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In celestial mechanics, the Lagrange points (/ l ... When the mass ratio of the two bodies is large enough, the L 4 and L 5 points are stable points, ...
Lagrange point colonization is a proposed form of space colonization [1] of the five equilibrium points in the orbit of a planet or its primary moon, called Lagrange points. The Lagrange points L 4 and L 5 are stable if the mass of the larger body is at least 25 times the mass of the secondary body. [2] [3] Thus, the points L 4 and L 5 in the ...
Lagrange stability is a concept in the stability theory of dynamical systems, named after Joseph-Louis Lagrange. For any point in the state space, in a real continuous dynamical system (,,), where is , the motion (,) is said to be positively Lagrange stable if the positive semi-orbit + is compact.
All of the Lagrange points are highlighted in red. In astronomy, a trojan is a small celestial body (mostly asteroids) that shares the orbit of a larger body, remaining in a stable orbit approximately 60° ahead of or behind the main body near one of its Lagrangian points L 4 and L 5. Trojans can share the orbits of planets or of large moons.
The orbits for two of the points, L 4 and L 5, are stable, but the halo orbits for L 1 through L 3 are stable only on the order of months. In addition to orbits around Lagrange points, the rich dynamics that arise from the gravitational pull of more than one mass yield interesting trajectories, also known as low energy transfers. [4]
The five equilibrium points of the circular problem are known as the Lagrangian points. See figure below: Restricted three-body problem. In the restricted three-body problem math model figure above (after Moulton), the Lagrangian points L 4 and L 5 are where the Trojan planetoids resided (see Lagrangian point); m 1 is the Sun and m 2 is Jupiter.
The name comes from the L 4 and L 5 Lagrangian points in the Earth–Moon system proposed as locations for the huge rotating space habitats that O'Neill envisioned. L 4 and L 5 are points of stable gravitational equilibrium located along the path of the Moon's orbit, 60 degrees ahead or behind it. [2]
In the absence of other influences, orbits about Lagrangian points L 4 and L 5 are dynamically stable so long as the ratio of the masses of the two main objects is greater than about 25. [2] The natural dynamics keep the spacecraft (or natural celestial body) in the vicinity of the Lagrangian point without use of a propulsion system, even when ...