It has been suggested that this article be split into multiple articles accessible from a disambiguation page. (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. Image File history File links Derived from public domain images featured at: http://commons. ... In physics, a force is an external cause responsible for any change of a physical system. ... In general, Attraction is a force, that moves one object to another. ... Mass is a property of a physical object that quantifies the amount of matter it contains. ... In the physical sciences, weight is the downward force exerted on matter as a result of gravity. ... Earth is the third planet from the Sun. ... For other uses, see Sun (disambiguation). ... ... Bulk composition of the moons mantle and crust estimated, weight percent Oxygen 42. ... This article is about tides in the ocean. ...

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. Sir Isaac Newton, PRS, (4 January [O.S. 25 December 1642] 1643 – 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, inventor and natural philosopher who is generally regarded as one of the most influential scientists in history. ... (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700. ... For other topics related to Einstein see Einstein (disambiguation). ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ...

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: Sir Isaac Newton, PRS, (4 January [O.S. 25 December 1642] 1643 – 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, inventor and natural philosopher who is generally regarded as one of the most influential scientists in history. ... The law of universal gravitation states that gravitational force between masses decreases with the distance between them, according to an inverse-square law. ... Events March 19 - The men under explorer Robert Cavelier de La Salle murder him while searching for the mouth of the Mississippi River. ... Newtons own copy of his Principia, with hand written corrections for the second edition. ...

"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]

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. Claudius Ptolemaeus (Greek: ; ca. ... -1... Events First condemnation of the Montanist heresy Last (7th) year of Xiping era and start of Guanghe era of the Chinese Han Dynasty. ... Brahmagupta (ब्रह्मगुप्त) (598_668) was an Indian mathematician and astronomer. ... Events Aethelfrith of Northumbria possibly defeats the northern British in a major battle at Catraeth. ... Events Childeric II succeeds Clotaire III as Frankish king Constantine IV becomes Byzantine Emperor, succeeding Constans II Theodore of Tarsus made archbishop of Canterbury. ... In astronomy, heliocentrism is the theory that the Sun is at the center of the Universe and/or the Solar System. ... Presentation of the solar system (not to scale) The solar system comprises the Earths Sun and the retinue of celestial objects gravitationally bound to it. ... Sanskrit ( संस्कृतम्) is an Indo-European Classical language of India and a liturgical language of Hinduism, Buddhism, and Jainism. ... Johannes Kepler Johannes Kepler (December 27, 1571 – November 15, 1630), a key figure in the scientific revolution, was a German mathematician, astrologer, and astronomer. ... Events January 11 - Austrian nobility is granted Freedom of religion. ... Events February 22 - Native American Quadequine introduces Popcorn to English colonists. ... Christiaan Huygens Christiaan Huygens (pronounced in English (IPA): ; in Dutch: ) (April 14, 1629–July 8, 1695), was a Dutch mathematician and physicist; born in The Hague as the son of Constantijn Huygens. ... A portrait, claimed by historian Lisa Jardine to be of Robert Hooke Robert Hooke, FRS (July 18, 1635 - March 3, 1703) was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ...

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, F = ma, (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. Galileo Galilei Galileo Galilei (Pisa, February 15, 1564 – Arcetri, January 8, 1642), was an Italian physicist, astronomer, and philosopher who is closely associated with the scientific revolution. ... Aristotle (Ancient Greek: Aristotelēs 384 BC – March 7, 322 BC) was an ancient Greek philosopher, who studied with Plato and taught Alexander the Great. ... Johannes Kepler Johannes Kepler (December 27, 1571 – November 15, 1630), a key figure in the scientific revolution, was a German mathematician, astrologer, and astronomer. ...

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. General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... THERE IS NO SUCH THING< MWAHAHAHAHAHAHAHA> In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ... This article is in need of attention from an expert on the subject. ... Curvature is the amount by which a geometric object deviates from being flat. ... In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ... A Redstone rocket, part of the Mercury program A rocket is a vehicle, missile or aircraft which obtains thrust by the reaction to the ejection of fast moving exhaust gas from within a rocket engine. ... A projectile is any object sent through space by the application of a force. ... Simple gravity pendulum assumes no air resistance and no friction of/at the nail/screw. ...

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. Earth is the third planet from the Sun. ...

Gravity keeps us to the ground.

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 gram or gramme, symbol g, is a unit of mass. ...

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. Credit ESA as the source of the image. ... Credit ESA as the source of the image. ... ... The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ... The eotvos is a unit of acceleration divided by distance in the older Centimeter-gram-second system of units. ... CGS is an acronym for centimetre-gram-second. ... In the above two images, the scalar field is in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows. ...

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. An objects weight, henceforth called actual weight, is the downward force exerted upon it by the earths gravity. ... Bulk composition of the moons mantle and crust estimated, weight percent Oxygen 42. ... For other uses, see Sun (disambiguation). ... The tide is the regular rising and falling of the oceans surface caused by changes in gravitational forces external to the Earth. ... The gal or galileo is the CGS unit of acceleration. ...

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. g (also gee, g-force or g-load) is a non-SI unit of acceleration defined as exactly 9. ...

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. Free Fall opens with one of the most stunning first paragraphs I have ever, or am ever likely to, read. ...

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. Earth is the third planet from the Sun. ... Earth is the third planet from the Sun. ...

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. The photosphere of an astronomical object is the region at which the optical depth becomes one. ...

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). For other uses, see Sun (disambiguation). ... Atmospheric characteristics Atmospheric pressure trace Potassium 31. ... (*min temperature refers to cloud tops only) Atmospheric characteristics Atmospheric pressure 9. ... Earth, also known as the Earth or Terra, is the third planet outward from the Sun. ... Bulk composition of the moons mantle and crust estimated, weight percent Oxygen 42. ... Mars is the fourth planet from the Sun in the solar system, named after the Roman god of war (the counterpart of the Greek Ares), on account of its blood red color as viewed in the night sky. ... Atmospheric characteristics Atmospheric pressure 70 kPa Hydrogen ~86% Helium ~14% Methane 0. ... Atmospheric characteristics Atmospheric pressure 140 kPa Hydrogen >93% Helium >5% Methane 0. ... Atmospheric characteristics Atmospheric pressure 120 kPa Hydrogen 83% Helium 15% Methane 1. ... Atmospheric characteristics Surface pressure ≫100 MPa Hydrogen - H2 80% ±3. ... Atmospheric characteristics Atmospheric pressure 0. ...

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). g (also gee, g-force or g-load) is a non-SI unit of acceleration defined as exactly 9. ...

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. Galileo Galilei Galileo Galilei (Pisa, February 15, 1564 – Arcetri, January 8, 1642), was an Italian physicist, astronomer, and philosopher who is closely associated with the scientific revolution. ... The word ramp can mean one of several things: Inclined plane A ramp is the area around an airport terminal where aircraft are loaded and unloaded. ... A water clock or clepsydra is a device for measuring time by letting water regularly flow out of a container usually by a tiny aperture. ...

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 terminal velocity of an object falling towards the ground, in non-vacuum, is the speed at which the gravitational force pulling it downwards is equal and opposite to the atmospheric drag (also called air resistance) pushing it upwards. ... David Randolph Scott (born June 6, 1932) a former NASA Astronaut, was one of the third group of astronauts named by NASA in October 1963 and is one of only twelve men who have walked on the moon. ... Bulk composition of the moons mantle and crust estimated, weight percent Oxygen 42. ...

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. This low pressure system over Iceland spins counter-clockwise due to the Coriolis effect. ...

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. The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ...

Distance d travelled by an object falling for time t:
Time t taken for an object to fall distance d:
Instantaneous velocity vi of a falling object after elapsed time t:
Instantaneous velocity vi of a falling object that has travelled distance d:
Average velocity va of an object that has been falling for time t (averaged over time):
Average velocity va of a falling object that has travelled distance d (averaged over time):

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 In mathematics and physics, a scalar field associates a scalar to every point in space. ... It has been suggested that this article or section be merged with Scalar potential. ... It has been suggested that this article or section be merged with Potential. ... Potential energy is stored energy. ...

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. In the above two images, the scalar field is in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows. ... In mathematics and physics, the Laplace operator or Laplacian, denoted by Δ, is a differential operator, specifically an important case of an elliptic operator, with many applications in mathematics and physics. ... In vector calculus, the divergence is an operator that measures a vector fields tendency to originate from or converge upon a given point. ...

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. In mathematics, Laplaces equation is a partial differential equation named after its discoverer Pierre-Simon Laplace. ... In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R (where U is an open subset of Rn) which satisfies Laplaces equation, i. ... In mathematics, Poissons equation is a partial differential equation with broad utility in electrostatics, mechanical engineering and theoretical physics. ...

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. Centrifugal force (from Latin centrum center and fugere to flee) is a term which may refer to two different forces which are related to rotation. ...

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:

where the symbol 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. According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... Henry Cavendish (October 10, 1731 - February 24, 1810) was a British scientist. ...

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. // This refers to the cosmological use of the term. ...

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. In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... The Galactic Center is the rotational center of the Milky Way galaxy. ... NGC 4414, a typical spiral galaxy in the constellation Coma Berenices, is about 56,000 light years in diameter and approximately 60 million light years distant. ... Superclusters are large groupings of smaller galaxy groups and clusters, and are among the largest structures of the cosmos. ...

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. Nicolaus Copernicus (in Latin; Polish Mikołaj Kopernik, German Nikolaus Kopernikus - February 19, 1473 – May 24, 1543) was a Polish astronomer, mathematician and economist who developed a heliocentric (Sun-centered) theory of the solar system in a form detailed enough to make it scientifically useful. ... Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ...

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. A centripetal force is a force pulling an object toward the center of a circular path as the object goes around the circle. ...

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.) Albireo from Yeovil 8 SCT Philips Toucam WebCam - Jim Spinner 26/10/2004 20:00 BST File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Albireo from Yeovil 8 SCT Philips Toucam WebCam - Jim Spinner 26/10/2004 20:00 BST File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Albireo (β Cyg / β Cygni / Beta Cygni) is the third brightest star in the constellation Cygnus. ... A binary star system consists of two stars both orbiting around their barycenter. ... This article is about the astronomical body. ... This article is about the celestial body. ... For other people named John Adams, see John Adams (disambiguation). ... Urbain Le Verrier. ...

Self-gravitating system

A self-gravitating system is a system of masses kept together by mutual gravity. An example is a binary star. A binary star system consists of two stars both orbiting around their barycenter. ...

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.

An intravenous drip in a hospital Intravenous therapy or IV therapy is the administration of liquid substances directly into a vein. ... The mushroom-shaped concrete water tower of Roihuvuori in Helsinki, Finland was built in the 1970s. ... This is a photo of the Dubuque Shot Tower in Dubuque, Iowa. ... This is a photo of the Dubuque Shot Tower in Dubuque, Iowa. ... the Dubuque Shot Tower in Dubuque, Iowa. ... 1856 was a leap year starting on Tuesday (see link for calendar). ... Downtown Dubuque and the Riverfront Dubuque is a city located in Dubuque County, Iowa. ... Hydroelectricity is electricity obtained from hydropower. ... Pulleys of a ship A pulley is a wheel with a groove along its edge, for holding a rope or cable. ... This article is about the chemical element. ... A shot tower is a tower designed for the production of shot balls, which were used for projectiles in firearms. ... A tektite Tektites (from Greek tektos, molten) are natural glass objects, up to a few centimeters in size, which — according to most scientists — have been formed by the impact of large meteorites on Earths surface, although a few researchers favor an origin from the Moon as volcanic ejecta. ... Free Fall opens with one of the most stunning first paragraphs I have ever, or am ever likely to, read. ... Fractional distillation is the separation of a mixture of compounds by their boiling point, by heating to high enough temperatures. ... The Eiffel Tower Fire-observation watchtower in Kostroma, Russia. ... Relative density (also known as specific gravity) is a measure of the density of a material. ... Time measuring instrument A clock (from the Latin cloca, bell) is an instrument for measuring time. ... A satellite is any object that orbits another object (which is known as its primary). ... Newtons own copy of his Principia, with hand written corrections for the second edition. ...

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: Image File history File links Splitsection. ...

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:

where: A point mass in physics is an idealisation of a body whose dimensions can be neglected compared to the distances of its movement. ... A point mass in physics is an idealisation of a body whose dimensions can be neglected compared to the distances of its movement. ... In physics, a force is an external cause responsible for any change of a physical system. ... A line, or straight line, can be described as an (infinitely) thin, (infinitely) long, perfectly straight curve (the term curve in mathematics includes straight curves). In Euclidean geometry, exactly one line can be found that passes through any two points. ... The word proportionality may have one of a number of meanings: In mathematics, proportionality is a mathematical relation between two quantities. ... Mass is a property of a physical object that quantifies the amount of matter it contains. ... This article is about proportionality, the mathematical relation. ... In algebra, the square of x is written x2 and is defined as the product of x with itself: x × x. ...

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). According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ... This article is about the SI unit of force. ... The international prototype, made of platinum-iridium, which is kept at the BIPM under conditions specified by the 1st CGPM in 1889. ... metre or meter, see meter (disambiguation) The metre is the basic unit of length in the International System of Units. ...

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.) In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... ‹ The template below has been proposed for deletion. ...

Acceleration due to gravity

Let a₁ be the acceleration due to gravity experienced by the first point mass. Newton's second law states that , meaning that . Substituting F from the earlier equation gives

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. The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ... Metres per second squared is the SI derived unit of acceleration (scalar) and (vector), defined by distance in metres divided by time in seconds and again divided by time in seconds. ... The galileo or gal is the CGS unit of acceleration. ... g (also gee, g-force or g-load) is a non-SI unit of acceleration defined as exactly 9. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

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. Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ...

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 calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. ... A physical body is an object which can be described by the theories of classical mechanics, or quantum mechanics, and experimented upon by physical instruments. ...

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. gravity at a macroscopic level File links The following pages link to this file: Gravity User:Patrick/w User talk:Ancheta Wis/g Categories: GFDL images ... gravity at a macroscopic level File links The following pages link to this file: Gravity User:Patrick/w User talk:Ancheta Wis/g Categories: GFDL images ... gravity in a room File links The following pages link to this file: Gravity User:Patrick/w User talk:Ancheta Wis/g Categories: GFDL images ... gravity in a room File links The following pages link to this file: Gravity User:Patrick/w User talk:Ancheta Wis/g Categories: GFDL images ... Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ... Download high resolution version (750x750, 82 KB)M13 in Hercules is one of the most prominent and best known globular clusters of the Northern celestial hemisphere. ... Download high resolution version (750x750, 82 KB)M13 in Hercules is one of the most prominent and best known globular clusters of the Northern celestial hemisphere. ... Messier Object 13, the Great Globular Cluster in Hercules; one of the most prominent and best known globular clusters of the Northern celestial hemisphere. ... In physics and in vector calculus, a spatial vector is a concept characterized by a magnitude, which is a scalar, and a direction (which can be defined in a 3-dimensional space by the Euler angles). ... In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables. ...

or

where

F₁₂ is the force on object 2 due to object 1

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

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. In mathematics, a unit vector in a normed vector space is a vector (most commonly a spatial vector) whose length is 1. ... The term scalar is used in mathematics, physics, and computing basically for quantities that are characterized by a single numeric value and/or do not involve the concept of direction. ...

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

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. Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ...

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 instead of and m instead of m₁ and define the gravitational field as:

so that we can write:

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. The International System of Units (abbreviated SI from the French language name Système International dUnités) is the modern form of the metric system. ...

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.

In physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. ... In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the direction in which, the object rotates about the reference point. ... Johannes Kepler Johannes Kepler (December 27, 1571 – November 15, 1630), a key figure in the scientific revolution, was a German mathematician, astrologer, and astronomer. ... Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. It replaced Newtonian notions of space and time and incorporated electromagnetism as represented by Maxwells equations. ... Cherenkov effect in a swimming pool nuclear reactor. ...

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.

Precession refers to a change in the direction of the axis of a rotating object. ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... A planet is generally considered to be a relatively large mass of accreted matter in orbit around a star that is not a star itself. ... Atmospheric characteristics Atmospheric pressure trace Potassium 31. ... A second of arc or arcsecond is a unit of angular measurement which comprises one-sixtieth of an arcminute, or 1/3600 of a degree of arc or 1/1296000 ≈ 7. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... THERE IS NO SUCH THING< MWAHAHAHAHAHAHAHA> In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ...

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). Causality - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... Although causality, the relationship between causes and effects, is often examined in the fields of philosophy, computer science, and statistics, it has a place in the study of physics as well. ...

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.) To meet Wikipedias quality standards, this article may require cleanup. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... 1915 (MCMXV) was a common year starting on Friday (see link for calendar). ... Mass is a property of a physical object that quantifies the amount of matter it contains. ... In physics, momentum is the product of the mass and velocity of an object. ... World line of the orbit of the Earth depicted in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, usually put as the vertical axis. ... Curvature is the amount by which a geometric object deviates from being flat. ... The principle of inertia is one of the fundamental laws of classical physics which are used to describe the motion of matter and how it is affected by applied forces. ... Free Fall opens with one of the most stunning first paragraphs I have ever, or am ever likely to, read. ... THERE IS NO SUCH THING< MWAHAHAHAHAHAHAHA> In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ...

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 so