Observatoire de Paris
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Paths in orbital space

Kepler's laws imply that the orbit of a planet is an ellipse with the star at one of the focuses. This elliptical orbit is characterized by 5 geometric parameters :

  • 2 angles to define the orientation of the plane of the ellipse
  • within this plane, one angle to define the direction of the major axis
  • the semi-major axis value a
  • the eccentricity e of the ellipse

Astronomers usually use slightly different angular parameters to characterize the orbital plane : i*,*omega*,*Omega

  • i, called the inclination of the orbit, is the angle between the orbital plane and the plane of the sky (90°-i is the angle between the orbital plane and the "line of sight" between the observer and the planetary system).
  • omega
  • Omega

The movement of the planet in its orbit is characterized by the period P of orbital rotation, and by the time of passage T_o at a given point in the orbit (the periapsis would be an example). For a given orbit, the period depends on the mass of the star : P=2*pi*racine(a^3/G*M_étoile)

The dynamic methods consist of detecting the perturbation of the movement of the star induced by the orbital rotation of the planet. These movements are governed by the laws of celestial mechanics. The star and the planet both move around the barycenter of the star-planet system. For a planet located at a distance a from its star, the star is at a distance
For a circular orbit, the planet, a is constant. Therefore a_(et) is constant too, so the star follows a circular path around the center of mass.
This displacement can be observed in several ways :