Tisserand's parameter (or Tisserand's invariant) is a value calculated from several orbital elements (semi-major axis, orbital eccentricity and inclination) of a relatively small object and a larger "perturbing body". It is used to distinguish different kinds of orbits. The term is named after French astronomer Félix Tisserand, and applies to restricted three-body problems in which the three objects all differ greatly in mass.
For a small body with semi-major axis , orbital eccentricity , and orbital inclination , relative to the orbit of a perturbing larger body with semimajor axis , the parameter is defined as follows:  
The quasi-conservation of Tisserand's parameter is a consequence of Tisserand's relation.
The parameter is derived from one of the so-called Delaunay standard variables, used to study the perturbed Hamiltonian in a three-body system. Ignoring higher-order perturbation terms, the following value is conserved:
Consequently, perturbations may lead to the resonance between the orbital inclination and eccentricity, known as Kozai resonance. Near-circular, highly inclined orbits can thus become very eccentric in exchange for lower inclination. For example, such a mechanism can produce sungrazing comets, because a large eccentricity with a constant semimajor axis results in a small perihelion.
A classical Kuiper belt object, also called a cubewano ( "QB1-o"), is a low-eccentricity Kuiper belt object (KBO) that orbits beyond Neptune and is not controlled by an orbital resonance with Neptune. Cubewanos have orbits with semi-major axes in the 40–50 AU range and, unlike Pluto, do not cross Neptune's orbit. That is, they have low-eccentricity and sometimes low-inclination orbits like the classical planets.
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in astronomy and orbital mechanics.
A centaur, in planetary astronomy, is a small Solar System body with either a perihelion or a semi-major axis between those of the outer planets. Centaurs generally have unstable orbits because they cross or have crossed the orbits of one or more of the giant planets; almost all their orbits have dynamic lifetimes of only a few million years, but there is one known centaur, 514107 Kaʻepaokaʻawela, which may be in a stable orbit. Centaurs typically exhibit the characteristics of both asteroids and comets. They are named after the mythological centaurs that were a mixture of horse and human. Observational bias toward large objects makes determination of the total centaur population difficult. Estimates for the number of centaurs in the Solar System more than 1 km in diameter range from as low as 44,000 to more than 10,000,000
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control.
Damocloids are a class of minor planets such as 5335 Damocles and 1996 PW that have Halley-type or long-period highly eccentric orbits typical of periodic comets such as Halley's Comet, but without showing a cometary coma or tail. David Jewitt defines a damocloid as an object with a Jupiter Tisserand invariant (TJ) of 2 or less, while Akimasa Nakamura defines this group with the following orbital elements:
A Sun-synchronous orbit (SSO), also called a heliosynchronous orbit, is a nearly polar orbit around a planet, in which the satellite passes over any given point of the planet's surface at the same local mean solar time. More technically, it is an orbit arranged so that it precesses through one complete revolution each year, so it always maintains the same relationship with the Sun. A Sun-synchronous orbit is useful for imaging, reconnaissance satellite, and weather satellites, because every time that the satellite is overhead, the surface illumination angle on the planet underneath it will be nearly the same.
In astrodynamics or celestial mechanics, a hyperbolic trajectory is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola. In more technical terms this can be expressed by the condition that the orbital eccentricity is greater than one.
In astronomy, perturbation is the complex motion of a massive body subject to forces other than the gravitational attraction of a single other massive body. The other forces can include a third body, resistance, as from an atmosphere, and the off-center attraction of an oblate or otherwise misshapen body.
The scattered disc (or scattered disk) is a distant circumstellar disc in the Solar System that is sparsely populated by icy small solar system bodies, which are a subset of the broader family of trans-Neptunian objects. The scattered-disc objects (SDOs) have orbital eccentricities ranging as high as 0.8, inclinations as high as 40°, and perihelia greater than 30 astronomical units (4.5×109 km; 2.8×109 mi). These extreme orbits are thought to be the result of gravitational "scattering" by the gas giants, and the objects continue to be subject to perturbation by the planet Neptune.
In celestial mechanics, the Kozai mechanism or Lidov–Kozai mechanism or Kozai–Lidov mechanism, also known as the Kozai, Lidov–Kozai or Kozai–Lidoveffect, oscillations, cycles or resonance, is a dynamical phenomenon affecting the orbit of a binary system perturbed by a distant third body under certain conditions, causing the orbit's argument of pericenter to oscillate about a constant value, which in turn leads to a periodic exchange between its eccentricity and inclination. The process occurs on timescales much longer than the orbital periods. It can drive an initially near-circular orbit to arbitrarily high eccentricity, and flip an initially moderately inclined orbit between a prograde and a retrograde motion.
The proper orbital elements or proper elements of an orbit are constants of motion of an object in space that remain practically unchanged over an astronomically long timescale. The term is usually used to describe the three quantities:
Tisserand's criterion is used to determine whether or not an observed orbiting body, such as a comet or an asteroid, is the same as a previously observed orbiting body.
In astronomy, an irregular moon, irregular satellite or irregular natural satellite is a natural satellite following a distant, inclined, and often eccentric and retrograde orbit. They have been captured by their parent planet, unlike regular satellites, which formed in orbit around them. Irregular moons have a stable orbit, unlike temporary satellites which often have similarly irregular orbits but will eventually depart. The term does not refer to shape as Triton is a round moon, but is considered irregular due to its orbit.
Detached objects are a dynamical class of minor planets in the outer reaches of the Solar System and belong to the broader family of trans-Neptunian objects (TNOs). These objects have orbits whose points of closest approach to the Sun (perihelion) are sufficiently distant from the gravitational influence of Neptune that they are only moderately affected by Neptune and the other known planets: This makes them appear to be "detached" from the rest of the Solar System, except for their attraction to the Sun.
In orbital mechanics, a frozen orbit is an orbit for an artificial satellite in which natural drifting due to the central body's shape has been minimized by careful selection of the orbital parameters. Typically, this is an orbit in which, over a long period of time, the satellite's altitude remains constant at the same point in each orbit. Changes in the inclination, position of the lowest point of the orbit, and eccentricity have been minimized by choosing initial values so that their perturbations cancel out. This results in a long-term stable orbit that minimizes the use of station-keeping propellant.
2005 VX3 is trans-Neptunian object and retrograde damocloid on a highly eccentric, cometary-like orbit. It was first observed on 1 November 2005, by astronomers with the Mount Lemmon Survey at the Mount Lemmon Observatory in Arizona, United States. The unusual object measures approximately 7 kilometers (4 miles) in diameter. It has the 3rd largest known heliocentric semi-major axis and aphelion. Additionally its perihelion lies within the orbit of Jupiter, which means it also has the largest orbital eccentricity of any known minor planet.
2002 RN109 is a trans-Neptunian object and damocloid on a highly eccentric, cometary-like orbit. It was first observed on 6 September 2002, by astronomers with the Lincoln Near-Earth Asteroid Research at the Lincoln Lab's ETS near Socorro, New Mexico, in the United States. The unusual object measures approximately 4 kilometers (2 miles) in diameter. It has the second highest orbital eccentricity of any known minor planet, after 2005 VX3.
(457175) 2008 GO98, provisional designation 2008 GO98 with cometary number 362P, is a Hildian asteroid and rare main-belt comet from the outermost regions of the asteroid belt, approximately 15 kilometers (9 miles) in diameter. It was discovered on 8 April 2008, by astronomers of the Spacewatch program at Kitt Peak National Observatory near Tucson, Arizona, in the United States. The presumably carbonaceous body has a rotation period of 10.7 hours.
(342842) 2008 YB3, provisional designation: 2008 YB3, is a sizable centaur and retrograde damocloid from the outer Solar System, approximately 67 kilometers (42 miles) in diameter. It was discovered on 18 December 2008, by astronomers with the Siding Spring Survey at the Siding Spring Observatory in Australia. The minor planet was numbered in 2012 and has since not been named.
2011 MM4, provisional designation: 2011 MM4, is a sizable centaur and retrograde damocloid from the outer Solar System, approximately 64 kilometers (40 miles) in diameter. It was discovered on 24 June 2011, by astronomers with the Pan-STARRS 1 at the Haleakala Obs. in Hawaii.