Relationship between the True and Mean Anomalies


FOR an elliptical orbit, we have the following relations1: whence, where r, a, and e have their usual meanings, and ν and M are the true and mean anomalies, respectively.

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  1. 1

    Moulton, F. A., An Introduction to Celestial Mechanics, 164, 172 (Macmillan, 1959).

  2. 2

    Brown, E. W., An Introductory Treatise on the Lunar Theory, 31 (Cambridge Univ. Press, 1896).

  3. 3

    Smart, W. M., Celestial Mechanics, 38 (Longmans, 1953).

  4. 4

    Smart, W. M., Celestial Mechanics, 32 (Longmans, 1953).

  5. 5

    Brown, E. W., and Shook, C. A., Planetary Theory, 37 (Cambridge Univ. Press, 1933).

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BROOKES, C. Relationship between the True and Mean Anomalies. Nature 190, 839–840 (1961).

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