Gravitation
Gravity (from the Latin gravitas, seriousness), also mass attraction, gravity is one of the four fundamental forces of physics. It causes the mutual attraction of masses and can not be shielded. It decreases with increasing distance, but has unlimited range. On Earth, gravity causes that all bodies fall down if they are not prevented by other people working on it. In the solar system the gravitational determined the orbits of the planets, moons, satellites and comets, and in the cosmos, the formation of stars and galaxies, as well as its development in the large.
Overview
According to Isaac Newton's Gravity is a force between masses. His law of gravity, one of the basic equations of classical mechanics, determines the magnitude and direction of the force between two point masses. Direct effect of this gravitational force is the gravitational acceleration, ie the constant change of direction or magnitude of the velocity of all of freely moving body. For a long time provided the equations of Newtonian theory values that were consistent with the astronomical observations and results of underground experiments.
In general relativity, Einstein's theory of gravity is generally interpreted differently. According to the principle of equivalence, the effect of gravity can not be distinguished from the effect of an acceleration of the reference system; in particular stand out in a freely falling reference system, the effects of gravity and acceleration exactly. They say that the gravity was " transformed away " by the transition to the new coordinates. In the general theory of relativity the corresponding local inertial frame is calculated at each point in space, where there is no gravity and special relativity applies to their four-dimensional spacetime in Euclidean geometry. The effect of gravity then comes to light in the reverse transformation to the reference system of the observer.
Similarly, that are straight and uniform Galilean force-free motion, moving in the general theory of relativity body without nichtgravitative forces on geodesics in a " curved " space with Riemannian geometry. For the determination of the ruling on a point of curvature of space-time are the Einstein's field equations. They were formulated in the limit of weak gravitational coincide with those calculated according to them results that are based on the Newtonian equation.
On a body in an inhomogeneous gravitational field occur tidal forces.
General relativity deals with gravity so as inertial force and provides them with centrifugal force, Coriolis force or the force that can be felt in a vehicle during acceleration or deceleration, on the same level. Within the solar system, where it is weak fields and small curvature of space-time, there are only small deviations from the predictions of the Newtonian law of gravitation. Thus, the perihelion shift of the path of Mercury was declared except for a small part by the action of the other planets until the late 19th century. Einstein could explain this small deviation by the general theory of relativity.
In case of strong curvature, as it is caused by excessive concentration of large mass in a small space, completely new phenomena as predicted eg black holes.
As a source as well as a point of gravitation applicable in the Newtonian mechanics alone the mass, which, starting from the originally inaccurate term of a given quantity of matter here learned their first precise physical definition. In general relativity, gravity is an expression of the curvature of space- time, which in turn is influenced not only by the presence of matter, but also of energy in any form and in addition of mass and energy flows.
All predictions of observation available to the general theory of relativity have been confirmed by measurements. Experimentally inaccessible are extremely high concentrations of mass and energy in a confined space, for their description in addition to the gravitational and quantum effects must be taken into account. Attempts at a quantum field theory of gravity there is in its infancy. It lacks, however, to predictions that were both predictable and observable.
In Newtonian gravitational you still came from an instantaneous propagation of gravitational effects, that is, that the effect over long distances is immediate. However, within the Einstein's view is that there is no effect, that is not the effect of gravity faster than the speed of light propagating. Gravitational waves are then generated by a rapid change in the position of masses, such as the star collapse, which propagate at the speed of light.
History
Aristotle described the severity in the context of his cosmology in which all strive sublunary elements (earth, water, air, fire ), and the existing body from the center of the world. This idea has long been the main physical argument for the geocentric worldview.
Altindische authors conducted free-fall back to a force that is proportional to the mass of an object and acts in the direction of the Erdmittelpunkts. The Persian astronomer Muhammad ibn Musa explained in the 9th century, the movements of the heavenly bodies by a force of attraction. Al -Biruni translated in the 11th century, the works of Indian authors into Arabic into Persian. His contemporary, Alhazen formulated a theory of gravitation. The Persian Al- Khazini introduced in the 12th century to the suggestion that the strength of gravity depends on the distance to the center of the earth, and differed between mass, weight and force.
Copernicus wrote De revolutionibus orbium Coelestium:
"... I at least am of the view that gravity is nothing more than a by the divine providence of the world champion the parts implanted, natural aspiration, whose virtue they fact that they join together to form a ball, its unity and wholeness form. And it is likely that this tendency as the sun, the moon and the other planets inherent ... "
Kepler published in his 1609 Astronomia nova:
" ... The true doctrine of severity is now based on the following axioms:
- Any physical substance, inasmuch as it is physically, inclined by nature to rest at any place where it is alone, outside the motor area of a related body.
- The severity is in the mutual physical desire between related bodies after association or connection (of this order is also the magnetic force ), so that the earth is much more attracts the stone; pursued as the stone upon the earth.
- The severity is (...) not to center of the world as such driven forth, but as the center of a related round body ...
- If the earth is not round, the severity would be driven forth, not to the center of the earth to anywhere in a straight line, but from different angles by different points.
- If you were to put two stones at any location in the world, close to each other outside the motor area of a third related body, then those stones would like two magnetic bodies unite at an intermediate location, wherein the one the other approaches by a distance which is proportional to the mass of the other.
...
- The range of the attraction of the moon extends to the earth ... "
Also at the beginning of the 17th century, described Galileo Galilei the free fall of a body as uniformly accelerated motion, which is independent of its mass or other characteristics.
The English scholar Robert Hooke stated in 1670 the effect of gravity with the help of " gravity hoppers " and declared that gravity is a property of all mass -prone body and greater, the closer two bodies befänden to each other. The theory that gravity is inversely proportional to the square of the distance from the center of mass, appeared in 1680 in a letter to Hooke to Newton for the first time.
Mathematically, the gravitational first described by Hooke's compatriot and contemporary Isaac Newton in his Principia. Formulated by him Newtonian law of gravitation was the first physical theory that could be applied in astronomy. It confirms the previously discovered Kepler 's laws of planetary motion and thus provided a fundamental understanding of the dynamics of the solar system with the possibility of more precise predictions about the movement of planets, moons and comets.
For an explanation of gravity in terms of a process happening a number of mechanical kinetic respectively explanations have been since the time of Newton to the development of the general theory of relativity in the early 20th century proposed (see Mechanical explanations of gravitation ). One of the most famous is developed by Fatio and Le Sage 's theory of Le Sage gravitation. This argues that the gravitational attraction of the two bodies due to the shielding from the direction of the respective other pressure acting. In connection with this, the theories of aether stand as mediators of interactions ( instead of a distance effect ), these interactions also include the electromagnetism. One of the last of these theories which was made around 1900 Lorentz ether theory, which was eventually displaced by the novel approach of Einstein's theory of relativity. In this in 1916 by Albert Einstein defined general relativity theory (ART) gravitation is attributed to a geometric property of space-time that is curved from any form of energy.
Gravity in classical mechanics
Cause of the gravitational force in classical mechanics is the gravitational field generated by each mass attracts every other mass on and has infinite propagation speed and width. Of particular importance is the Newtonian gravitational law that the force acting between two masses at a distance and indicating:
Because of this Act, the acceleration can be determined, experienced both masses. undergoes mass
The same applies to. The description of gravitation in this way is sufficiently accurate for many use cases, but fails in extreme conditions such as black holes or the perihelion of Mercury. If the problem is described in a reference frame that rotates with the celestial bodies (eg the reference system of the resting surface), then inertia forces must be taken into account. Since they just proportional to the sample mass are like gravity, they can be combined with this force of gravity (see also gravity field ).
Gravitational constant
The gravitational constant is a fundamental constant of physics. Your exact determination is very difficult, because between two determined by weighing the masses, the gravitational force is extremely low. Its value is therefore known to four decimal places, in contrast to the at least eight decimal places other fundamental constants.
The first determination succeeded in 1798 Henry Cavendish. The carried out in his laboratory experiment has historical significance for the development of experimental and theoretical foundations of gravity.
Newtonian Schalentheorem
Newton derived the following three theorems from his law of gravitation from:
Because of the mathematical similarity of the Newtonian law of gravitation to the Coulomb law, these theorems also apply to electric forces in electrostatics.
General Theory of Relativity
In the general relativity theory (ART) gravity is not treated as a force in the sense of classical physics. The theory is therefore not an ordinary field theory. Rather, spatial and temporal coordinates as in special relativity theory are combined to form a four-dimensional space-time, which is described by a four-dimensional pseudo- Riemannian manifold. This spacetime is now no longer "flat", but is curved locally by the presence of mass or energy. A body that just follows the influence of gravity, ( events ) moves between two spacetime points always along those connecting line, which - according to the sign convention of the usual metric in the ART [note 1] measured - is the longest. Where the space-time is flat, this is a straight line. In a curved manifold we speak generally of a geodesic. The curvature of spacetime is just so determined by the Einstein field equations that the uniform motion on a geodesic if one converts it into the usual coordinates for place and time as the movement of the body looks like in the prevailing gravitational field (ie, free-fall parabola, planetary orbit, etc.). The gravity can be interpreted in this way as a purely geometrical phenomenon, for its explanation any more special power must be used. In contrast to the theories of the other fundamental forces, the general theory of relativity is therefore not a field theory in a range defined by predetermined coordinates for place and period, but the space-time itself is the object of the theory.
In this sense, the theory of general relativity reduces the gravitational force on the status of an apparent force: If you feel sitting on a chair, how to be pulled through a " gravitational force " towards the earth, the ART indicated this to mean that you stopped by the chair surface continuously striving is the geodesic to follow through the curved spacetime of the Earth's mass (that would be the free fall ). It is the force with which the chair surface acting on the seat of the observer, not an apparent force. It is ultimately returned to the electrostatic repulsion in the contact of the surface atoms of the chair by the atoms of the observer. After the point of view of general relativity, therefore, shifts the interpretation of events. While according to classical mechanics, the earth is an inertial frame in which the downward force of gravity is compensated to the observer by the upward support force of the chair, so that the observer can remain at rest, the crashes according to the general theory of relativity correct inertial system with acceleration due to gravity down, but in this inertial frame of the chair exerts a force on the observer, the speed it constant at the top.
Vertical free-falling body, however, as well as satellites, planets, comets or parabolic flights follow a geodesic through spacetime. Their movements are considered free of force in general relativity theory as a ( net). Because the Earth's mass (or mass of the Sun ) affected by the spacetime curvature, the definition of what " straight " in the sense of inertia of bodies means. Direct to astronomical observations occurs spacetime curvature, for example, in appearance, in which the influence of large masses could be detected on the straightness of the beams (see figure).
According to Einstein's field equations contributes not only mass but also any form of energy to the curvature of space-time, including the energy itself associated with gravity. Therefore, the equations are non-linear. They can be approximated in the region of weak curvature by linear equations in which the Newtonian law of gravitation can find in approach. Among the computed according to the Newtonian law phenomena thus result in small corrections which could be confirmed by all accurate observations (see tests of general relativity ). Completely new phenomena, however, arise with a strong curvature of spacetime, in particular the black holes.
Gravity and quantum theory
In a quantum field theory of gravity is described in linear approximation by the exchange of a massless particle called a graviton, which has spin 2. Moreover, already the formulation of a quantum theory of gravity leads to fundamental problems that are still unresolved. The supersymmetric extension is not so far led to a consistent theory. As is currently the most promising candidate string theory and loop quantum gravity apply. A key objective is that gravitational interactions with the other to a "Grand Unified Theory" (GUT) to unite so as to formulate a theory that can describe all the forces of nature at once. This means that the gravity, which does not consider the effects of quantum field theory, this would be to expand. As part of the United superstring theories, M-theory, the universe is described as elfdimensionale manifold. In this case, the portion of the universe in which we exist, a higher-dimensional membrane ( D- brane ), which is itself embedded in a still höherdimensionalere manifold, could swing in the additional branes and thus represent parallel space-times within the same universe. In the M - theory gravitons are shown as closed strings, which are not bound by the limits of a Brane. Therefore, they are able to propagate through all the extra space dimensions and to come into other branes. In this way, the strength of gravity is sufficiently attenuated so that they appear as part of our four-dimensional world of experience as the weakest of the four interactions.
Speculation in the field of gravity
In the field of science fiction, there are numerous concepts of gravitational shielding or anti-gravity. Beyond the scientific enterprise and the scientific mainstream, there are always efforts to demonstrate such an effect. Relative experiments have awareness of Quirino Majorana, who wants to have around 1920 a shielding effect found by heavy elements ( invalidated, inter alia, by Henry Norris Russell), and by Yevgeny Podkletnow, the case of rotating superconductors claimed a decrease in the weight force in 1995, but this also could not be confirmed.
Gravity on earth
The " gravity " is not always identified with the term " gravitational force " but often equated as " effective gravity " with the " weight ". In this case, the terms " gravitational force " mean and " gravity " is not the same: while the gravitational force ( and related terms gravitational acceleration, gravitational field or potential ) only the mass attraction plays a role, flows into the heavy or weight ( and the related concepts gravitational acceleration, gravity field, gravity potential, or specifically gravitational acceleration and earth gravity ) due to the Earth's rotation also the centrifugal force (or centrifugal ) with a. Common feature is that both gravity and weight or gravity of a body is always proportional to its mass, in the sum of:
As amount of gravitational acceleration results on the Earth's surface, an average numerical value of g = 9.81 m/s2, but varies regionally because of Earth flattening, centrifugal force and elevation profile to few parts per thousand. According to international convention their default value was set at g = 9.80665 m/s2.
Gravity anomalies
The actually observed ( for example with a gravimeter ) value deviates from a rule from above average. For such gravity anomalies there are several reasons:
Deviation from the spherical shape
First of these deviations are due to the fact that the Earth is not a perfect homogeneous sphere: Local differences in the density of the substrate (eg, ore, or tectonic plates, or seas ) as well as the flattening of the earth draw a geoid local variations the gravitational acceleration of up to ± 0.5 percent after themselves.
Centrifugal force
Another aspect is the fact that the real observed gravity contributes not only the gravitational force, but also due to the Earth's rotation, a centrifugal force varies with latitude. This also causes the Earth flattening, which makes up about 0.3 percent ( the Earth's radius is shorter than at the equator to the poles to 21 km).
Gravitational acceleration and effective gravitational acceleration are therefore not the same, but only at the north and south poles of the same, where no centrifugal acceleration occurs. The effective gravitational acceleration increases from the poles towards the equator by about 0.5 %, of which one half of the increasing centrifugal force and on the larger equatorial radius of the earth ellipsoid.
Height effect
The third effect is the dependence of the gravitational acceleration on the distance to the attracting mass into play, where the entire mass of the earth is assumed in the approximation of the earth as a sphere in the center of the earth. The gravity is reduced even more, depending on the place of an observer from the Earth's center. Compared to the initial value at the Earth's surface ( sea level), the local gravitational acceleration decreases in a flying altitude of 10 km airliner already at about 99.7 percent, in a satellite orbit of 200 km height to just 94.0 percent.
Because of these local differences, it is necessary to specify the location with, the figures relate. The acceleration of gravity is therefore also called spatial factor. The methods by which the local gravitational field of the earth is measured, we group together under gravimetry.
Weightlessness
When speaking of " weightlessness " is (usually) meant weightlessness, not the absence of gravity, but the absence of an appreciable weight as one of their usually noticeable consequences. This occurs, for example if and only if the ( spatially constant ) gravity as the only external force acts on the body at all and all opposing forces acting normally missing. This happens for example in a free fall in a vacuum or in a satellite, approximately in a too violent already moving down the elevator or the ferris wheel before and after reaching the highest point. The free event has an early end on Earth. Outside the earth's atmosphere, it is possible to constantly falling around the earth, when the rotational speed is at least 8 km / s. For larger body tidal forces limit the possible orbits, see Roche limit.
Weightlessness without movement relative to the line connecting two celestial bodies, such as the Earth and Sun is in a few places, the so-called Lagrange points possible. There, the gravitational force of the earth, the gravitational force of the sun and the centrifugal force of the path motion cancel each other out. This is used for example for the Planck Space Telescope.
Gravisphäre
Near masses have more influence on the gravitational acceleration as distant masses. Therefore, satellite orbits are also possible by relatively small bodies in the gravitational field of a large body. The space area in which this is the case, the Gravisphäre of each celestial body. For the same reason, the gravitational acceleration of an irregularly shaped body is not aligned at all points in space to its barycenter.