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Encyclopedia > True anomaly

In astronomy, the true anomaly (, also written ) is the angle between the direction z-s of periapsis and the current position p of an object on its orbit, measured at the focus s of the ellipse (the point around which the object orbits). In the diagram below, true anomaly is the angle z-s-p.

Calculation from state vectors

For elliptic orbits true anomaly can be calculated from orbital state vectors as:

(if then replace T by 2π − T)


For circular orbits this can be simplified to:

(if then replace T by 2π − T)


  • is vector pointing towards the ascending node (i.e. the z-component of is zero).

For circular orbits with the inclination of zero this can be simplified further to:

(if then replace T by 2π − T)


Other relations

The relation between T and E, the eccentric anomaly, is:

or equivalently

The relations between the radius (position vector magnitude) and the anomalies are:


where a is the orbit's semi-major axis (segment cz).

See also

  Results from FactBites:
Anomaly - LoveToKnow 1911 (428 words)
Mean R anomaly is the anomaly which the body would have if it moved from the pericentre around F with a uniform angular motion such that its revolution would be completed in its actual time (see Orbit).
Eccentric anomaly is defined thus: - Draw the circumscribing circle of the elliptic orbit around the centre C of the orbit.
In the ancient astronomy the anomaly was taken as the angular distance of the planet from the point of the farthest recession from the earth.
anomaly: Definition, Synonyms and Much More from Answers.com (665 words)
The true anomaly is observed from the primary (I.e., from the orbit's focus);
The eccentric anomaly is observed from the centre of the ellipse, using a projection of the planet's position onto the circumscribing circle; and
In spacecraft operations, an anomaly is an event that results in an unexpected and unwanted event that may cause a negative impact to the state of health of the spacecraft.
  More results at FactBites »



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