### James Webb Space Telescope Special Exhibit

## The L2 Orbit

Joseph-Louis Lagrange was an 18th century mathematician. Lagrange was searching for a stable configuration in which three bodies could mutually orbit each other and stay in the same position relative to each other. This is know as the *three-body problem*. He found five such solutions (pictured below), called the five Lagrange points in honor of their discoverer. The L2 orbit is an elliptical orbit about the semi-stable second Lagrange point.

In three of the solutions found by Lagrange, the bodies are in line; in the other two the bodies are at the points of equilateral triangles. The five Lagrangian points for the Sun-Earth system are shown in the figure (not drawn to scale) below. An object placed at any one of these 5 points will stay in place relative to the other two.

In this case, the 3 bodies involved are the Sun, the Earth and the JWST. (The gravitational pull of other bodies in the Solar System on JWST will be very small---small enough that we don't have to worry about it in this discussion.) Normally, an object circling the Sun further out than the Earth would take more than one year to complete its orbit. However, the balance of gravitational pull at the L2 point means that JWST will keep up with the Earth as it goes around the Sun.

*Published: April 2007
Text Reviewed: September 2018*