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- Two-body_problem_in_general_relativity abstract "The two-body problem in general relativity is to determine the motion and gravitational field of two bodies interacting with one another by gravitation, as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun. Solutions are also used to describe the motion of binary stars around each other, and estimate their gradual loss of energy through gravitational radiation. It is customary to assume that both bodies are point-like, so that tidal forces and the specifics of their material composition can be neglected.General relativity describes the gravitational field by curved space-time; the field equations governing this curvature are nonlinear and therefore difficult to solve in a closed form. Only one exact solution, the Schwarzschild solution, has been found for the Kepler problem; this solution pertains when the mass M of one body is overwhelmingly greater than the mass m of the other. If so, the larger mass may be taken as stationary and the sole contributor to the gravitational field. This is a good approximation for a photon passing a star and for a planet orbiting its sun. The motion of the lighter body (called the "particle" below) can then be determined from the Schwarzschild solution; the motion is a geodesic ("shortest path between two points") in the curved space-time. Such geodesic solutions account for the anomalous precession of the planet Mercury, which is a key piece of evidence supporting the theory of general relativity. They also describe the bending of light in a gravitational field, another prediction famously used as evidence for general relativity.If both masses are considered to contribute to the gravitational field, as in binary stars, the Kepler problem can be solved only approximately. The earliest approximation method to be developed was the post-Newtonian expansion, an iterative method in which an initial solution is gradually corrected. More recently, it has become possible to solve Einstein's field equation using a computer instead of mathematical formulae. As the two bodies orbit each other, they will emit gravitational radiation; this causes them to lose energy and angular momentum gradually, as illustrated by the binary pulsar PSR B1913+16.".
- Two-body_problem_in_general_relativity thumbnail Elliptic_orbit.gif?width=300.
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- Two-body_problem_in_general_relativity subject Category:Exact_solutions_in_general_relativity.
- Two-body_problem_in_general_relativity type Abstraction100002137.
- Two-body_problem_in_general_relativity type ExactSolutionsInGeneralRelativity.
- Two-body_problem_in_general_relativity type Matter100020827.
- Two-body_problem_in_general_relativity type Mixture114586258.
- Two-body_problem_in_general_relativity type Part113809207.
- Two-body_problem_in_general_relativity type PhysicalEntity100001930.
- Two-body_problem_in_general_relativity type Relation100031921.
- Two-body_problem_in_general_relativity type Solution114589223.
- Two-body_problem_in_general_relativity type Substance100019613.
- Two-body_problem_in_general_relativity comment "The two-body problem in general relativity is to determine the motion and gravitational field of two bodies interacting with one another by gravitation, as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun.".
- Two-body_problem_in_general_relativity label "Problema di Keplero nella relatività generale".
- Two-body_problem_in_general_relativity label "Two-body problem in general relativity".
- Two-body_problem_in_general_relativity label "Задача Кеплера в общей теории относительности".
- Two-body_problem_in_general_relativity label "广义相对论中的开普勒问题".
- Two-body_problem_in_general_relativity sameAs Problema_di_Keplero_nella_relatività_generale.
- Two-body_problem_in_general_relativity sameAs m.02rp7mn.
- Two-body_problem_in_general_relativity sameAs Q1006428.
- Two-body_problem_in_general_relativity sameAs Q1006428.
- Two-body_problem_in_general_relativity sameAs Two-body_problem_in_general_relativity.
- Two-body_problem_in_general_relativity wasDerivedFrom Two-body_problem_in_general_relativity?oldid=605427602.
- Two-body_problem_in_general_relativity depiction Elliptic_orbit.gif.
- Two-body_problem_in_general_relativity isPrimaryTopicOf Two-body_problem_in_general_relativity.
