Trojan (celestial body)

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.

The trojan points are located on the L 4 and L 5 Lagrange points , on the orbital path of the secondary object (blue), around the primary object (yellow). All of the Lagrange points are highlighted in red.
The Jupiter trojans are seen in this graphic as Greek camp at L 4 ahead of Jupiter and as Trojan camp at L 5 trailing Jupiter along its orbital path. It also shows the asteroid belt between Mars and Jupiter and the Hilda asteroids .
Jupiter trojans Asteroid belt Hilda asteroids
The Sun, the planets, their moons, and several trans-Neptunian objects The Sun Mercury Venus The Moon Earth Mars Phobos and Deimos Ceres The main asteroid belt Jupiter Moons of Jupiter Rings of Jupiter Saturn Moons of Saturn Rings of Saturn Uranus Moons of Uranus Rings of Uranus Neptune Moons of Neptune Rings of Neptune Pluto Moons of Pluto Haumea Moons of Haumea Makemake S/2015 (136472) 1 The Kuiper Belt Eris Dysnomia The Scattered Disc The Hills Cloud The Oort Cloud