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Two-body problem

Index Two-body problem

In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. [1]

42 relations: Addison-Wesley, Angular momentum, Atomic nucleus, Barycenter, Binary star, Center of mass, Center-of-momentum frame, Central force, Classical mechanics, Classical Mechanics (Goldstein book), Conservative force, Cross product, Earth, Electron, Ellipse, Energy drift, Equation of the center, Euler's three-body problem, Gravitational two-body problem, Kepler orbit, Kepler problem, Mass, Mechanical energy, Momentum, Moon, N-body problem, Newton's laws of motion, Pergamon Press, Perpendicular, Planet, Potential, Potential energy, Reduced mass, Satellite, Star, Three-body problem, Torque, Two-body problem (career), Unit vector, Virial theorem, Wolfram Research, 2.


Addison-Wesley is a publisher of textbooks and computer literature.

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Angular momentum

In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.

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Atomic nucleus

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.

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The barycenter (or barycentre; from the Ancient Greek βαρύς heavy + κέντρον centre) is the center of mass of two or more bodies that are orbiting each other, which is the point around which they both orbit.

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Binary star

A binary star is a star system consisting of two stars orbiting around their common barycenter.

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Center of mass

In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero, or the point where if a force is applied it moves in the direction of the force without rotating.

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Center-of-momentum frame

In physics, the center-of-momentum frame (also zero-momentum frame or COM frame) of a system is the unique (up to velocity but not origin) inertial frame in which the total momentum of the system vanishes.

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Central force

In classical mechanics, a central force on an object is a force that is directed along the line joining the object and the origin: where \scriptstyle \vec is the force, F is a vector valued force function, F is a scalar valued force function, r is the position vector, ||r|| is its length, and \scriptstyle \hat.

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Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

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Classical Mechanics (Goldstein book)

Classical Mechanics is a textbook about the subject of that name written by Herbert Goldstein.

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Conservative force

A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the taken path.

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Cross product

In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.

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Earth is the third planet from the Sun and the only astronomical object known to harbor life.

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The electron is a subatomic particle, symbol or, whose electric charge is negative one elementary charge.

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In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

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Energy drift

In computer simulations of mechanical systems, energy drift is the gradual change in the total energy of a closed system over time.

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Equation of the center

In two-body, Keplerian orbital mechanics, the equation of the center is the angular difference between the actual position of a body in its elliptical orbit and the position it would occupy if its motion were uniform, in a circular orbit of the same period.

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Euler's three-body problem

In physics and astronomy, Euler's three-body problem is to solve for the motion of a particle that is acted upon by the gravitational field of two other point masses that are fixed in space.

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Gravitational two-body problem

←For further relevant mathematical developments see also Two-body problem, also Kepler orbit, and Kepler problem, and Equation of the center – Analytical expansions The gravitational two-body problem concerns the motion of two point particles that interact only with each other, due to gravity.

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Kepler orbit

In celestial mechanics, a Kepler orbit (or Keplerian orbit) is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space.

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Kepler problem

In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force F that varies in strength as the inverse square of the distance r between them.

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Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.

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Mechanical energy

In physical sciences, mechanical energy is the sum of potential energy and kinetic energy.

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In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.

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The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite.

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N-body problem

In physics, the -body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.

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Newton's laws of motion

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics.

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Pergamon Press

Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, which published scientific and medical books and journals.

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In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

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A planet is an astronomical body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.

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Potential generally refers to a currently unrealized ability.

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Potential energy

In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

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Reduced mass

In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics.

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In the context of spaceflight, a satellite is an artificial object which has been intentionally placed into orbit.

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A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity.

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Three-body problem

In physics and classical mechanics, the three-body problem is the problem of taking an initial set of data that specifies the positions, masses, and velocities of three bodies for some particular point in time and then determining the motions of the three bodies, in accordance with Newton's laws of motion and of universal gravitation, which are the laws of classical mechanics.

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Torque, moment, or moment of force is rotational force.

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Two-body problem (career)

The two-body problem is a dilemma for life partners (for e.g. spouses or any other couple) in academia, relating to the difficulty of both spouses obtaining jobs at the same university or within a reasonable commuting distance from each other.

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Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

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Virial theorem

In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy, \left\langle T \right\rangle, of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, \left\langle V_\text \right\rangle, where angle brackets represent the average over time of the enclosed quantity.

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Wolfram Research

Wolfram Research is a private company that creates computational technology.

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2 (two) is a number, numeral, and glyph.

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[1] https://en.wikipedia.org/wiki/Two-body_problem

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