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## Gravity
"Gravity is the force that pulls you down." -- Merlin in Disney's Merlin was right, of course, but gravity does much more than just hold you in your chair. It was the genius of Isaac Newton to recognize that. Newton recalled in a late memoir that while he was trying to figure out what kept the Moon in the sky, he saw an apple fall to the ground in his orchard, and he realized that the Moon was not suspended in the sky, but continuously falling, like a cannon ball that was shot so fast that it continuously misses the ground as it falls away due to the curvature of the Earth.
If one wishes to be precise, one should distinguish between By Newton's third law, any two objects exert equal and oppositely directed gravitational pull on each other.
## Newton's Law of Universal Gravitation
Newton explains, Newton eventually published his still famous law of universal gravitation in his Principia Mathematica as follows:
- F = gravitational force between two objects
- m
_{1}= mass of first object - m
_{2}= mass of second object - r = distance between the objects
- G = universal constant of gravitation
## Vector Form
The above form is a simplified version. It is more properly expressed as vector equation. (All quantities in
- is the force on by
- and are the masses
- and are the position vectors of their respective masses
- is the gravitational constant
The primary difference between the two formulations is that the second form uses the difference in position to construct a vector that points from one mass to the other, and then divides that vector by its length to prevent it from changing the magnitude of the force. ## Newton's ReservationsIf science is eventually able to discover the cause of the gravitational force, Newton's wish could eventually be fullfiled as well.## Comparison with electromagnetic force
The gravitational attraction of protons is approximately a factor 10 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 force of the entire earth. Gravity is small unless at least one of the two bodies is large, but the small gravitational force exerted by bodies of ordinary size can fairly easily be detected through experiments such as the Cavendish torsion bar experiment. ## Self-gravitating systemA self-gravitating system is a system of masses kept together by mutual gravity. An example is a star. ## HistoryNobody knows for sure if Newton's recollection about the apple was accurate, but his insight is the same nevertheless. Philosophers had thought since the Greeks that the "natural" movement of stars, planets, the Sun and the Moon was circular, Kepler established that orbits are actually elliptical, but still thought that the movements of the planets was dictated by some "divine force" emanated from the sun, but Newton realized that the same force that causes a thrown rock to fall back to the Earth keeps the planets in orbit of the Sun, and the Moon in orbit of 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 that was enough for him. Galileo, however, actually tried dropping objects of different mass at the same time. Aside from differences due to friction from the air, Galileo observed that all masses accelerate the same. Using Newton's equation, , it is plain to us why:
r divided by the initial r is so small that the acceleration due to gravity appears to be perfectly constant. The acceleration due to gravity on Earth is usually called g, and its value is about 9.8 m/s^{2} (or 32 ft/s^{2}). Galileo didn't have Newton's equations, though, so his insight into gravity's proportionality to mass was invaluable, and possibly even affected Newton's formulation on how gravity works.However, across a large body, variations in can create a significant tidal force. ## Einstein's General Theory of Relativity- It assumes that changes in the gravitational force are transmitted instantaneously when positions of gravitating bodies change. However, this contradicts the fact that there exists a maximum velocity at which signals can be transmitted (speed of light in vacuum).
- Assumption of absolute space and time contradicts Einstein's theory of Special relativity.
- It predicts that light is deflected by gravity only half as much as observed.
- It does not explain gravitational waves or black holes.
- Under newtonian gravity (with instantaneous transmission of gravitational force), if the Universe is Euclidean, static, of uniform, average, positive density and infinite, then the total gravitational force on a point is a divergent series. In other words, newtonian gravity is inconsistent with a Universe which is Euclidean, static, of uniform, average, positive density and infinite.
Although General Relativity is, as a theory, more accurate than Newton's law of gravity, it also requires a significantly more complicated mathematical formalism. Instead of describing the effect of gravitation as a "force", Einstein introduced the concept of curved space-time in which bodies move along curved trajectories. Today General Relativity is accepted as the standard description of classical gravitational phenomena. (Alternative theories of gravitation exist but are more complicated than General Relativity.) General Relativity is consistent with all currently available measurements. 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. Crucial experiments that justified the adoption of General Relativity over Newtonian gravity were 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 gravitational waves from orbiting binary stars, the existence of neutron stars and black holes, gravitational lensing, and the convergence of measurements in observational cosmology to an ## LeSage's theorySee Gravity (LeSage) for an alternative theory.## Quantum Mechanics and WavesGravity is the only one of the four fundamental forces of nature that stubbornly refuses to be quantised (the other three: Electromagnetism, the Strong Force, and the Weak Force, can be quantised). Quantisation means that the force is measured in discrete steps that cannot be reduced in size, no matter what; alternatively, that gravitational interaction is transmitted by particles called gravitons. Scientists have theorized about the graviton for years, but have been frustrated in their attempts to find a consistent quantum theory for 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. See also: Gravitational binding energy, Gravity Research Foundation, Weight.
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