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Full-Text Articles in Physical Sciences and Mathematics
Euler's Three-Body Problem, Sylvio R. Bistafa
Euler's Three-Body Problem, Sylvio R. Bistafa
Euleriana
In physics and astronomy, Euler's three-body problem is to solve for the motion of a body that is acted upon by the gravitational field of two other bodies. This problem is named after Leonhard Euler (1707-1783), who discussed it in memoirs published in the 1760s. In these publications, Euler found that the parameter that controls the relative distances among three collinear bodies is given by a quintic equation. Later on, in 1772, Lagrange dealt with the same problem, and demonstrated that for any three masses with circular orbits, there are two special constant-pattern solutions, one where the three bodies remain …
Orbital Dynamics And Stability Of Circumbinary Planetary Systems And Small Bodies In The Solar System, Cheng Chen
Orbital Dynamics And Stability Of Circumbinary Planetary Systems And Small Bodies In The Solar System, Cheng Chen
UNLV Theses, Dissertations, Professional Papers, and Capstones
My main research focuses on the dynamics and stability of circumbinary planetary systems and of small bodies in the solar system. Unlike the two-body problem, the three-body problem is more complex as there are stronger interactions with two massive bodies in the system. In the outer solar system, the apsidal precession secular resonance with Neptune makes comets in the Kuiper belt unstable in the early stages of the solar system. This resonance a likely origin for the nitrogen-delivering comets that impacted the Earth bringing some of the nitrogen in the Earth’s atmosphere today. Beyond the solar system, we have observed …