Gravity
- ''This article covers the physics of gravitation.
Gravitation is the tendency of masses to move toward each other.
The first mathematical formulation of the theory of gravitation was made by Isaac Newton and proved astonishingly accurate. He postulated the force of "universal gravitational attraction".
Newton's theory has now been replaced by Albert Einstein's theory of General relativity but for most purposes dealing with weak gravitational fields (for example, sending rockets to the moon or around the solar system) Newton's formulae are sufficiently accurate. For this reason Newtons law is often used and will be presented first.
Newton's Law of Universal Gravitation
Newton's law of universal gravitation states the following:
- Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects.
- F is the magnitude of the gravitational force between two objects
- m_{1} is the mass of first object
- m_{2} is the mass of second object
- r is the distance between the objects
- G is the gravitational constant
This law of universal gravitation was originally formulated by Isaac Newton in his work, the Principia Mathematica (1687). The history of the gravitation as a physical concept is considered in more detail below.
Vector Form
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 formulation, quantities in bold represent vectors.
- F_{12} is the force on object 1 due to object 2
- r_{21} = | r_{1} − r_{2} | is the distance between objects 1 and 2
- is the unit vector from object 2 to 1
Einstein's Theory of Gravity
- It assumes that gravitational force is tramsmitted instantaneously and by some unknown method ("action at a distance"). This was always felt to be unsatisfactory. More recently, special relativity has been successfully built on the backbone of the experimentally supported assumption there exists a maximum velocity at which signals can be transmitted (speed of light in vacuum).
- The assumption of absolute space and time was never very satisfactory in itself. Also, it contradicts Einstein's theory of special relativity.
- It does not explain the small portion of precession of orbit of Mercury of order of one angular second per century that kept astronomers baffled for more then a century as to the reason for it.
- It predicts that light is deflected by gravity only half as much as observed (this was only observed after GR was developed).
- The observed fact that gravitation and inertial mass are the same (or at least proportional) for all bodies is curious and unexplained within Newtons system. See equivalence principle.
How curvatures of spacetime simulate gravitational force
Those two components make the whole Einsteinian gravitation. If, as we believe, Einstein's theory is true, only those two components can be responisible for all the gravitational phenomena in the universe.The first component, the curvature of space, is negligible in all cases when velosities of objects are much smaller than speed of light and ratios of masses to distances to them are much smaller than ratio of speed of light squared to Newtonian gravitational constant: . So for the majority of cases in the universe, and certainly for almost all cases in our solar system except two already specified as #3 and #4 at the beginning, we may treat the space as flat, as ordinary Euclidean space. It leaves us only with the gravitational time dilation as a possible reasons for the illusion of "gravitational force" acting at a distance.
The reason for this illusion is this: any mass in the universe modifies the rate of time in its vicinity this way that time runs slower closer to the mass and the change of time rate is controlled by an equation having exactly the same form as the equation that Newton discovered as his "Law of Universal Gravitation". The difference between them is in essence not in form since the Newtonian potential is replaced by the Einsteinian time rate , where is the time at a point at vicinity of the mass and is the time at observer at infinity, with the right side of the equation staying the same as in Newtonian equation (with accuracy to irrelevant constants). Because of the same form of both equations the extremum of proper time of any object traveling in vicinity of a mass, which corresponds to a geodesic in spacetime is exactly the same as Newtonian orbit of this object around the mass.
So without any force involved into keeping the traveling object in line the object follows the Newtonian orbit in space just by following a geodesic in spacetime. This is Einstein's explanation why without any "gravitational forces" all the objects follow Newtonian orbits and at the same time why the Newtonian gravitation is the approximation of the Einsteinian gravitation.
In this way the Newton's "Law of Universal Gravitation" that looked to people who tried to interpret it as an equation describing some "force of gravitational attraction" acting at a distance (except to Newton himself who didn't believe that "action at a distance" is possible) turned out to be really an equation describing spacetime geodesics in Euclidean space. We may say that Newton discovered the geodesic motion in spacetime and Einstein, by applying Riemannian geometry to it, extended it to curved spacetime, disclosed the hidden Newtonian physics, and made its math accurate.
How energy is conserved if no forces act at a distance
Why Einsteins' gravity differs from Newton's
E.g. before 1998 a group of prominent gravity physicists maintained that to make Einstein's field equation even simpler requires to remove Einstein's cosmological constant from it. They advertised this constant as an "Einstein's biggest blunder" (apparently a term coined by Einstein himself). Lack of this constant in Einstein's field equation predicted a decelerating expansion of space, which in turn was strongly advocated by almost all gravity physicists at that time. It was called standard model of cosmology. Proving that the expansion is decelerating due to "tremendous gravitational attraction of all masses of the universe" (in Einsteinian theory where there is no "gravitational attraction" at all) was supposed to be the first proof ever that cosmology is science after all, since finally it would be able to predict something. A team of enthusiastic young astronomers has been appointed to confirm this prediction. In 1998 the results came in. It turned out that the prediction is false: the space of our universe looks as if it were expanding at accelerating rate.
Units of Measurement and Variations in Gravity
Gravitational phenomena are measured in various units, depending on the purpose. The gravitational constant is measured in newtonss times metre squared per kilogram squared. Gravitational acceleration, and acceleration in general, is measured in metre per second squared or in galileoss or gees. The acceleration due to gravity at the Earth's surface is approximately 9.81 m/s2, depending on the location. A standard value of the Earth's gravitational acceleration has been adopted, called g. When the typical range of interesting values is from zero to several thousand galileos, as in aircraft, acceleration is often stated in multiples of g. When used as a measurement unit, the standard acceleration is often called "gee", as g can be mistaken for g, the gram symbol. For other purposes, measurements in multiples of milligalileo (1/1000 galileo) are typical, as in geophysics. A related unit is the eotvos, which is the unit of the gravitational gradient. Mountains and other geological features cause subtle variations in the Earth's gravitional field; the magnitude of the variation per unit distance is measured in eotvos.
Typical variations with time are 0.2 mgal during a day, due to the tides, i.e. the gravity due to the moon and the sun.
Gravity, and the acceleration of objects near the Earth
Comparison with electromagnetic force
The gravitational interaction of protons is approximately a factor 10^{36} 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. However, the main interaction between common objects and the earth and between celestial bodies is gravity, because gravity is electrically neutral: even if in both bodies there were a surplus or deficit of only one electron for every 10^{18} 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 interaction).
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 interaction of the entire earth.
Gravity is small unless at least one of the two bodies is large or one body is very dense and the other is close by, but the small gravitational interaction exerted by bodies of ordinary size can fairly easily be detected through experiments such as the Cavendish torsion bar experiment.
globular star cluster
Gravitational field demonstrated]]
Gravity and Quantum Mechanics
Since Einstein discovered his theory of gravitation the gravity is not one of the fundamental forces of nature so it is a small wonder that it has not been fitted into the formalism of quantum mechanics (the three fundamental forces: Electromagnetism, the Strong Force, and the Weak Force, can be). This is because general relativity is essentially a geometric theory of gravity. 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. It never can be for obvious reasons (for non existence of "gravitational attraction" explained in section "Einstein's Theory of Gravity") if Einstein's theory is true.
Experimental tests of theories
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.
General relativity also explains the equivalence of gravitational and inertial mass, which has to be assumed in Newtonian theory.
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.
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 exampled, in 2004 a dedicated satellite for gravity experiments, called Gravity Probe B, was launched. Also, land-based experiments like LIGO are gearing up to possibly detect gravitational waves directly.
Speed of gravity: 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 consistent with 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.
Alternate Theories
- In the modified Newtonian dynamics (MOND), Mordehai Milgrom proposes a weakening of Newton's law at high distance as a possible explanation of the fast galaxy rotation.
- Nikola Tesla challenged Albert Einstein's theory of relativity, announcing he was working on a Dynamic theory of gravity and argued that a field of force was a better concept and did away with the curvature of space.
- George Louis LeSage proposed a gravity mechanism, referred to as "LeSage gravity, based on a fluid-based explanation where a light gas fills the entire universe.
History
Although the law of universal gravitation was first clearly and rigorously formulated by Isaac Newton, the phenomenon was more or less seen by others. Even Ptolemy 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. Johannes Kepler 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 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:
However, across a large body, variations in can create a significant tidal force.
Newton's reservations
If science is eventually able to discover the cause of the gravitational force, Newton's wish could eventually be fulfilled as well.Self-gravitating system
A self-gravitating system is a system of masses kept together by mutual gravity. An example is a binary star.
Special applications of gravity
A height difference can provide a useful pressure in a liquid, as in the case of an intravenous drip and a water tower.
A weight hanging from a cable over a pulley provides a constant tension in the cable, also in the part on the other side of the pulley.
Comparative gravities of different planets
The acceleration due to gravity at the Earth's surface is, by convention, equal to 9.80665 metres per second squared. (The actual value varies slightly over the surface of the Earth; see gee for details.) This quantity is known variously as g_{n}, g_{e}, g_{0}, gee, or simply g. The following is a list of the gravity forces (in multiples of g) at the surfaces of each of the planets in the solar system:
Mercury | 0.376 | |
Venus | 0.903 | |
Earth | = | 1 |
Mars | 0.38 | |
Jupiter | 2.34 | |
Saturn | 1.16 | |
Uranus | 1.15 | |
Neptune | 1.19 | |
Pluto | 0.066 |
Note: The "surface" is taken to mean the clouds tops of the gas giants (Jupiter, Saturn, Uranus and Neptune) in the above table.
See also
- Gravity wave
- Gravitational binding energy
- Gravity Research Foundation
- Weight
- N-body problem
- Gravity Probe B Experiment