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Circular Restricted Three-Body Problem — Orbital Mechanics & Astrodynamics

orbital-mechanics.space · 1,873 words · saved by 2 readers

There are two primary masses, and the mass of the tertiary object is extremely small in comparison to 𝑚 1 and 𝑚 2 The mass of 𝑚 1 is larger than 𝑚 2 The two primary objects orbit in a circle around their center of mass Although these assumptions seem fairly restrictive, they actually represent several very important physical situations: the Earth-Moon system, as well as the orbits of many of the planets around the Sun, with a man-made object as the third mass! This is called the Circular Restricted Three-Body Problem (CRTBP or CR3BP), because the orbits are restricted to circles and the mass of the third body is restricted to be much smaller than the other two. We’ll see in a later section that the eccentricity of an orbit determines how close to a circle the orbit is. An eccentricity of 0 gives the equation for a circle, while vales up to 1.0 are ellipses. The orbit of the moon around the Earth is approximately circular, with a mean eccentricity of 0.054, and semi-major and

Circular Restricted Three-Body Problem # In this section, we solve the three-body problem, subject to some restrictions. In particular: There are two primary masses, and the mass of the tertiary object is extremely small in comparison to \(m_1\) and \(m_2\) The mass of \(m_1\) is larger than \(m_2\) The two primary objects orbit in a circle around their center of mass Although these assumptions seem fairly restrictive, they actually represent several very important physical situations: the Earth-Moon system, as well as the orbits of many of the planets around the Sun, with a man-made object as

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