1998
DOI: 10.1103/revmodphys.70.589
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Moon-Earth-Sun: The oldest three-body problem

Abstract: The daily motion of the Moon through the sky has many unusual features that a careful observer can discover without the help of instruments. The three different frequencies for the three degrees of freedom have been known very accurately for 3000 years, and the geometric explanation of the Greek astronomers was basically correct. Whereas Kepler's laws are sufficient for describing the motion of the planets around the Sun, even the most obvious facts about the lunar motion cannot be understood without the gravi… Show more

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Cited by 126 publications
(114 citation statements)
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“…Hill's original aim has been to study the Moon-Earth-Sun system [8,9]. Later, his technique has been applied to stellar dynamics [10][11][12][13], and it is this second context that we have in mind here.…”
Section: The Hill Problemmentioning
confidence: 99%
See 1 more Smart Citation
“…Hill's original aim has been to study the Moon-Earth-Sun system [8,9]. Later, his technique has been applied to stellar dynamics [10][11][12][13], and it is this second context that we have in mind here.…”
Section: The Hill Problemmentioning
confidence: 99%
“…Remember that Hill originally devised his method for finding approximate solutions of the three-body problem, and in particular for the Moon-Earth-Sun system [8,9]. Further applications involve stellar dynamics [10][11][12][13]].…”
mentioning
confidence: 99%
“…The very first premises of analytical works involving a perturbative scheme dates back to the eighteenth century. The main developments have then been pushed forward from the end of the nineteenth century and the pioneering works of Poincaré, Lindstedt, Birkhoff and Lyapunov, among others, for solving difficult problems in celestial mechanics like the three-body problem [1][2][3]. They are now widely used in all fields of applied mathematics and have been very successful in providing a large amount of predictive results.…”
Section: Introductionmentioning
confidence: 99%
“…Earth's velocity through its orbital path is not constant, sweeping out equal areas in equal intervals of time (Kepler's 2 nd law of planetary motion), thereby moving faster at perihelion and slower at aphelion. Conversely, lunar orbital speed increases at perihelion and slows at aphelion (Gutzwiller, 1998). The current Sun-Earth distance at perihelion is ~147.09 x 10 6 km, and at aphelion is ~152.1 x 10 6 km, a variation of around 3%.…”
Section: Earth's Astronomical Setting 311 the Celestial Neighbourhoodmentioning
confidence: 90%