# L 2

by on November 30, 2010

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The Sun from Earth

There is a total of five Lagrangian points. L2 is the point that lies on the line defined by the two large masses, beyond the smaller of the two. At this point the gravitational forces of the two large masses balance the centrifugal effect on the smaller mass.

The three collinear Lagrange points were first discovered by Leonhard Euler around 1750. In 1772, mathematician Joseph Lagrange was working on the three-body problem, he had set out to discover an easy way to calculate the gravitational interaction between arbitrary numbers of bodies in a system. What he eventually ended up were the five Lagrangian points. These points are the five positions in an orbit where a small object affected only by gravity can be stationary(or theoretically close to it) relative to two larger objects. 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.

L2 is the point on the far side of a second body in a system. In the Earth/Sun system, L2 is on the side of Earth that is farthest from the Sun. Normally an object on that side of the Earth would have an orbital period that is greater than Earth’s, but the Earth’s gravitational pull changes that orbit making it roughly equal to Earth’s.

The L2 point for the Sun-Earth system is a good spot for space-based observatories. Because an object around it will maintain the same orientation with respect to the Sun and Earth, making shielding and calibration much simpler. It is slightly beyond the reach of Earth’s shadow, so solar radiation is not completely blocked. The Wilkinson Microwave Anistrophy Probe, Herschel Space Observatory, and the Planck Space Observatory are in varying orbits at this point. In the future, the Gaia Probe and the James Webb Space Telescope will be parked in orbit at the Earth/Sun L2 point. The improved technology of the James Webb may enable greater study of extrasolar planets.

We have written many articles about L 2 for Universe Today. Here’s an article about deadly asteroids stuck in Earth’s Lagrangian points, and here’s an article about Lagrangian points.

If you’d like more info on Lagrangian points, check out NASA’s discussion about Lagrangian Points. And here’s a link to ESA’s page on Lagrange points.

We’ve also recorded an episode of Astronomy Cast all about Lagrange Points. Listen here, Episode 76: Lagrange Points.

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