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The Orbit of the Moon

  • Oliver Montenbruck
  • Thomas Pfleger

Abstract

The motion of the Moon is principally determined by two bodies, the Earth and the Sun. If we consider the gravitational forces that affect the Moon, we find that it is not its nearest neighbour, the Earth, that has the greatest effect, but the more distant Sun. Although gravitational force decreases as the square of the distance, the Sun’s gravity exceeds that of the Earth, because of its far greater mass. Putting figures to this (Earth-Moon distance r ≈ 380000 km, Sun-Moon distance R ≈ 150 million km, Sun/Earth mass ratio M/m ≈ 330 000), we find that the Sun’s gravitational attraction is about twice as great as that of the Earth:
$$ \frac{{{F_ \odot }}}{{{F_ \otimes }}} = \frac{M}{{{R^2}}}/\frac{m}{{{r^2}}} \approx 2 $$
Regardless of the relative positions of the Sun, Earth, and Moon, the sum of the two forces therefore always has a component directed towards the Sun, and never away from it. The Moon may thus be described as following an elliptical orbit around the Sun at a distance of some 150 million km, superimposed upon which there are small monthly oscillations. Because the gravitational force is never directed away from the Sun, the orbit, despite these oscillations, is always concave towards the Sun.

Keywords

Chebyshev Polynomial Perturbation Term Lunar Orbit Earth Radius Chebyshev Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    E. W. Brown; An introductory treatise on the Lunar Theory; Cambridge University Press (1896), Dover Publications (1960). Description of the various perturbation-theory methods of analytically handling the motion of the Moon.MATHGoogle Scholar
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    M. Chapront-Touzé, J. Chapront; ELP 2000–85: a semi-analytical lunar ephemeris adequate for historical times; Astronomy and Astrophysics, vol. 190, p. 342; (1988). Mean orbital elements and perturbation terms describing the orbit of the Moon over long periods of time.ADSGoogle Scholar
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    M. C. Gutzwilier, D. S. Schmidt; The motion of the moon as computed by the method of Hill, Brown and Eckert; Astronomical Papers of the American Ephemeris, vol. XXIII, part 1; Washington (1986). Analytical series expansions of the main problem relating to the motion of the Moon (without taking planetary perturbations into account).Google Scholar
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    Improved Lunar Ephemeris 1952–1959; Nautical Almanac Office; Washington, 1954. Revised version of Brown’s lunar theory of 1954 with all necessary perturbation terms and mean arguments.Google Scholar
  5. A good introduction to the theory of the lunar orbit and the basic perturbations can be found in the volume Himmelsmechanik II by Bucerius and Schneider [2]. The method of approximating functions by Chebyshev polynomials is explained in textbooks on numerical mathematics (see [11] and [13]).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Oliver Montenbruck
    • 1
  • Thomas Pfleger
    • 2
  1. 1.DLR-GSOCWeßlingGermany
  2. 2.HennefGermany

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