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Orbits, Direct Broadcasting and Solar Power
Published in Francis Lyall, Paul B. Larsen, Space Law, 2016
There are five astronomic Lagrange points. Joseph-Louis Lagrange, for whom they are named, was a French mathematician who, working on the ‘three body problem’ in 1772, inter alia discovered that the position of a third body of negligible mass will remain relatively static relative to two other considerably larger bodies that themselves are in near-circular orbits. A number of Lagrange points in the solar system have been identified as various solar bodies are in appropriate mutual configuration. The Sun–Earth Lagrange Point L-1 lies between the Earth and the Sun and has been used by two scientific satellites, SOHO and ACE.12 Sun–Earth Lagrange Point L-2 lies beyond the Earth, and is the site for various probes, including in due course the new James Webb Space Telescope when it is launched.13 Lagrange Point L-3 is on the other side of the Sun in the Sun–Earth configuration and at present has no planned use. Sun–Earth Lagrange Points L-4 and L-5 are 60° ahead and behind the Earth in its orbit and are not at present of great interest. Of greater interest are Lagrange Points L-4 and L-5 in the Moon–Earth configuration (sometimes known as the Trojan points) which are 60° ahead and behind the Moon in its orbit of the Earth. Satellites located at these points, or in halo or Lissajous orbits round them, are relatively stable,14 and could be of use either for scientific purposes or for Earth–Moon telecommunications from some of the parts of the Moon not normally visible from the Earth.15
Of boundaries and orbits
Published in Francis Lyall, Paul B. Larsen, Space Law, 2017
There are five astronomic Lagrange points. Joseph-Louis Lagrange, for whom they are named, was a French mathematician who, working on the ‘three body problem’ in 1772, inter alia discovered that the position of a third body of negligible mass will remain relatively static relative to two other considerably larger bodies that themselves are in near-circular orbits. A number of Lagrange points in the solar system have been identified as various solar bodies are in appropriate mutual configuration. The Sun – Earth Lagrange Point L-1 lies between the Earth and the Sun and has been used by two scientific satellites, SOHO and ACE.118 Sun – Earth Lagrange Point L-2 lies beyond the Earth, and is the site for various probes, including in due course the new James Webb Space Telescope when it is launched in 2018.119 The L-2 Point has also been used as a staging point for explorations further out into the solar system. Lagrange Point L-3 is on the other side of the Sun in the Sun – Earth configuration and at present has no planned use. Sun – Earth Lagrange Points L-4 and L-5 are 60° ahead and behind the Earth in its orbit and are not at present of great interest. Of greater interest are Lagrange Points L-4 and L-5 in the Moon – Earth configuration (sometimes known as the Trojan points) which are 60° ahead and behind the Moon in its orbit of the Earth. Satellites located at these points, or in halo or Lissajous orbits round them, are relatively stable,120 and could be of use either for scientific purposes or for Earth – Moon telecommunications from some parts of the Moon not normally visible from the Earth.121
Robust control of the circular restricted three-body problem with drag
Published in International Journal of Control, 2022
David J. N. Limebeer, Deon Sabatta
In the classical case, in which external forces are neglected, the Lagrange points are points in space where the gravitational and centripetal forces cancel. At these points, (see Moulton, 1920).