At its core, Newton’s law of gravity is simply a mutual attraction of masses. But when more than two bodies attract each other their motion can become wondrously complex. So complex that even the motion of three masses is often unpredictable. But there are also some amazing effects of gravitational dynamics, such as the ability to orbit a point where there is no mass.
Joseph-Louis Lagrange first studied the complexities of gravitational motion in the late 1700s. He had no way to calculate the motion of a particular object, but instead focused on the gravitational potential of large bodies in motion, such as the Sun-Earth or Earth-Moon systems. He found that the gravitational pull of objects and their motions about each other could create balance points, now known as Lagrange points. These balance points move with the motion of the masses, but relative to each mass they don’t appear to move. So if you could put an object exactly at a Lagrange point, the gravitational pull of the other masses and their orbital motion would make it appear as if the object were stationary.
For three of these points, any slight deviation from their exact position would cause a small body to fly off in a strange orbit. But two of them (known as L4 and L5) are stable balance points. This means if a body deviates slightly from the position the effects of gravity and motion will work to bring it back towards the point. It’s similar to the effect of a mass hanging on a string. If you give it a little push it will wobble around its original position.
The L4 and L5 points for the Sun-Jupiter system have captured asteroids over time, and are now known as the Trojans. Another group of asteroids known as the Hilda family tend to cluster near Jupiter’s L3 point. The Sun-Earth L4 and L5 points contain some interplanetary dust. The L4 point also contains a small asteroid, which is Earth’s only known trojan. Mars has four Lagrange asteroids. Lagrange points have also become important for astronomical missions. Several satellites such as Planck and Gaia are located near the Sun-Earth L2 point. The SOHO satellite orbits near Sun-Earth L1. Satellites at L3 could provide a way to communicate continuously with missions to Mars and the outer solar system.
It’s all a part of Lagrange’s gravitational dance.