This article summarizes equations in the theory of gravitation.
A common misconception occurs between centre of mass and centre of gravity. They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts. They are equal if and only if the external gravitational field is uniform.
Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
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Centre of gravity | rcog (symbols vary) | ith moment of mass Centre of gravity for a set of discrete masses: Centre of gravity for a continuum of mass: | m | [L] |
Standard gravitational parameter of a mass | μ | N m2 kg−1 | [L]3 [T]−2 | |
Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
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Gravitational field, field strength, potential gradient, acceleration | g | N kg−1 = m s−2 | [L][T]−2 | |
Gravitational flux | ΦG | m3 s−2 | [L]3[T]−2 | |
Absolute gravitational potential | Φ, φ, U, V | J kg−1 | [L]2[T]−2 | |
Gravitational potential difference | ΔΦ, Δφ, ΔU, ΔV | J kg−1 | [L]2[T]−2 | |
Gravitational potential energy | Ep | J | [M][L]2[T]−2 | |
Gravitational torsion field | Ω | Hz = s−1 | [T]−1 | |
In the weak-field and slow motion limit of general relativity, the phenomenon of gravitoelectromagnetism (in short "GEM") occurs, creating a parallel between gravitation and electromagnetism. The gravitational field is the analogue of the electric field, while the gravitomagnetic field, which results from circulations of masses due to their angular momentum, is the analogue of the magnetic field.
Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
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Gravitational torsion flux | ΦΩ | N m s kg−1 = m2 s−1 | [M]2 [T]−1 | |
Gravitomagnetic field | H, Bg, B, ξ | Hz = s−1 | [T]−1 | |
Gravitomagnetic flux | Φξ | N m s kg−1 = m2 s−1 | [M]2 [T]−1 | |
Gravitomagnetic vector potential [1] | h | m s−1 | [M] [T]−1 | |
It can be shown that a uniform spherically symmetric mass distribution generates an equivalent gravitational field to a point mass, so all formulae for point masses apply to bodies which can be modelled in this way.
Physical situation | Nomenclature | Equations |
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Gravitational potential gradient and field |
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Point mass | ||
At a point in a local array of point masses | ||
Gravitational torque and potential energy due to non-uniform fields and mass moments |
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Gravitational field for a rotating body |
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General classical equations.
Physical situation | Nomenclature | Equations |
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Potential energy from gravity, integral from Newton's law | ||
Escape speed |
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Orbital energy |
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Physical situation | Nomenclature | Equations |
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Gravitomagnetic field for a rotating body | ξ = gravitomagnetic field | |
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, two distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles, causing an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs exclusively between charged particles in relative motion. These two effects combine to create electromagnetic fields in the vicinity of charged particles, which can accelerate other charged particles via the Lorentz force. At high energy, the weak force and electromagnetic force are unified as a single electroweak force.
In physics, the fundamental interactions or fundamental forces are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist:
In physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, meaning a change in speed or direction, unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force is the newton (N), and force is often represented by the symbol F.
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalises special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations.
The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.
In physics, gravity (from Latin gravitas 'weight') is a fundamental interaction which causes mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics.
In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as the gravitational force field exerted on another massive body. It has dimension of acceleration (L/T2) and it is measured in units of newtons per kilogram (N/kg) or, equivalently, in meters per second squared (m/s2).
A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically intended to describe electromagnetism and gravitation, two of the fundamental forces of nature.
In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light c. As a result, classical mechanics is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of electromagnetism with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at any speed, including faster than light. The foundations of relativistic mechanics are the postulates of special relativity and general relativity. The unification of SR with quantum mechanics is relativistic quantum mechanics, while attempts for that of GR is quantum gravity, an unsolved problem in physics.
A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, in non-inertial frames, they vary from frame to frame depending on the acceleration.
The following outline is provided as an overview of and topical guide to black holes:
Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. Gravitomagnetism is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles.
In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. For example, on a weather map, the surface temperature is described by assigning a number to each point on the map; the temperature can be considered at a certain point in time or over some interval of time, to study the dynamics of temperature change. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field, i.e. a 1-dimensional (rank-1) tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank-1 tensor field, while electrodynamics can be formulated in terms of two interacting vector fields at each point in spacetime, or as a single-rank 2-tensor field.