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To calculate 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
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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
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from the simulation which remain unchanged over this long timespan; for example, the mean inclination, mean eccentricity, and mean semi-major axis. These are the proper orbital elements.
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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
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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:
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Z. Knežević: COMPUTATION OF ASTEROID PROPER ELEMENTS: RECENT ADVANCES, Serbian
Astronomical Journal, vol. 195, pp. 1-8 (2017).
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and (in principle) predictable manner due to such effects as perturbations from planets or other bodies, and precession (e.g.
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Historically, various approximate analytic calculations were made, starting with those of
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Distribution of the difference between proper and osculating orbital elements for
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At present the most prominent use of proper orbital elements is in the study of
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Latest calculations of proper elements for numbered minor planets at astDys
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is the lowest numbered asteroid to not have any proper orbital elements.
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Asteroid proper orbital elements dataset at
Asteroid Families Portal
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while its proper orbital elements (independent of epoch) are
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Osculating (left) and proper (right) orbital elements for
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A notable exception to this small-difference rule are
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46:. Unsourced material may be challenged and removed.
453:"AstDyS-2 Ceres Synthetic Proper Orbital Elements"
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234:. Those osculating elements change in a
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146:. Note how
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439:References
416:132 Aethra
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523:Astronomy
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324:10.5868°
251:asteroids
140:asteroids
124:asteroids
581:Category
422:See also
374:9.6474°
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321:0.080015
509:Portals
253:in the
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