page_title: Lagrange point
section_title: Sun–Earth
hierarchical_section_title: Lagrange point / Spaceflight applications / Sun–Earth
caption_attribution_description: English: ACE in its orbit around L1.
context_page_description: In celestial mechanics, the Lagrange points are orbital points near two large co-orbiting bodies. At the Lagrange points the gravitational forces of the two large bodies cancel out in such a way that a small object placed in orbit there is in equilibrium relative to the center of mass of the large bodies.
  There are five such points, labeled L₁ to L₅, all in the orbital plane of the two large bodies. L₁, L₂, and L₃ are on the line through the centers of the two large bodies, while L₄ and L₅ each act as the third vertex of an equilateral triangle formed with the centers of the two large bodies. L₁, L₂, L₃ are unstable equilibria, whereas L₄ and L₅ are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.
  For each given combination of co-orbiting planetary bodies there are five Lagrange points L₁ to L₅ for the Sun–Earth system, and in a similar way there are five different Lagrange points for the Earth–Moon system. Several planets have trojan satellites near their L₄ and L₅ points with respect to the Sun. Jupiter has more than a million of these trojans.
context_section_description: Sun–Earth L₁ is suited for making observations of the Sun–Earth system. Objects here are never shadowed by Earth or the Moon and, if observing Earth, always view the sunlit hemisphere. The first mission of this type was the 1978 International Sun Earth Explorer 3 (ISEE-3) mission used as an interplanetary early warning storm monitor for solar disturbances.  Since June 2015, DSCOVR has orbited the L₁ point. Conversely it is also useful for space-based solar telescopes, because it provides an uninterrupted view of the Sun and any space weather (including the solar wind and coronal mass ejections) reaches L₁ a few hours before Earth. Solar telescopes currently located around L₁ include the Solar and Heliospheric Observatory and Advanced Composition Explorer.
  Sun–Earth L₂ is a good spot for space-based observatories. Because an object around L₂ will maintain the same relative position with respect to the Sun and Earth, shielding and calibration are much simpler. It is, however, slightly beyond the reach of Earth's umbra, so solar radiation is not completely blocked at L₂. Spacecraft generally orbit around L₂, avoiding partial eclipses of the Sun to maintain a constant temperature. From locations near L₂, the Sun, Earth and Moon are relatively close together in the sky; this means that a large sunshade with the telescope on the dark-side can allow the telescope to cool passively to around 50 K – this is especially helpful for infrared astronomy and observations of the cosmic microwave background. The James Webb Space Telescope is due to be positioned at L₂.
  Sun–Earth L₃ was a popular place to put a "Counter-Earth" in pulp science fiction and comic books. Once space-based observation became possible via satellites and probes, it was shown to hold no such object. The Sun–Earth L₃ is unstable and could not contain a natural object, large or small, for very long. This is because the gravitational forces of the other planets are stronger than that of Earth (Venus, for example, comes within 0.3 AU of this L₃ every 20 months).
  A spacecraft orbiting near Sun–Earth L₃ would be able to closely monitor the evolution of active sunspot regions before they rotate into a geoeffective position, so that a 7-day early warning could be issued by the NOAA Space Weather Prediction Center. Moreover, a satellite near Sun–Earth L₃ would provide very important observations not only for Earth forecasts, but also for deep space support (Mars predictions and for manned mission to near-Earth asteroids). In 2010, spacecraft transfer trajectories to Sun–Earth L₃ were studied and several designs were considered.
  Missions to Lagrangian points generally orbit the points rather than occupy them directly.
  Another interesting and useful property of the collinear Lagrangian points and their associated Lissajous orbits is that they serve as "gateways" to control the chaotic trajectories of the Interplanetary Transport Network.
caption: The satellite ACE in an orbit around Sun–Earth L1.
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