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Sitnikov problem : ウィキペディア英語版
Sitnikov problem

The Sitnikov problem is a restricted version of the three-body problem named after Russian mathematician Kirill Alexandrovitch Sitnikov that attempts to describe the movement of three celestial bodies due to their mutual gravitational attraction. A special case of the Sitnikov problem was first discovered by the American scientist William Duncan MacMillan in 1911, but the problem as it currently stands wasn't discovered until 1961 by Sitnikov.
== Definition ==
The system consists of two primary bodies with the same mass \left(m_1 = m_2 = \tfrac\right), which move in circular or elliptical Kepler orbits around their center of mass. The third body, which is substantially smaller than the primary bodies and whose mass can be set to zero (m_3 = 0), moves under the influence of the primary bodies in a plane that is perpendicular to the orbital plane of the primary bodies (see Figure 1). The origin of the system is at the focus of the primary bodies. The combined mass of the primary bodies (m = 1), the orbital period of the bodies (2\pi), and the radius of the orbit of the bodies (a = 1) are used for this system. In addition, the gravitational constant is 1. In such a system that the third body only moves in one dimension – it moves only along the z-axis.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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