Abstract
The determination of the motion of N point-like masses subject to their mutual gravitational forces is the fundamental problem in celestial mechanics, with important astrophysical applications, including the dynamics of planetary and satellite systems and the evolution of stellar systems (ranging from multiple stars to stellar clusters and galaxies). From the perspective of theoretical physics, this has always been a core problem in gravitation theory; through observations of the motion of celestial bodies it can be tested, quantitatively validated, or even disproved. However, even for N as small as 3, it is impossible to find general solutions in terms of simple analytical functions (as for the two-body problem). A great variety of orbits are possible and it can be shown that only particular initial conditions give rise to periodic behaviour. Even the perturbative techniques worked out in Ch. 12 can be successfully applied only in the particular case of hierarchical systems, where the attraction of one body prevails (see Sec. 15.1). As a consequence, the general gravitational N-body problem has been studied by two alternative methods which can yield only partial results, but are in some way complementary. The first is numerical integration, starting from given initial conditions. In this way the motion can be determined in detail, but only for a limited span of time (due to both limitations in computer time and accumulation of numerical errors; see Sec. 15.1); in addition, it is often impossible to determine the region of phase space where a property of the numerically determined orbits holds. The second method is the search for general constraints or criteria regarding qualitative features of the motion, such as its periodic character, its stability and its geometrical and topological properties.
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© 2003 Springer Science+Business Media Dordrecht
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Bertotti, B., Farinella, P., Vokrouhlický, D. (2003). The Three-Body Problem. In: Physics of the Solar System. Astrophysics and Space Science Library, vol 293. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0233-2_13
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DOI: https://doi.org/10.1007/978-94-010-0233-2_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-1509-0
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