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There are five Lagrangian points. L1 lies on the line defined by the two large masses M1 and M2 and between them. It is the most intuitively understood of the Lagrangian points: the one where the gravitational attraction of M2 partially cancels M1 gravitational attraction.
The Lagrangian points are the five positions in an orbit where a small object affected only by gravity can be stationary(in theory) relative to two larger objects. Essentially the gravity of both bodies is equal and should not effect the object, usually a satellite. The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to rotate with them. They can be equated to geostationary orbits in that they allow an object to be in a fixed position in space rather than an orbit in which its relative position changes continuously. These points are the stationary solutions for the circular restricted three-body problem. If you have two massive bodies in circular orbits around a common center of mass, then there are five positions in space where a third body of much smaller mass could be placed and the third body would maintain its position relative to the two massive bodies.
The L1 point between Earth and the Sun is frequently used to place scientific satellites because it is never in the shadow of either body, so information can be gathered continuously. The Solar and Heliospheric Observatory(SOHO), the Advanced Composition Explorer(ACE), and the WIND program are based in varying types of orbits at the Earth/Sun L1 point. The information gathered from either of these spacecraft could change our understanding of the Universe.
We have written many articles about L 1 for Universe Today. Here’s an article about deadly asteroids stuck in Earth’s Lagrangian points, and here’s an article about Lagrangian points.
We’ve also recorded an episode of Astronomy Cast all about Lagrange Points. Listen here, Episode 76: Lagrange Points.