Math 2.0

Mechanics of particles and systems Particle systems and celestial mechanics Concept

Binet equation

Builds on Central forceAngular momentumOrdinary differential equation

Summary

The Binet equation describes the shape of an orbit in a central force field, with the polar angle as the variable instead of time. It is written for u=1/ru = 1/r, the reciprocal of the distance to the centre, and it is a second-order differential equation in the angle. For the inverse-square force it becomes a harmonic oscillator equation, whose solutions are exactly the conic sections. It also answers the inverse question: which central force produces a given orbit.

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Cross product, concept, no evidence levelCross productconceptDerivative, concept, no evidence levelDerivativeconceptEuclidean space, object, no evidence levelEuclidean spaceobjectEuclidean vector, concept, no evidence levelEuclidean vectorconceptFunction, concept, no evidence levelFunctionconceptOrdinary differential equation, concept, no evidence levelOrdinary differential…conceptTotal derivative, concept, no evidence levelTotal derivativeconceptVelocity, concept, no evidence levelVelocityconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptVector-valued function, concept, no evidence levelVector-valued functionconceptClassical mechanics, concept, no evidence levelClassical mechanicsconceptDifferentiable function of several variables, concept, no evidence levelDifferentiable functi…conceptPartial derivative, concept, no evidence levelPartial derivativeconceptMomentum, concept, no evidence levelMomentumconceptVector field, concept, no evidence levelVector fieldconceptGradient, concept, no evidence levelGradientconceptAngular momentum, concept, no evidence levelAngular momentumconceptScalar potential, concept, no evidence levelScalar potentialconceptConservative vector field, concept, no evidence levelConservative vector f…conceptCentral force, concept, no evidence levelCentral forceconceptBinet equation, concept, no evidence levelBinet equationconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Cross product concept
  2. Derivative concept
  3. Euclidean space object
  4. Euclidean vector concept
  5. Function concept
  6. Ordinary differential equation concept
  7. Total derivative concept
  8. Velocity concept
  9. Function of several variables concept
  10. Vector-valued function concept
  11. Classical mechanics concept
  12. Differentiable function of several variables concept
  13. Partial derivative concept
  14. Momentum concept
  15. Vector field concept
  16. Gradient concept
  17. Angular momentum concept
  18. Scalar potential concept
  19. Conservative vector field concept
  20. Central force concept
  21. Binet equation concept

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Further reading

  1. Web https://en.wikipedia.org/wiki/Binet_equation
About this page
TagJQMZ5Y3E8G
URIm2://JQMZ5Y3E8G
Kindconcept
WritingW0 stub
MSC70F05, 70F15
UsesCentral force, Angular momentum, Ordinary differential equation
Same as
Changed3 November 2026

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