Bondi k-calculus: Difference between revisions
en>Helpful Pixie Bot m ISBNs (Build KE) |
No edit summary |
||
Line 1: | Line 1: | ||
= | '''Tisserand's parameter''' (or '''Tisserand's invariant''') is a combination of [[orbital elements]]{{Vague|date=August 2011}} used in a restricted [[N-body_problem#Three-body problem|three-body problem]], named after French astronomer [[Félix Tisserand]]. | ||
==Definition== | |||
For a small body with [[semimajor axis]] <math>a\,\!</math>, [[eccentricity (orbit)|eccentricity]] <math>e\,\!</math>, and [[inclination]] <math>i\,\!</math>, relative to the orbit of a perturbing larger body with semimajor axis <math>a_P</math>, the parameter is defined as follows:<ref>{{cite book |last1=Murray |first1= C. D.| last2=Dermot | first2=S. F. |year= 2000|title=Solar System Dynamics|publisher=Cambridge University Press |isbn=0-521-57597-4}}</ref> | |||
:<math>T_P\ = \frac{a_P}{a} + 2\cdot\sqrt{\frac{a}{a_P} (1-e^2)} \cos i</math> | |||
The quasi-conservation of Tisserand's parameter is a consequence of [[Tisserand's relation]]. | |||
== Applications == | |||
* T<sub>J</sub>, Tisserand’s parameter with respect to [[Jupiter]] as perturbing body, is frequently used to distinguish [[asteroid]]s (typically <math>T_J > 3</math>) from [[List of periodic comets|Jupiter-family comet]]s (typically <math>2< T_J < 3</math>). | |||
* The roughly constant value of the parameter before and after the interaction (encounter) is used to determine whether or not an observed orbiting body is the same as a previously observed in [[Tisserand's Criterion]]. | |||
*The quasi-conservation of Tisserand's parameter constrains the orbits attainable using [[gravity assist]] for outer Solar system exploration. | |||
* T<sub>N</sub>, Tisserand's parameter with respect to [[Neptune]], has been suggested to distinguish Near [[scattered disc|Scattered Objects]] (believed to be affected by Neptune) from Extended Scattered [[trans-Neptunian objects]] (e.g. [[90377 Sedna]]). | |||
* Tisserand's parameter could be used to infer the presence of an [[intermediate-mass black hole]] at the center of the [[Milky Way]] galaxy using the motions of orbiting stars.<ref name=DEGN>{{cite book|last=Merritt|first=David|title=Dynamics and Evolution of Galactic Nuclei|year=2013|publisher=Princeton University Press|location=Princeton, NJ|isbn=9781400846122|url=http://openlibrary.org/works/OL16802359W/Dynamics_and_Evolution_of_Galactic_Nuclei}}</ref> | |||
==Related notions== | |||
The parameter is derived from one of the so-called [[Charles-Eugène Delaunay|Delaunay]] standard variables, used to study the perturbed [[Energy#The Hamiltonian|Hamiltonian]] in a 3-body system. Ignoring higher-order perturbation terms, the following value is conserved: | |||
:<math> \sqrt{a (1-e^2)} \cos i</math> | |||
Consequently, perturbations may lead to the [[resonance]] between the orbital inclination and eccentricity, known as [[Kozai mechanism|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 comet]]s, because a large eccentricity with a constant semimajor axis results in a small perihelion. | |||
==See also == | |||
*[[Tisserand's relation]] for the derivation and the detailed assumptions | |||
== External links == | |||
* [[David Jewitt]]'s page on [http://www2.ess.ucla.edu/~jewitt/tisserand.html Tisserand's parameter] | |||
==References== | |||
{{reflist|colwidth=30em}} | |||
[[Category:Orbits]] |
Latest revision as of 09:10, 10 June 2013
Tisserand's parameter (or Tisserand's invariant) is a combination of orbital elementsTemplate:Vague used in a restricted three-body problem, named after French astronomer Félix Tisserand.
Definition
For a small body with semimajor axis , eccentricity , and inclination , relative to the orbit of a perturbing larger body with semimajor axis , the parameter is defined as follows:[1]
The quasi-conservation of Tisserand's parameter is a consequence of Tisserand's relation.
Applications
- TJ, Tisserand’s parameter with respect to Jupiter as perturbing body, is frequently used to distinguish asteroids (typically ) from Jupiter-family comets (typically ).
- The roughly constant value of the parameter before and after the interaction (encounter) is used to determine whether or not an observed orbiting body is the same as a previously observed in Tisserand's Criterion.
- The quasi-conservation of Tisserand's parameter constrains the orbits attainable using gravity assist for outer Solar system exploration.
- TN, Tisserand's parameter with respect to Neptune, has been suggested to distinguish Near Scattered Objects (believed to be affected by Neptune) from Extended Scattered trans-Neptunian objects (e.g. 90377 Sedna).
- Tisserand's parameter could be used to infer the presence of an intermediate-mass black hole at the center of the Milky Way galaxy using the motions of orbiting stars.[2]
Related notions
The parameter is derived from one of the so-called Delaunay standard variables, used to study the perturbed Hamiltonian in a 3-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.
See also
- Tisserand's relation for the derivation and the detailed assumptions
External links
- David Jewitt's page on Tisserand's parameter
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534