Please use this identifier to cite or link to this item: http://hdl.handle.net/11189/6324
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dc.contributor.authorSun, BoHuaen_US
dc.date.accessioned2018-05-28T08:57:04Z-
dc.date.available2018-05-28T08:57:04Z-
dc.date.issued2018-
dc.identifier.citationB. H. Sun, Kepler’s third law of n-body periodic orbits in a Newtonian gravitation field, Sci. China-Phys. Mech. Astron. 61, 054721 (2018), https://doi.org/10.1007/s11433-017-9154-0en_US
dc.identifier.issn1869-1927-
dc.identifier.urihttp://hdl.handle.net/11189/6324-
dc.description.abstractOne of the central and most vivid problems of celestial mechanics in the 18th and 19th centuries was the motion description of the Sun-Earth-Moon system under the Newtonian gravitation field (Figure 1(a)). Notable work was done by Euler (1760), Lagrange (1776), Laplace (1799), Hamilton (1834), Liouville (1836), Jacobi (1843), and Poincare (1889) ´ [1] and Xia (1992) [2]. The study of the motion between the two bodies was solved by Kepler (1609) and Newton (1687) early in the 17th century. For the elliptic periodic orbit of 2- body system, Kepler’s third law of the two-body system [3] is given by T|E| 3/2 = π√ 2 Gm1m2 √ m1m2 m1+m2 , where the gravitation constant, G = 6.673 × 10−11m3 kg−1 s −2 , the orbit period, T, the total energy of the 2-body system, |E|, and point masses m1 and m2 (Figure 1(b)). However, the 3-body system (Figure 1(c)) cannot be solved analytically because unlike the 2-body problem, the 18 variables that describe the system cannot be reduced to a single variable. Simplification of the two-body problem was allowed by invariance and conserved quantities as “first integrals”. It was proven impossible to reduce the 18 variables of the 3-body problem in order to produce an analytic solution. Notwithstanding that the analytic solution cannot be found, it is possible to find a numerical solution for the 3- body problem, in which the study of the periodic 3-body orbit has received particular attention in recent years [4-11].en_US
dc.language.isoenen_US
dc.publisherScience China Press and Springer-Verlag GmbH Germanyen_US
dc.relation.ispartofSCIENCE CHINA Physics, Mechanics and Astronomyen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/za/-
dc.rights.urihttps://doi.org/10.1007/s11433-017-9154-0-
dc.subjectCelestial mechanicsen_US
dc.subjectSun-Earth-Moon systemen_US
dc.subjectChenciner Montgomeryen_US
dc.titleKepler’s third law of n-body periodic orbits in a Newtonian gravitation fielden_US
dc.type.patentArticleen_US
dc.identifier.doihttps://doi.org/10.1007/s1143-
Appears in Collections:Eng - Journal articles (DHET subsidised)
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