Proper orbital elements


Proper orbital elements

The proper orbital 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:
*"proper semimajor axis" ("ap"),
*"proper eccentricity" ("ep"), and
*"proper inclination" ("ip").

The proper elements are to be contrasted with the osculating Keplerian orbital elements observed at a particular time or epoch, such as the semi-major axis, eccentricity, and inclination. Those osculating elements change in a quasi-periodic and (in principle) predictable manner due to such effects as perturbations from planets or other bodies, and precession (e.g. perihelion precession). In the solar system, such changes usually occur on timescales of thousands of years, while proper elements are meant to be practically constant over at least tens of millions of years.

For most bodies, the osculating elements are relatively close to the proper elements because precession and perturbation effects are relatively small (See diagram). For over 99% of asteroids in the main belt, the differences are less than 0.02 AU (for semi-major axis "a"), 0.1 (for eccentricity "e"), and 2° (for inclination "i").

Nevertheless, this difference is non-negligible for any purposes where precision is of importance. As an example, the asteroid 1 Ceres has osculating orbital elements (at epoch November 26, 2005)while its proper orbital elements (independent of epoch) areA notable exception to this small-difference rule are asteroids lying in the Kirkwood gaps, which are in strong orbital resonance with Jupiter.

To obtain proper elements for an object, one usually conducts a detailed simulation of its motion over timespans of several millions of years. Such a simulation must take into account many details of celestial mechanics including perturbations by the planets. Subsequently, one extracts quantities from the simulation which remain unchanged over this long timespan, and makes them the proper orbital elements. For example, the mean inclination, eccentricity, and semi-major axis.

Historically, various approximate analytic calculations were made, starting with those of Kiyotsugu Hirayama in the early 20th century. Later analytic methods often included thousands of perturbing corrections for each particular object. Presently, the method of choice is to use a computer to numerically integrate the equations of celestial dynamics, and extract constants of motion directly from a numerical analysis of the predicted positions.

At present the most prominent use of proper orbital elements is in the study of asteroid families, following in the footsteps of the pioneering work of Hirayama.

References

*Z. Knežević et al, "The Determination of Asteroid Proper Elements", p. 603-612 in Asteroids III, University of Arizona Press (2002).

External links

* [http://hamilton.dm.unipi.it/cgi-bin/astdys/astibo?proper_elements:0;main Latest calculations of proper elements for numbered minor planets at astDys] .


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Orbital elements — are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two body systems, where a Kepler orbit is used (derived from Newton s laws of motion and Newton s law… …   Wikipedia

  • Ceres (dwarf planet) — For other uses of the name Ceres , see Ceres. Ceres   Ceres as seen by Hubble Space Telescope (ACS). The …   Wikipedia

  • Asteroid family — An asteroid family is a population of asteroids that share similar orbital elements, such as semimajor axis, eccentricity, and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions. General… …   Wikipedia

  • 9 Metis — For the moon of Jupiter, see Metis (moon). 9 Metis   Discovery Discovered by A. Graham Discovery date 25 April 1848 …   Wikipedia

  • 10 Hygiea — 10 Hygiea   …   Wikipedia

  • Massalia family — The Massalia family of asteroids is a grouping of S type asteroids in the inner main belt at very low inclination. About 0.8% of known asteroids belong to this family. Contents 1 Characteristics 2 Location and size 3 Interlopers …   Wikipedia

  • Osculating orbit — In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space (at a given moment of time) is the gravitational Kepler orbit (i.e. ellipse or other conic) that it would have about its central body (corresponding to… …   Wikipedia

  • Hirayama families — A Hirayama family of asteroids is a group of minor planets that share similar orbital elements, such as semimajor axis, eccentricity, and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions.… …   Wikipedia

  • Eunomia family — The Eunomia family of asteroids is a large grouping of S type asteroids named after the Greek goddess Eunomia. It is the most prominent family in the intermediate main belt. About 5% of all main belt asteroids belong to this… …   Wikipedia

  • Comet Hyakutake — C/1996 B2 (Hyakutake) Comet Hyakutake captured by the Hubble Space Telescope on April 4, 1996, with an infrared filter. Discovery and designation …   Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.