Definition
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: [2] [3]
Tisserand's parameter (or Tisserand's invariant) is a number 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 who derived it [1] 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: [2] [3]
In the three-body problem, the quasi-conservation of Tisserand's invariant is derived as the limit of the Jacobi integral away from the main two bodies (usually the star and planet). [2] Numerical simulations show that the Tisserand invariant of orbit-crossing bodies is conserved in the three-body problem on Gigayear timescales. [4] [5]
The Tisserand parameter's conservation was originally used by Tisserand to determine whether or not an observed orbiting body is the same as one previously observed. This is usually known as the Tisserand's criterion.
The value of the Tisserand parameter with respect to the planet that most perturbs a small body in the solar system can be used to delineate groups of objects that may have similar origins.
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.
In astronomy, the plutinos are a dynamical group of trans-Neptunian objects that orbit in 2:3 mean-motion resonance with Neptune. This means that for every two orbits a plutino makes, Neptune orbits three times. The dwarf planet Pluto is the largest member as well as the namesake of this group. The next largest members are Orcus, (208996) 2003 AZ84, and Ixion. Plutinos are named after mythological creatures associated with the underworld.
In planetary astronomy, a centaur is a small Solar System body that orbits the Sun between Jupiter and Neptune and crosses the orbits of one or more of the giant planets. Centaurs generally have unstable orbits because of this; 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.
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:
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 is a dynamical phenomenon affecting the orbit of a binary system perturbed by a distant third body under certain conditions. The mechanism is also named von Zeipel-Kozai-Lidov, Lidov–Kozai, Kozai–Lidov, or some combination of Kozai, Lidov, and/or von Zeipel. It also termed an effect, oscillations, cycles, or resonance. This effect causes 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.
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 highly elliptical 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; Triton, for example, is a round moon but is considered irregular due to its orbit and origins.
(434620) 2005 VD, provisional designation 2005 VD, is a centaur and damocloid on a retrograde orbit from the outer Solar System, known for having the second most highly inclined orbit of any small Solar System body, behind 2013 LA2. It was the most highly inclined known object between 2005 and 2013. The unusual object measures approximately 6 kilometers in diameter.
(612093) 1999 LE31, prov. designation: 1999 LE31, is a centaur and damocloid on a retrograde and eccentric orbit from the outer region of the Solar System. It was first observed on 12 June 1999, by astronomers with the LINEAR program at the Lincoln Lab's ETS near Socorro, New Mexico, in the United States. The unusual object measures approximately 17 kilometers (11 miles) in diameter.
2002 RN109 is a trans-Neptunian astronomical object and damocloid on a highly eccentric, cometary-like orbit. It was first observed on 6 September 2002, by astronomers of the Lincoln Near-Earth Asteroid Research project at its ETS near Socorro, New Mexico, United States. The unusual object is approximately 4 kilometers (2 miles) in diameter. It has the second-highest orbital eccentricity of any known minor planet, after 2005 VX3.
2000 DG8 is a dark centaur and damocloid on a retrograde and highly eccentric orbit from the outer region of the Solar System. It was first observed on 25 February 2000, by astronomers with the LINEAR program at the Lincoln Lab's ETS near Socorro, New Mexico, United States. It has not been observed since 2001. The unusual object measures approximately 16 kilometers (9.9 miles) in diameter.
(127546) 2002 XU93, provisional designation 2002 XU93, is a trans-Neptunian object and centaur on highly inclined and eccentric orbit in the outer region of the Solar System. It measures approximately 170 kilometers (110 mi) in diameter and is one of few objects with such an unusual orbit. It was discovered on 4 December 2002, by American astronomer Marc Buie at the Kitt Peak National Observatory in Arizona, United States.
2017 MB7 is a trans-Neptunian object and damocloid on a cometary-like orbit from the outer Solar System, approximately 6 kilometers (4 miles) in diameter. It was first observed on 22 June 2017 by the Pan-STARRS survey at Haleakala Observatory in Hawaii, United States. This unusual object has the largest heliocentric aphelion, semi-major axis, orbital eccentricity and orbital period of any known periodic minor planet, even larger than that of 2014 FE72; it is calculated to reach several thousand AU (Earth-Sun) distances at the farthest extent of its orbit.
2014 FZ71 is a trans-Neptunian object, a scattered disc classified as a scattered and detached object, located in the outermost region of the Solar System. It was first observed on 24 March 2014, by a team led by American astronomer Scott Sheppard at the Cerro Tololo Inter-American Observatory in Chile. With its perihelion of almost 56 AU, it belongs to a small and poorly understood group of very distant objects with moderate eccentricities. The object is not a dwarf planet candidate as it only measures approximately 150 kilometers (93 miles) in diameter.
2015 FJ345 is a trans-Neptunian object and detached object, located in the scattered disc, the outermost region of the Solar System. It was first observed on 17 March 2015, by a team led by American astronomer Scott Sheppard at the Mauna Kea Observatories, in Hawaii, United States. With its perihelion of almost 51 AU, it belongs to a small and poorly understood group of very distant objects with moderate eccentricities. The object is not a dwarf planet candidate as it only measures approximately 120 kilometers (75 miles) in diameter.
2015 KQ174 is a trans-Neptunian object, both considered a scattered and detached object, located in the outermost region of the Solar System. The object with a moderately inclined and eccentric orbit measures approximately 154 kilometers (96 miles) in diameter. It was first observed on 24 May 2015, by astronomers at the Mauna Kea Observatories in Hawaii, United States.
(468861) 2013 LU28, provisional designation 2013 LU28 is a highly eccentric trans-Neptunian object, retrograde centaur and damocloid from the outer regions of the Solar System. It was discovered on 8 June 2013 by astronomers with the Mount Lemmon Survey at the Mount Lemmon Observatory in Arizona, United States. The object is unlikely a dwarf planet as it measures approximately 110 kilometers (68 miles) in diameter. It was numbered in 2016 and has not been named since.
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.
In planetary science, the term unusual minor planet, or unusual object, is used for a minor planet that possesses an unusual physical or orbital characteristic. For the Minor Planet Center (MPC), which operates under the auspices of the International Astronomical Union, any non-classical main-belt asteroid, which account for the vast majority of all minor planets, is an unusual minor planet. These include the near-Earth objects and Trojans as well as the distant minor planets such as centaurs and trans-Neptunian objects. In a narrower sense, the term is used for a group of bodies – including main-belt asteroids, Mars-crossers, centaurs and otherwise non-classifiable minor planets – that show a high orbital eccentricity, typically above 0.5 and/or a perihelion of less than 6 AU. Similarly, an unusual asteroid (UA) is an inner Solar System object with a high eccentricity and/or inclination but with a perihelion larger than 1.3 AU, which does exclude the near-Earth objects.
