Where are the five Lagrange points located in a two-body system?

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Geocentric system — Celestial mechanics Ptolemaic diagram of a geocentric system, from the star atlas *Harmonia Macrocosmica* by the cartographer Andreas Cellarius, 1660.

In celestial mechanics, a Lagrange point is a position in space where a small object can remain at rest relative to two larger orbiting bodies due to the balance of gravitational and centripetal forces.1

The five points are located as follows:

L1, L2, and L3: These three points lie along a straight line that passes through the centers of the two large bodies.1
- L1 is situated between the two large bodies.1
- L2 is located on the opposite side of the smaller body from the larger body.1
- L3 is positioned on the opposite side of the larger body from the smaller body.1
L4 and L5: These points are located at the vertices of two equilateral triangles that share the two large bodies as their base.1
- L4 is known as the leading point, as it precedes the smaller body in its orbit.1
- L5 is the trailing point, following the smaller body in its orbit.1

While L1, L2, and L3 are unstable, L4 and L5 are stable under specific mass ratio conditions, often hosting Trojan asteroids.1