Mean longitude

Mean longitude is the ecliptic longitude at which an orbiting body could be found if its orbit were circular and free of perturbations. While nominally a simple longitude, in practice the mean longitude is a hybrid angle.

Definition

  • Define a reference direction, ♈, along the ecliptic. Typically, this is the direction of the vernal equinox. At this point, ecliptic longitude is 0°.
  • The body's orbit is generally inclined to the ecliptic, therefore define the angular distance from ♈ to the place where the orbit crosses the ecliptic from south to north as the longitude of the ascending node, \mathit{\Omega}.
  • Define the angular distance along the plane of the orbit from the ascending node to the pericenter as the argument of the pericenter, \omega.
  • Define the mean anomaly, M, as the angular distance from the pericenter which the body would have if it moved in a circular orbit, in the same orbital period as the actual body in its elliptical orbit.

    • From these definitions, the mean longitude, l, is the angular distance the body would have from the reference direction if it moved with uniform speed,

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