Gravity

For other uses, see Gravity (disambiguation).

It has been suggested that gravitation be merged into this article or section. (Discuss)

Gravity is a force of attraction that acts between bodies that have mass. It is a physical phenomenon of fundamental importance, profoundly affecting the workings of the world around us and the universe beyond. Most familiarly, it is the gravitational attraction of the earth that endows objects with weight and causes them to fall to the ground when dropped. In fact, gravity is also the reason for the very existence of the earth, the sun and other celestial bodies; without it matter would not have coalesced into these bodies and life as we know it would not exist. Gravity is also responsible for keeping the earth and the other planets in their orbits around the sun, the moon in its orbit around the earth, for the tides, and for various other natural phenomena that we observe.

In common usage "gravity" and "gravitation" are either used interchangeably, or the distinction is sometimes made that "gravity" is specifically the attractive force of the earth, while "gravitation" is the general property of mutual attraction between bodies of matter. In technical usage, "gravitation" is the tendency of bodies to accelerate towards one another, and "gravity" is the force that some theories use to explain this acceleration.

Gravity was rather poorly understood until Isaac Newton formulated his law of gravitation in the 17th century. Newton's theory is still widely used for many practical purposes, though for more advanced work it has been supplanted by Einstein's general relativity. While a great deal is now known about the properties of gravity, the ultimate cause of the gravitational force remains an open question and gravity remains an important topic of scientific research.

Overview of the history of gravitational theory

The first mathematical formulation of gravity was Isaac Newton's law of universal gravitation, published in his 1687 work Principia Mathematica. Professor William Whewell of Cambridge University, author of History of the Inductive Sciences (1837) stated:

"The law of gravitation is indisputably and incomparably the greatest scientific discovery ever made, whether we look at the advance which it involved, the extent of the truth disclosed, or the fundamental and satisfactory nature of this truth." [In A Treasury of Science ed. Harlow Shapley et al, Harper & Bros. NY: 1946]

Although the law of universal gravitation was first clearly and rigorously formulated by Isaac Newton, the phenomenon was observed and recorded by others. Even Ptolemy (c. 100-178) had a vague conception of a force tending toward the center of the Earth which not only kept bodies upon its surface, but in some way upheld the order of the universe. Indian astronomer Brahmagupta (598-668), who followed a heliocentric solar system, was the first to recognize gravity as a force of attraction. He explained that "bodies fall towards the Earth as it is in the nature of the Earth to attract bodies, just as it is in the nature of water to flow". The Sanskrit term he used for gravity, 'gruhtvaakarshan' [similar sounding to the English 'gravity' when pronounced correctly] had roughly the same meaning as "attraction". Johannes Kepler (1571–1630) inferred that the planets move in their orbits under some influence or force exerted by the Sun; but the laws of motion were not then sufficiently developed, nor were Kepler's ideas of force sufficiently clear, to make a precise statement of the nature of the force. Christiaan Huygens and Robert Hooke, contemporaries of Newton, saw that Kepler's third law implied a force which varied inversely as the square of the distance. Newton's conceptual advance was to understand that the same force that causes a thrown rock to fall back to the Earth keeps the planets in orbit around the Sun, and the Moon in orbit around the Earth.

Newton was not alone in making significant contributions to the understanding of gravity. Before Newton, Galileo Galilei corrected a common misconception, started by Aristotle, that objects with different mass fall at different rates. To Aristotle, it simply made sense that objects of different mass would fall at different rates, and the ancient Greeks relied more on philosophic thought experiments than experimentation. Galileo, however, used experiments that actually observed falling objects of different mass released simultaneously. Most of Galileo's work was done with objects on inclined planes. Aside from differences due to friction, Galileo observed that all masses accelerate at the same rate. Newton's equation, <math>F = m a</math>, (see Acceleration due to gravity) showed insight into gravity's proportionality to mass that was missing from Galileo's law of inertia. However, both the work of Johannes Kepler and Galileo influenced Isaac Newton's formulation of the law of gravity.

Newton's law remained the standard theory of gravity until it was replaced by Einstein's theory of gravitation (general relativity) in the early part of the 20th century. Motivated by the equivalence principle, this more accurate theory postulates that mass and energy curve space-time, resulting in the phenomenon known as gravity. However, because general relativity's influence on gravity calculations is minimal or even imperceptible at speeds much less than the speed of light, Newtonian gravity is sufficiently accurate for calculations involving weak gravitational fields (e.g., launching rockets, projectiles, pendulums, etc.), and Newton's formulae are generally still preferred where they are applicable.

A number of alternative theories of gravitation have been proposed over the years, but none has gained general acceptance. Current theoretical work largely focuses on the relationship between gravity and quantum mechanics.

The Earth's gravity

The acceleration due to gravity at the Earth's surface, denoted g, is approximately 9.8 m/s² (metres per second squared) or 32 ft/sec². This means that, ignoring air resistance, an object falling freely near the earth's surface increases in speed by 9.8 m/s (around 22 mph) for each second of its descent. Thus, an object starting from rest will attain a speed of 9.8 m/s after one second, 19.6 m/s after two seconds, and so on. The earth itself experiences an equal and opposite force to that of the falling object, meaning that the earth also accelerates towards the object. However, because of the immense mass of the earth this acceleration is vanishingly small.

Non-gravitational acceleration of a roughly similar order of magnitude, such as is experienced in an aircraft or racing car, is often stated in multiples of g. When used as a measurement unit, the quantity is often called "gee", as g can be mistaken for g, the gram symbol.

The Gravity Field and Steady-State Ocean Circulation Explorer project (GOCE) will measure high-accuracy gravity gradients and provide a global model of the Earth's gravity field and of the geoid. (ESA image)

Precise values of g vary depending on the location on the Earth's surface. The standard acceleration due to gravity at the Earth's surface is, by definition, 9.80665 m/s². This quantity is known variously as g_n, g_e (though this sometimes means the normal equatorial value on Earth, 9.78033 m/s²), g₀, gee, or simply g (which is also used for the variable local value). The variation in gravitational strength per unit distance is measured in inverse seconds squared or in eotvoses, a cgs unit of gravitational gradient.

When measuring g with precision, it is important to distinguish between the actual strength of gravity and the apparent strength of gravity. Local variations in the actual strength of the Earth's gravitational field arise because the earth is not a perfect sphere and is not of uniform density. The main deviation from sphericity is the earth's equatorial bulge, which causes gravity to be weaker at the equator than the poles. The local topography (such as the presence of mountains) and geology (the density of rocks in the vicinity) also influence the gravitional field to a small extent.

Other forces acting on an object may augment or oppose the earth's actual gravitational field, causing variations in the apparent force of gravity (see also Apparent weight.) One example is the centrifugal force caused by the earth's rotation, which imparts an upwards force opposing gravity and diminishing its apparent effect. This effect is stronger at lower latitudes (i.e. nearer the equator), reducing to zero at the poles. Another example is buoyancy: even in air, objects experience a small supporting force which reduces the apparent strength of gravity. Finally, the gravitational effects of the Moon and the Sun (also the cause of the tides) also have a small effect on apparent gravity, depending on their relative positions; typical variations are 2 µm/s² (0.2 mGal) over the course of a day.

In combination, the equatorial bulge and the effects of centrifugal force mean that sea-level gravitational acceleration increases from about 9.780 m/s² at the equator to about 9.832 m/s² at the poles, so an object will weigh about 0.5% more at the poles than at the equator [1]. See Gee for further information.

Gravity also decreases with altitude (since greater altitude means greater distance from the earth's centre). All other things being equal, an increase in altitude from sea level to the top of Mount Everest (8,850 metres) causes a weight decrease of about 0.28%. 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 250 miles (roughly the height that the space shuttle flies) gravity is still nearly 90% as strong as at the earth's surface, and weightlessness actually occurs because orbiting objects are in free-fall.

If the earth was of perfectly uniform composition then, during a descent to the centre of the earth, gravity would decrease linearly with distance, reaching zero at the centre. In reality, the gravitational field peaks within the Earth at the core-mantle boundary where it has a value of 10.7 m/s².

Comparative gravities of the Earth, Sun, Moon and planets

The table below shows gravitational accelerations (in multiples of g) at the surface of the Sun, the Earth's moon, and each of the planets in the solar system. The "surface" is taken to mean the cloud tops of the gas giants (Jupiter, Saturn, Uranus and Neptune). It is usually specified as the location where the pressure is equal to a certain value (normally 75 kPa?). For the Sun, the "surface" is taken to mean the photosphere.

For spherical bodies, surface gravity in m/s² is 2.8 × 10⁻¹⁰ times the radius in metres times the average density in kg/m³ (kilograms per cubic metre).

When flying from Earth to Mars, climbing against the field of the Earth at the start is 100 000 times heavier than climbing against the force of the sun for the rest of the flight.

Mathematical equations for a falling body

The equations below describe a value of the force pulling down a falling body, assuming that the acceleration due to gravity is a constant, g (in which case Newton's law of gravitation simplifies to F = mg where m is the mass of the body). This assumption is reasonable for objects falling to earth over the relatively short vertical distances of our everyday experience, but is very much untrue over larger distances (such as spacecraft trajectories).

Galileo was the first to demonstrate and then formulate these equations. He used a ramp to study rolling balls, the ramp slowing the acceleration enough to measure the time taken for the ball to roll a known distance. He measured elapsed time with a water clock, using an "extremely accurate balance" to measure the amount of water².

The equations ignore air resistance, which has a dramatic effect on objects falling an appreciable distance in air, causing them to quickly approach a terminal velocity. For example, a person jumping headfirst from an airplane will never exceed a speed of about 200 mph due to air resistance. The effect of air resistance varies enormously depending on the size and geometry of the falling object – for example, the equations are hopelessly wrong for a feather, which has a low mass but offers a large resistance to the air. (In the absence of an atmosphere all objects fall at the same rate, as astronaut David Scott demonstrated by dropping a hammer and a feather on the surface of the Moon.)

The equations also ignore the rotation of the Earth, failing to describe the Coriolis effect for example. Nevertheless, they are usually accurate enough for dense and compact objects falling over heights not exceeding the tallest man-made structures.

Near the surface of the Earth, use g = 9.8 m/s² (metres per second per second), approximately. For other planets, multiply g by the appropriate scaling factor. It is essential to use consistent units for g, d, t and v. Assuming SI units, g is measured in metres per second per second, so d must be measured in metres, t in seconds and v in metres per second. To convert metres per second to kilometres per hour (km/h) multiply by 3.6. In all cases the body is assumed to start from rest.

Example: the first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1² = 4.9 meters. After two seconds it will have fallen 1/2 × 9.8 × 2² = 19.6 metres; and so on.

Gravitational potential

For any mass distribution there is a scalar field, the gravitational potential (a scalar potential), which is the gravitational potential energy per unit mass of a point mass, as function of position. It is

<math>- G \int{1 \over r} dm</math>

where the integral is taken over all mass. Minus its gradient is the gravity field itself, and minus its Laplacian is the divergence of the gravity field, which is everywhere equal to -4πG times the local density.

Thus when outside masses the potential satisfies Laplace's equation (i.e., the potential is a harmonic function), and when inside masses the potential satisfies Poisson's equation with, as right-hand side, 4πG times the local density.

Acceleration relative to the rotating Earth

The acceleration measured on the rotating surface of the Earth is not quite the same as the acceleration that is measured for a free-falling body because of the centrifugal force. In other words, the apparent acceleration in the rotating frame of reference is the total gravity vector minus a small vector toward the north-south axis of the Earth, corresponding to staying stationary in that frame of reference.

Gravity and astronomy

"I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centres about which they revolve, and thereby compared the force requisite to keep the moon in her orb with the force of gravity at the surface of the earth and found them to answer pretty nearly." -- Isaac Newton, 1666

So Newton's original formula was:

<math>{\rm Force\,of\,gravity} \propto \frac{\rm mass\,of\,object\,1\,\times\,mass\,of\,object\,2}{\rm distance\,from\,centers^2}</math>

where the symbol <math>\propto</math> means "is proportional to".

To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them. This gravitational constant was discovered in 1797 by Henry Cavendish.

Thus the discovery and application of Newton's law of gravity accounts for the detailed information we have about the planets in our solar system, the mass of the sun, the distance to stars and even the theory of dark matter. Although we haven't traveled to all the planets nor to the sun, we know their mass. This is through the study of the law of gravity.

In space everything is in an orbit around some massive object. They maintain orbit because of the force of gravity between them. Planets orbit stars, stars orbit galactic centers, galaxys orbit a center of mass in clusters, and clusters orbit in superclusters.

By watching how the position of a planet changes with respect to earth over the course of a year, we can determine by using geometry how far that planet is from the sun compared to how far the earth is, thus getting the distance from that planet to the sun. Copernicus calculated the distances of the inner planets and Kepler noticed a relation between them and their orbits. When Newton formulated his law of gravity, he generalized Kepler's third law to show that the masses of the sun and the planets were involved in the calculation. From Newton's law of gravity, science calculated the mass of the sun basically using Kepler's third law that the sidereal period of an object in orbit around another object cubed is equal to the distance between them, the radius, squared, in conjunction with Newton's law of gravity applying the product of the masses.

From this calculation using Newton's law of gravity any two orbiting objects in the universe could be compared and their masses could be calculated. Where the sidereal period is known then the centripetal acceleration is known given the distance between the objects. Therefore, from a known velocity of an astronomical object orbiting around another astronomical object and from the known distance between them, you can calculate the masses of the objects. This is all due to the law of gravity where the force between objects is proportional to their masses and inversely proportional to the distance between them.

Albireo, binary star system.

The calculations from Newton's law of gravity are so exact for astronomical measurements (except near black holes and neutron stars) that in 1846 two astronomers, John Couch Adams and Urbain Le Verrier, working independently, located an undiscovered planet later called Neptune simply by mathematical calculations using the law of gravity. (In fact, these calculations have been described as "totally wrong", and the agreement of Neptune's actual position with its calculated position an "accident" [2]. However, this was due to human error, not a flaw in the law of gravity.)

Self-gravitating system

A self-gravitating system is a system of masses kept together by mutual gravity. An example is a binary star.

Practical uses of gravity

A vast number of mechanical contrivances depend in some way on gravity for their operation. This list includes applications where gravity plays a central or particularly interesting role.

• A height difference can provide a useful pressure in a liquid, as in the case of an intravenous drip or a water tower.

Shot Tower, 1856 Dubuque, Iowa

• The gravitational potential energy of water supplies hydroelectricity. It can also be used to power a tramcar up an incline, using a system of water tanks and pulleys. An example is the Lynton & Lynmouth Cliff Railway in Devon, England.

• A weight hanging from a cable over a pulley provides a constant tension in the cable, including the part on the other side of the pulley to the weight.

• Molten lead, when poured into the top of a shot tower, will coalesce into a rain of spherical lead shot, first separating into droplets, forming molten spheres, and finally freezing solid, undergoing many of the same effects as meteoritic tektites, which will cool into spherical, or near-spherical shapes in free-fall.

• A fractionation tower can be used to manufacture some materials by separating out the material components based on their specific gravity.

• Weight-driven clocks are powered by gravitational potential energy, and pendulum clocks depend on gravity to regulate time.

• Artificial satellites are an application of gravitation which was mathematically described in Newton's Principia.

Newton's law of universal gravitation

It has been suggested that this section be split into a new article. (Discuss)

Newton's law of universal gravitation states the following:

Every point mass attracts every other point mass by a force directed along the line connecting the two. This force is proportional to the product of the masses and inversely proportional to the square of the distance between them:

<math>F = G \frac{m_1 m_2}{r^2}</math>

where:

F is the magnitude of the (repulsive) gravitational force between the two point masses

G is the gravitational constant

m₁ is the mass of the first point mass

m₂ is the mass of the second point mass

r is the distance between the two point masses

Assuming SI units, F is measured in newtons (N), m₁ and m₂ in kilograms (kg), r in metres (m), and the constant G is approximately equal to 6.67 × 10⁻¹¹ N m² kg⁻² (newtons times metres squared per kilogram squared).

It can be seen that the repulsive force F is always negative, which means that the net attractive force is positive. (This sign convention is adopted in order to be consistent with Coulomb's Law, where a positive force means repulsion between two charges.)

Acceleration due to gravity

Let a₁ be the acceleration due to gravity experienced by the first point mass. Newton's second law states that <math>F= m_1\ a_1</math>, meaning that <math>a_1=\frac{F}{m_1}</math>. Substituting F from the earlier equation gives

<math>a_1 = -G \frac{m_2}{r^2}</math>

and similarly for a₂.

Assuming SI units, gravitational acceleration (as acceleration in general) is measured in metres per second squared (m/s² or m s⁻²). Non-SI units include galileos, gees (see later), and feet per second squared.

Notice in the above equation that a₁, the acceleration of the mass m₁, does not actually depend on the magnitude of m₁. One consequence is that all bodies, regardless of their mass, fall to earth at the same rate (ignoring air resistance).

If r changes proportionally very little during an object's travel – such as an object falling near the surface of the earth – then the acceleration due to gravity appears very nearly constant (see also The Earth's gravity). Across a large body, variations in r, and the consequent variation in gravitational strength, can create a significant tidal force.

Bodies with spatial extent

If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies. In the limit, as the component point masses become "infinitely small", this entails integrating the force (in vector form, see below) over the extents of the two bodies.

In this way it can be shown that an object with a spherically-symmetric distribution of mass exerts the same gravitational attraction on external bodies as if all the object's mass were concentrated at a point at its centre¹. (This is not generally true for non-spherically-symmetrical bodies.

Vector form

Gravity on Earth from a macroscopic perspective.

Gravity in a room: the curvature of the Earth is negligible at this scale, and the force lines can be approximated as being parallel and pointing straight down to the center of the Earth

Globular Cluster M13 demonstrates gravitational field.

Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors.

<math>

\mathbf{F}_{12} =
G {m_1 m_2 \over r_{21}^2}
\, \mathbf{\hat{r}}_{21}

</math> or <math>

\mathbf{F}_{12} =
- G {m_1 m_2 \over r_{21}^2}
\, \mathbf{\hat{r}}_{12}

</math>

where

F₁₂ is the force on object 1 due to object 2

G is the gravitational constant

m₁ and m₂ are respectively the masses of objects 1 and 2

r₂₁ = | r₂ − r₁ | is the distance between objects 2 and 1

<math> \mathbf{\hat{r}}_{21} \equiv \frac{\mathbf{r}_2 - \mathbf{r}_1}{\vert\mathbf{r}_2 - \mathbf{r}_1\vert} </math> is the unit vector from object 1 to 2

It can be seen that the vector form of the equation is the same as the scalar form given earlier, except that F is now a vector quantity, and the right hand side is multiplied by the appropriate unit vector. Also, it can be seen that F₁₂ = − F₂₁.

The vector formula for gravitational acceleration is similarly analogous to the scalar formula:

<math>

 \mathbf{a}_1 =
 G {m_2 \over r^2_{21}}
 \, \mathbf{\hat{r}}_{21}
</math>

Gravitational field

The gravitational field is a vector field that describes the gravitational force which would be applied on an object in any given point in space, per unit mass. It is actually equal to the gravitational acceleration at that point.

It is a generalization of the vector form, which becomes particularly useful if more than 2 objects are involved (such as a rocket between the Earth and the Moon). For 2 objects (e.g. object 1 is a rocket, object 2 the Earth), we simply write <math>\mathbf r</math> instead of <math>\mathbf r_{21}</math> and <math>m</math> instead of <math>m_1</math> and define the gravitational field <math> \mathbf g(\mathbf r) </math> as:

<math>

\mathbf g(\mathbf r) =
G {m_2 \over r^2}
\, \mathbf{\hat{r}}

</math>

so that we can write:

<math>\mathbf{F}( \mathbf r) = m \mathbf g(\mathbf r) </math>

This formulation is independent of the objects causing the field. The field has units of force divided by mass; in SI, this is N·kg⁻¹.

Problems with Newton's theory

Although Newton's description of gravity is sufficiently accurate for many practical purposes, it suffers from several theoretical problems and is demonstrably not exactly correct.

Theoretical concerns

• There is no prospect of identifying the mediator of gravity. Newton himself felt the inexplicable action at a distance to be unsatisfactory (see "Newton's reservations" below).
• Newton's theory requires that gravitational force is transmitted instantaneously. Given classical assumptions of the nature of space and time, this is necessary to preserve the conservation of angular momentum observed by Johannes Kepler. However, it is in direct conflict with Einstein's theory of special relativity which places an upper limit—the speed of light in vacuum—on the velocity at which signals can be transmitted.

Disagreement with observation

• Newton's theory does not fully explain the precession of the perihelion of the orbit of the planet Mercury. There is a 43 arcsecond per century discrepancy between the Newtonian prediction (resulting from the gravitational tugs of the other planets) and the observed precession³.
• The predicted deflection of light by gravity using Newton's theory is only half the deflection actually observed. General relativity is in closer agreement with the observations.
• The observed fact that gravitational and inertial masses are the same for all bodies is unexplained within Newton's system. General relativity takes this as a postulate. See equivalence principle.

Newton's reservations

While Newton was able to formulate his law of gravity in his monumental work, he was deeply uncomfortable with the notion of "action at a distance" which his equations implied. He never, in his words, "assigned the cause of this power". In all other cases, he used the phenomenon of motion to explain the origin of various forces acting on bodies, but in the case of gravity, he was unable to experimentally identify the motion that produces the force of gravity. Moreover, he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was contrary to sound science.

He lamented the fact that "philosophers have hitherto attempted the search of nature in vain" for the source of the gravitational force, as he was convinced "by many reasons" that there were "causes hitherto unknown" that were fundamental to all the "phenomena of nature". These fundamental phenomena are still under investigation and, though hypotheses abound, the definitive answer is yet to be found. While it is true that Einstein's hypotheses are successful in explaining the effects of gravitational forces more precisely than Newton's in certain cases, he too never assigned the cause of this power in his theories. It is said that in Einstein's equations, "matter tells space how to curve, and space tells matter how to move", but this new idea, completely foreign to the world of Newton, did not enable Einstein to assign the "cause of this power" to curved space any more than the Law of Universal Gravitation enabled Newton to assign its cause. In Newton's own words:

I have not yet been able to discover the cause of these properties of gravity from phenomena and I feign no hypotheses... It is enough that gravity does really exist and acts according to the laws I have explained, and that it abundantly serves to account for all the motions of celestial bodies. That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.

If science is eventually able to discover the cause of the gravitational force, Newton's wish could eventually be fulfilled as well.

It should be noted that the word "cause" here is not being used in the same sense as "cause and effect" or "the defendant caused the victim to die". Rather, when Newton uses the word "cause," he (apparently) is referring to an "explanation". In other words, a phrase like "Newtonian gravity is the cause of planetary motion" means simply that Newtonian gravity explains the motion of the planets. See Causality and Causality (physics).

Einstein's theory of gravitation

Einstein's theory of gravitation answered the problems with Newton's theory noted above. In a revolutionary move, his theory of general relativity (1915) stated that the presence of mass, energy, and momentum causes spacetime to become curved. Because of this curvature, the paths that objects in inertial motion follow can "deviate" or change direction over time. This deviation appears to us as an acceleration towards massive objects, which Newton characterized as being gravity. In general relativity however, this acceleration or free-fall is actually inertial motion. So in a gravitational field it is relative, a matter of relativity, whether objects are falling at the same rate due to their being in inertial motion or whether the observer is the one being accelerated. (This identification of free fall and inertia is known as the Equivalence principle.)

The relationship between the presence of mass/energy/momentum and the curvature of spacetime is given by the Einstein field equations. The actual shapes of spacetime are described by solutions of the Einstein field equations. In particular, the Schwarzschild solution (1916) describes the gravitational field around a spherically symmetric massive object. The geodesics of the Schwarzschild solution describe the observed behavior of objects being acted on gravitationally, including the anomalous perihelion precession of Mercury and the bending of light as it passes the Sun.

Today General Relativity is accepted as the standard description of gravitational phenomena. (Alternative theories of gravitation exist but are more complicated than General Relativity.) For weak gravitational fields and bodies moving at slow speeds at small distances, Einstein's General Relativity gives almost exactly the same predictions as Newton's law of gravitation.

Experimental tests

General Relativity is consistent with all currently available measurements of large-scale phenomena. Arthur Eddington found observational evidence for the bending of light passing the Sun as predicted by general relativity in 1919. Subsequent observations have confirmed Eddington's results, and observations of a pulsar which is occulted by the Sun every year have permitted this confirmation to be done to a high degree of accuracy. There have also in the years since 1919 been numerous other tests of general relativity, all of which have confirmed Einstein's theory. Crucial experiments that justified the adoption of General Relativity over Newtonian gravity were the classical tests: the gravitational redshift, the deflection of light rays by the Sun, and the precession of the orbit of Mercury.

More recent experimental confirmations of General Relativity were the (indirect) deduction of gravitational waves being emitted from orbiting binary stars, the existence of neutron stars and black holes, gravitational lensing, and the convergence of measurements in observational cosmology to an approximately flat model of the observable Universe, with a matter density parameter of approximately 30% of the critical density and a cosmological constant of approximately 70% of the critical density.

The equivalence principle, the postulate of general relativity that presumes that inertial mass and gravitational mass are the same, is also under test. Past, present, and future tests are discussed in the equivalence principle article.

Even to this day, scientists try to challenge General Relativity with more and more precise direct experiments. The goal of these tests is to shed light on the yet unknown relationship between gravity and quantum mechanics. Space probes are used to either make very sensitive measurements over large distances, or to bring the instruments into an environment that is much more controlled than it could be on Earth. For example, in 2004 a dedicated satellite for gravity experiments, called Gravity Probe B, was launched to test general relativity's predicted frame-dragging effect, among others. Also, land-based experiments like LIGO and a host of "bar detectors" are trying to detect gravitational waves directly. A space-based hunt for gravitational waves, LISA, is in its early stages. It should be sensitive to low frequency gravitational waves from many sources, perhaps including the Big Bang.

Einstein's theory of relativity predicts that the speed of gravity (defined as the speed at which changes in location of a mass are propagated to other masses) should be the speed of light. In 2002, the Fomalont-Kopeikin experiment produced measurements of the speed of gravity which matched this prediction. However, this experiment has not yet been widely peer-reviewed, and is facing criticism from those who claim that Fomalont-Kopeikin did nothing more than measure the speed of light in a convoluted manner.

The Pioneer anomaly is an empirical observation that the positions of the Pioneer 10 and Pioneer 11 space probes differ very slightly from what would be expected according to known effects (gravitational or otherwise). The possibility of new physics has not been ruled out, despite very thorough investigation in search of a more prosaic explanation.

Comparison with electromagnetic force

The gravitational attraction between protons is approximately a factor of 10³⁶ weaker than the electromagnetic repulsion. This factor is independent of distance, because both interactions are inversely proportional to the square of the distance. Therefore on an atomic scale mutual gravity is negligible. Even so, the main interaction between everyday objects and the Earth and between celestial bodies is gravity, because at this scale matter is electrically neutral. This means that there is an equal number of positively charged particles in the universe to negatively charged particles. For example, there aren't any positively charged planets that zoom into negatively charged planets. This means that gravity dominates the universe even though it is the weaker force. However, to show the delicate balance of gravity over the electromagnetic force, given two bodies if even there were a surplus or deficit of only one electron for every 10¹⁸ protons and neutrons this would already be enough to cancel gravity (or in the case of a surplus in one and a deficit in the other, double the force of attraction).

Though the force of gravity dominates the visible macro universe, the main interactions such as fusion between the charged particles in cosmic plasma, of which the sun is composed and which make up over 99% of the universe by volume, are due to the nuclear forces.

In terms of Planck units, the charge of a proton is 0.085, while the mass is only 8 × 10⁻²⁰. From that point of view, the gravitational force is not small as such, but because masses are small.

The relative weakness of gravity can be demonstrated with a small magnet picking up pieces of iron. The small magnet is able to overwhelm the gravitational effect of the entire Earth.

Even though gravity is relatively weak, the small gravitational interaction exerted by bodies of ordinary size can fairly easily be detected through experiments such as the Cavendish torsion bar experiment.

Further reading

• Jefimenko, Oleg D., "Causality, electromagnetic induction, and gravitation : a different approach to the theory of electromagnetic and gravitational fields". Star City [West Virginia] : Electret Scientific Co., c1992. ISBN 0917406095
• Heaviside, Oliver, "A gravitational and electromagnetic analogy". The Electrician, 1893.

Gravity and quantum mechanics

It is widely believed that three of the four fundamental forces (the strong nuclear force, the weak nuclear force, and the electromagnetic force) are manifestations of a single, more fundamental force. Combining gravity with these forces of quantum mechanics to create a theory of quantum gravity is currently an important topic of research amongst physicists.

General relativity is an essentially geometric theory that requires no exchange of particles in its explanation of gravity, whereas quantum mechanics relies on interactions between particles. Scientists have theorized about the graviton (a messenger particle that transmits the force of gravity) for years, but have been frustrated in their attempts to find a consistent quantum theory to describe it. Many believe that string theory holds a great deal of promise to unify general relativity and quantum mechanics, but this promise has yet to be realized.

It is notable that in general relativity gravitational radiation (which under the rules of quantum mechanics must be composed of gravitons) is created only in situations where the curvature of spacetime is oscillating, such as is the case with co-orbiting objects. The amount of gravitational radiation emitted by the solar system is far too small to measure. However, gravitational radiation has been indirectly observed as an energy loss over time in binary pulsar systems such as [[PSR1913+16]]. It is believed that neutron star mergers and black hole formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as LIGO have been created to study the problem. No confirmed detections have been made of this hypothetical radiation, but as the science behind LIGO is refined and as the instruments themselves are endowed with greater sensitivity over the next decade, this may change.

Alternative theories

Recent alternative theories

• Brans-Dicke theory of gravity
• Rosen bi-metric theory of gravity
• In the modified Newtonian dynamics (MOND), Mordehai Milgrom proposes a modification of Newton's Second Law of motion for small accelerations.
• The new and "highly controversial" Process Physics theory attempts to address gravity
• The Self creation cosmology theory of gravity in which the Brans-Dicke theory is modified to allow mass creation.
• The satirical theory of Intelligent falling

Historical alternative theories

• Aristotelian theory of gravity
• Nikola Tesla challenged Albert Einstein's theory of relativity, announcing he was working on a Dynamic theory of gravity (which began between 1892 and 1894) and argued that a "field of force" was a better concept and focused on media with electromagnetic energy that fill all of space.
• Induced gravity: In 1967 Andrei Sakharov proposed something similar, if not essentially identical. His theory has been adopted and promoted by Messrs. Haisch, Rueda and Puthoff who, among other things, explain that gravitational and inertial mass are identical and that high speed rotation can reduce (relative) mass. Combining these notions with those of Thomas Townsend Brown, it is relatively easy to conceive how field propulsion vehicles such as "flying saucers" could be engineered given a suitable source of power.
• LeSage gravity, proposed by Georges-Louis LeSage, based on a fluid-based explanation where a light gas fills the entire universe.
• Nordström's theory of gravitation, an early competitor of general relativity.
• Whitehead's theory of gravitation, another early competitor of general relativity.

Notes

• Note 1: Proposition 75, Theorem 35: p.956 - I.Bernard Cohen and Anne Whitman, translators: Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy. Preceded by A Guide to Newton's Principia, by I.Bernard Cohen. University of California Press 1999 ISBN 0-520-08816-6 ISBN 0-520-08817-4
• Note 2: See the works of Stillman Drake, for a comprehensive study of Galileo and his times, the Scientific Revolution.
• Note 3: Max Born (1924), Einstein's Theory of Relativity (The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and Earth.)

See also

Gravitation Portal

• General relativity
• Gravitation wave
• Gravitational binding energy
• Gravity Research Foundation
• Standard gravitational parameter
• Weight
• Weightlessness
• n-body problem
• Pioneer anomaly
• Table of velocities required for a spacecraft to escape a planet's gravitational field
• Application to gravity of the divergence theorem
• Gravity field
• Gravitation
• Scalar Gravity
• Newton's laws of motion
• Artificial gravity
• Kepler's third law

References

• Halliday, David, Robert Resnick; Kenneth S. Krane (2001). Physics v. 1, New York: John Wiley & Sons. ISBN 0471320579.
• Serway, Raymond A., Jewett, John W. (2004). Physics for Scientists and Engineers, 6th ed., Brooks/Cole. ISBN 0534408427.
• Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics, 5th ed., W. H. Freeman. ISBN 0716708094.

External links

• Gravity Probe B Experiment The Official Einstein website from Stanford University