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Precession and Nutation of the Earth

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Tides in Astronomy and Astrophysics

Part of the book series: Lecture Notes in Physics ((LNP,volume 861))

Abstract

Precession and nutation of the Earth originate in the tidal forces exerted by the Moon, the Sun, and the planets on the equatorial bulge of the Earth. Discovered respectively in the 2nd century B.C. by Hipparcus and in the 18th century by Bradley, their existence and characteristics were deduced theoretically by Newton for the precession and by d’Alembert for the nutation. After a historical review we explain, both in an intuitive manner and by simple calculations, the gravitational origin and the main characteristics of the precession-nutation. Then we describe in detail two fundamental theories, one using the Lagrangian formalism, the other the Hamiltonian one. A large final part is devoted to successive improvements of the precession-nutation theory in the last decades, both when considering the Earth as a rigid body and when taking into account the small effects of non-rigidity.

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Notes

  1. 1.

    No writing by Hipparcus survives. According to O. Neugbauer in A History of Ancient Mathematical Astronomy, he lived between 190 and 120 B.C., whereas Ptolemy lived between 100 and 170. The observations attributed to Timocharis seem to date back to a period between 300 and 270 B.C.

  2. 2.

    The discovery of nutation, following that of aberration, by Bradley, is officially recorded in a memoir as a letter to Lord Macclesfield, his protector and friend, later President of the Royal Society 1752–1764. Bradley’s memoir, dated 31 December 1747, was read at the Royal Society on 14 February 1748, and published later in the Philosophical Transactions.

  3. 3.

    Notice that Newton in his Principia predicted the semi-annual and semi-monthly nutations which their small amplitude rendered undetectable at his time.

  4. 4.

    The reader must pay attention to the sign conventions: here ψ and h as well as ε and I have the same signs. This follows the classical geometrical rules of a positive sign in the trigonometric (counter clockwise) sense, whereas for conventional astronomical rules ψ and ε are counted positively in the clockwise sense.

  5. 5.

    α E must not be confused with the classical right ascension α measured from an equinox.

  6. 6.

    In the case of axisymmetry, H d =(C−A)/C.

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  1. SYRTE, UMR8630 CNRS & UPMC, Observatoire de Paris, 61, av. de l’Observatoire, 75014, Paris, France

    Jean Souchay & Nicole Capitaine

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  1. Jean Souchay
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  2. Nicole Capitaine
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Correspondence to Jean Souchay .

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  1. Dépt. Astronomie Fondamental, Observatoire de Paris, avenue de l Observatoire 61, Paris, 75014, France

    Jean Souchay

  2. IRFU/SAP Centre de Saclay, Laboratoire AIM Paris Saclay Diderot, Bat. 709, Gif-sur-Yvette, 91191, France

    Stéphane Mathis

  3. University of Cambridge, Trinity Hall, Cambridge, CB2 1TJ, United Kingdom

    Tadashi Tokieda

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Souchay, J., Capitaine, N. (2013). Precession and Nutation of the Earth. In: Souchay, J., Mathis, S., Tokieda, T. (eds) Tides in Astronomy and Astrophysics. Lecture Notes in Physics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32961-6_4

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