### Gravity

In physics, gravitation or gravity is the tendency of objects with mass to accelerate toward each other. Gravitation is one of the four fundamental interactions in nature, the other three being the electromagnetic force, the weak nuclear force, and the strong nuclear force. Gravitation is the weakest of these interactions, but acts over great distances and is always attractive. In classical mechanics, gravitation arises out of the force of gravity (which is often used as a synonym for gravitation). In general relativity, gravitation arises out of spacetime being curved by the presence of mass, and is not a force. In quantum gravity theories, either the graviton is the postulated carrier of the gravitational force, or time-space itself is envisioned as discrete in nature, or both.

The gravitational attraction of the earth endows objects with weight and causes them to fall to the ground when dropped (the earth also moves toward the object, but only by an infinitesimal amount). Moreover, gravitation is 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. Gravitation 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 formation of tides, and for various other natural phenomena that we observe.

Since the time of the Greek philosopher Aristotle in the 4th century BC, there have been numerous attempts to understand and explain gravitation. Although these attempted explanations can not be called "scientific" in the modern sense of the word, they are nonetheless precursors of a scientific attitude towards natural phenomena. Aristotle believed that there was no effect without a cause, and therefore no motion without a force. He concluded that all things tried to move toward their proper place in the crystalline spheres of the heavens, and that bodies fell toward the center of the Earth in proportion to their weight. Another example of an attempted explanation is that of the Indian astronomer Brahmagupta who, in 628, wrote 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, 'gurutv-ākarshanam' (center-attraction), means "the pulling of weight".

In 1687 English mathematician Sir Isaac Newton published the famous Principia, which postulated the inverse-square law of universal gravitation. In his own words, "I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orb with force of gravity at the surface of the Earth; and found them answer pretty nearly." Most modern non-relativistic gravitational calculations are based on Newton's work.

Newton's conception and quantification of gravitation held until the beginning of the 20th century, when the German-born physicist Albert Einstein proposed the general theory of relativity. In this theory Einstein proposed that inertial motion occurs when objects are in free-fall instead of when they are at rest with respect to a massive object such as the Earth (as is the case in classical mechanics). The problem is that in flat spacetimes such as those of classical mechanics and special relativity, there is no way that inertial observers can accelerate with respect to each other, as free-falling bodies can do as they each are accelerated towards the center of a massive object.

To deal with this difficulty, Einstein proposed that spacetime is curved by the presence of matter, and that free-falling objects are following the geodesics of the spacetime. More specifically, Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations whose solutions are metric tensors of spacetime. These metric tensors describe the squares of the spatial-temporal separations between the coordinates against which the spacetime manifold is being mapped, thereby describing the spacetime itself. Notable solutions of the Einstein field equations include:

* The Schwarzschild solution, which describes spacetime surrounding a spherically symmetric non-rotating uncharged massive object. For compact enough objects, this solution generated a black hole with a central singularity.

* The Reissner-Nordström solution, in which the central object has an electrical charge. For charges with a geometrized length which are less than the geometrized length of the mass of the object, this solution produces black holes with two event horizons.

* The Kerr solution solution for rotating massive objects. This solution also produces black holes with multiple event horizons.

* The cosmological Robertson-Walker solution, which predicts the expansion of the universe.

General relativity has enjoyed much success because of how its predictions have been regularly confirmed. For example:

* General relativity accounts for the anomalous precession of the planet Mercury.

* The prediction that time runs slower at lower potentials has been confirmed by the Pound-Rebka experiment, the Hafele-Keating experiment, and the GPS.

* The prediction of the deflection of light was first confirmed by Arthur Eddington in 1919, and has more recently been strongly confirmed through the use of a quasar which passes behind the Sun as seen from the Earth. See also gravitational lensing.

* The time delay of light passing close to a massive object was first identified by Shapiro in 1964 in interplanetary spacecraft signals.

* Gravitational radiation has been indirectly confirmed through studies of binary pulsars.

* The expansion of the universe (predicted by the Robertson-Walker metric) was confirmed by Edwin Hubble in 1929.

Every planetary body, including the Earth, is surrounded by its own gravitational field, which exerts an attractive force on any object that comes under its influence. This field is proportional to the body's mass and varies inversely with the square of distance from the body. The gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the Earth's surface, denoted g, is approximately 9.81 m/s² or 32.2 ft/s². This means that, ignoring air resistance, an object falling freely near the earth's surface increases in speed by 9.81 m/s (around 22 mph) for each second of its descent. Thus, an object starting from rest will attain a speed of 9.81 m/s after one second, 19.62 m/s after two seconds, and so on. According to Newton's 3rd Law, the earth itself experiences an equal and opposite force to that acting on the falling object, meaning that the earth also accelerates towards the object. However, because the mass of the earth is huge, the acceleration produced on the earth by this same force is negligable.

Under normal earth-bound conditions, when objects move owing to a constant gravitational force a set of kinematical and dynamical equations describe the resultant trajectories. For example, 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, because the acceleration far from the surface of the Earth will not in general be g.A further example is the expression that we use for the calculation of potential energy of a body = mgh.This expression can be used only over small distances from the earth.Similarly the expression for the maximum height reached by a vertically projected body,"h = u^2/2g " is useful for small heights and small initial velocities only.In case of large initial velocities we have to use the principle of conservation of energy to find the maximum heigt reached.

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. The mass is obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters.

It is important to note, in some contexts, that gravitation is not gravity, per se. Gravitation is a phenomenon independent of any particular cause. Some theorize that it is possible for gravitation to exist without a force; according to general relativity, that is indeed the case. 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 gravitation remains an open question and gravity remains an important topic of scientific research.

A vast number of mechanical contrivances depend in some way on gravity for their operation. For example, a height difference can provide a useful pressure in a liquid, as in the case of an intravenous drip or a water tower. The gravitational potential energy of water supplies hydroelectricity can also be used to power a tramcar up an incline, using a system of water tanks and pulleys. Also, 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.

Examples are numerous: For example 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. Also, 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.

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