Trojan (celestial body) in the context of "Jupiter trojan"

A Klemperer rosette is a gravitational system of (optionally) alternating heavier and lighter bodies orbiting in a symmetrical pattern around a common barycenter. It was first described by W.B. Klemperer in 1962, and is a special case of a central configuration.

Klemperer described rosette systems as follows:

An Earth trojan is an asteroid that orbits the Sun in the vicinity of the Earth–Sun Lagrange points L₄ (leading 60°) or L₅ (trailing 60°), thus having an orbit similar to Earth's. Only two Earth trojans have so far been discovered. The name "trojan" was first used in 1906 for the Jupiter trojans, the asteroids that were observed near the Lagrangian points of Jupiter's orbit.

The Mars trojans are a group of trojan objects that share the orbit of the planet Mars around the Sun. They can be found around the two Lagrangian points 60° ahead of and behind Mars. The origin of the Mars trojans is not well understood. One hypothesis suggests that they were primordial objects left over from the formation of Mars that were captured in its Lagrangian points as the Solar System was forming. However, spectral studies of the Mars trojans indicate this may not be the case. Another explanation involves asteroids chaotically wandering into the Mars Lagrangian points later in the Solar System's formation. This is also questionable considering the short dynamical lifetimes of these objects. The spectra of Eureka and two other Mars trojans indicates an olivine-rich composition. Since olivine-rich objects are rare in the asteroid belt it has been suggested that some of the Mars trojans are captured debris from a large orbit-altering impact on Mars when it encountered a planetary embryo.

Presently, this group contains 17 asteroids confirmed to be stable Mars trojans by long-term numerical simulations but only nine of them are accepted by the Minor Planet Center.

A Uranus trojan is an asteroid that shares an orbit with Uranus and the Sun. Predicted in simulations earlier, two trojans have been discovered in Uranus’s Lagrangian point L₄ (leading Uranus).

(687170) 2011 QF99 was the first body to be classified as such a trojan in 2013, while in 2017 (636872) 2014 YX49 became the second.

In orbital mechanics, a libration point orbit (LPO) is a quasiperiodic orbit around a Lagrange point. Libration is a form of orbital motion exhibited, for example, in the Earth–Moon system. Trojan bodies also exhibit libration dynamics.

Two varieties of libration point orbits amenable to Lyapunov stability are halo orbits and Lissajous orbits

A Kirkwood gap is a gap or dip in the distribution of the semi-major axes (or equivalently of the orbital periods) of the orbits of main-belt asteroids. They correspond to the locations of orbital resonances with Jupiter. The gaps were first noticed in 1866 by Daniel Kirkwood, who also correctly explained their origin in the orbital resonances with Jupiter while a professor at Jefferson College in Canonsburg, Pennsylvania.

For example, there are very few asteroids with semimajor axis near 2.50 AU, period 3.95 years, which would make three orbits for each orbit of Jupiter (hence, called the 3:1 orbital resonance). Other orbital resonances correspond to orbital periods whose lengths are simple fractions of Jupiter's. The weaker resonances lead only to a depletion of asteroids, while spikes in the histogram are often due to the presence of a prominent asteroid family (see List of asteroid families).