Lagrange points

Lagrange points refer to five locations in space relative to two celestial objects that are gravitationally bound -- typical a planet orbiting a star, or a moon orbiting a planet. For this article, we will refer to a planet in orbit about a star, as this is less cumbersome that talking about a "smaller celestial object in orbit about a larger celestial object."

For a third, small object located at one of the Lagrange points, the combined gravitational forces exerted by both the planet and the star will be just the right strength and in just the right direction to keep the object in a circular orbit about the center of mass of the two celestial objects, with the period of the orbit equal to that of the planet.

The five points are labeled L1 through L5. L1 and L2 are both near the planet, with L1 slightly closer to the star and L2 slightly farther away. L3 is in the planet's orbit, but on the far side of the star. L4 and L5 are also in the planet's orbit, and each forms an equilateral triangle with the planet and the star.

Of the 5 Lagrange points, the L1 point lies closest to the planet. As such, it is generally considered to be at the limit of how far away a moon can be and still remain in orbit about the planet. It is therefore equated with the Hill sphere radius.