In turn, a much smaller mass than both the star and the planet, located at one of the Lagrangian points of the star–planet system, is subject to a combined gravitational force that acts through this barycenter.
More than a million Jupiter trojans larger than one kilometer are thought to exist,[2] of which more than 7,000 are currently catalogued.
In 1772, the Italian–French mathematician and astronomer Joseph-Louis Lagrange obtained two constant-pattern solutions (collinear and equilateral) of the general three-body problem.
[6] Later on, objects were found orbiting near the Lagrangian points of Neptune, Mars, Earth,[7] Uranus, and Venus.
[8] Whether or not a system of star, planet, and trojan is stable depends on how large the perturbations are to which it is subject.
And if the star were hyper-massive, m1→+∞, then under Newtonian gravity, the system is stable whatever the planet and trojan masses.
Jupiter trojans | Asteroid belt | Hilda asteroids |