Goku first arrives on King Kai's planet, he is nearly crushed by the gravity, which is ten times that of Earth's. By the end of his visit, nearly a year later, he is able to move at great speed under such conditions. This method of training gradually appears more and more in the universe, and the gravity gets stronger as well. Ten times Earth's gravity goes from a seemingly indomitable level of opposition to nothing, and several hundred times Earth's gravity becomes the standard. Vegeta even had a Gravity Room built into his house.
Gravitational biology
Gravitational biology is the study of the effects gravity has on living organisms. Throughout the history of the Earth life has evolved to survive changing conditions, such as changes in the climate and habitat. However, one constant factor in evolution since life first began on Earth is the force of gravity. As a consequence, all biological processes are accustomed to the ever-present force of gravity and even small variations in this force can have significant impact on the health and function and the system of organisms.
IK Pegasi
The massive, compact nature of a white dwarf produces a strong surface gravity. Astronomers denote this value by the decimal logarithm of the gravitational force in cgs units, or log "g". For IK Pegasi B, log "g" is 8.95. By comparison, log "g" for the Earth is 2.99. Thus the surface gravity on IK Pegasi is over 900,000 times the gravitational force on the Earth.
Surface gravity
Surface gravity is measured in units of acceleration, which, in the SI system, are meters per second squared. It may also be expressed as a multiple of the Earth's standard surface gravity, "g" = 9.80665 m/s². In astrophysics, the surface gravity may be expressed as log "g", which is obtained by first expressing the gravity in cgs units, where the unit of acceleration is centimeters per second squared, and then taking the base-10 logarithm. Therefore, the surface gravity of Earth could be expressed in cgs units as 980.665 cm/s², with a base-10 logarithm (log "g") of 2.992.
Gravity
The force of gravity on Earth is the resultant (vector sum) of two forces: (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The force of gravity is the weakest at the equator because of the centrifugal force caused by the Earth's rotation and because points on the equator are furthest from the center of the Earth. The force of gravity varies with latitude and increases from about 9.780 m/s at the Equator to about 9.832 m/s at the poles.
Introduction to general relativity
Compared with planets and other astronomical bodies, the objects of everyday life (people, cars, houses, even mountains) have little mass. Where such objects are concerned, the laws governing the behavior of test particles are sufficient to describe what happens. Notably, in order to deflect a test particle from its geodesic path, an external force must be applied. A chair someone is sitting on applies an external upwards force preventing the person from falling freely towards the center of the Earth and thus following a geodesic, which they would otherwise be doing without matter in between them and the center of the Earth. In this way, general relativity explains the daily experience of gravity on the surface of the Earth "not" as the downwards pull of a gravitational force, but as the upwards push of external forces. These forces deflect all bodies resting on the Earth's surface from the geodesics they would otherwise follow. For matter objects whose own gravitational influence cannot be neglected, the laws of motion are somewhat more complicated than for test particles, although it remains true that spacetime tells matter how to move.
Earth mass
The figure of the Earth has been known to better than four significant digits since the 1960s (WGS66), so that since that time, the uncertainty of the Earth mass is determined essentially by the uncertainty in measuring the gravitational constant.
Relative uncertainty was cited at 0.06% in the 1970s, and at 0.01% (10) by the 2000s. 
The current relative uncertainty of 10 amounts to in absolute terms, of the order of the mass of a minor planet (70% of the mass of Ceres).
Earth's magnetic field
At any location, the Earth's magnetic field can be represented by a three-dimensional vector. A typical procedure for measuring its direction is to use a compass to determine the direction of magnetic North. Its angle relative to true North is the "declination" () or "variation". Facing magnetic North, the angle the field makes with the horizontal is the "inclination" () or "magnetic dip". The "intensity" () of the field is proportional to the force it exerts on a magnet. Another common representation is in (North), (East) and (Down) coordinates.
The intensity of the field is often measured in gauss (G), but is generally reported in nanoteslas (nT), with 1 G = 100,000 nT. A nanotesla is also referred to as a gamma (γ). The tesla is the SI unit of the magnetic field, B. The Earth's field ranges between approximately 25,000 and 65,000 nT (0.25–0.65 G). By comparison, a strong refrigerator magnet has a field of about .
Gravitational potential
A spherically symmetric mass distribution behaves to an observer completely outside the distribution as though all of the mass was concentrated at the center, and thus effectively as a point mass, by the shell theorem. On the surface of the earth, the acceleration is given by so-called standard gravity "g", approximately 9.8 m/s, although this value varies slightly with latitude and altitude: The magnitude of the acceleration is a little larger at the poles than at the equator because Earth is an oblate spheroid.