Lagrange point
In celestial mechanics, the Lagrange points (/ l ə ˈ ɡ r ɑː n dʒ /; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies. Mathematically, this involves the solution of the restricted three-body problem.

Normally, the two massive bodies exert an unbalanced gravitational force at a point, altering the orbit of whatever is at that point. At the Lagrange points, the gravitational forces of the two large bodies and the centrifugal force balance each other. This can make Lagrange points an excellent location for satellites, as orbit corrections, and hence fuel requirements, needed to maintain the desired orbit are kept at a minimum.

For any combination of two orbital bodies, there are five Lagrange points, L to L, all in the orbital plane of the two large bodies. There are five Lagrange points for the Sun–Earth system, and five different Lagrange points for the Earth–Moon system. L, L, and L are on the line through the centers of the two large bodies, while L and L each act as the third vertex of an equilateral triangle formed with the centers of the two large bodies.

When the mass ratio of the two bodies is large enough, the L and L points are stable points, meaning that objects can orbit them and that they have a tendency to pull objects into them. Several planets have trojan asteroids near their L and L points with respect to the Sun; Jupiter has more than one million of these trojans.

Some Lagrange points are being used for space exploration. Two important Lagrange points in the Sun-Earth system are L, between the Sun and Earth, and L, on the same line at the opposite side of the Earth; both are well outside the Moon's orbit. Currently, an artificial satellite called the Deep Space Climate Observatory (DSCOVR) is located at L to study solar wind coming toward Earth from the Sun and to monitor Earth's climate, by taking images and sending them back. The James Webb Space Telescope, a powerful infrared space observatory, is located at L. This allows the satellite's large sunshield to protect the telescope from the light and heat of the Sun, Earth and Moon. The L and L Lagrange points are located about 1,500,000 km (930,000 mi) from earth.

The European Space Agency's earlier Gaia telescope, and its newly launched Euclid, also occupy orbits around L. Gaia keeps a tighter Lissajous orbit around L, while Euclid follows a halo orbit similar to JWST. Each of the space observatories benefit from being far enough from Earth's shadow to utilize solar panels for power, from not needing much power or propellant for station-keeping, from not being subjected to the Earth's magnetospheric effects, and from having direct line-of-sight to Earth for data transfer.
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