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Perturbation (astronomy)

In astronomy, perturbation is the complex motion of a massive body subjected to forces other than the gravitational attraction of a single other massive body.[1] The other forces can include a third (fourth, fifth, etc.) body, resistance, as from an atmosphere, and the off-center attraction of an oblate or otherwise misshapen body.[2]

Mathematical analysis[edit]

General perturbations[edit]

In methods of general perturbations, general differential equations, either of motion or of change in the orbital elements, are solved analytically, usually by series expansions. The result is usually expressed in terms of algebraic and trigonometric functions of the orbital elements of the body in question and the perturbing bodies. This can be applied generally to many different sets of conditions, and is not specific to any particular set of gravitating objects.[5] Historically, general perturbations were investigated first. The classical methods are known as variation of the elements, variation of parameters or variation of the constants of integration. In these methods, it is considered that the body is always moving in a conic section, however the conic section is constantly changing due to the perturbations. If all perturbations were to cease at any particular instant, the body would continue in this (now unchanging) conic section indefinitely; this conic is known as the osculating orbit and its orbital elements at any particular time are what are sought by the methods of general perturbations.[2]


General perturbations takes advantage of the fact that in many problems of celestial mechanics, the two-body orbit changes rather slowly due to the perturbations; the two-body orbit is a good first approximation. General perturbations is applicable only if the perturbing forces are about one order of magnitude smaller, or less, than the gravitational force of the primary body.[4] In the Solar System, this is usually the case; Jupiter, the second largest body, has a mass of about 11000 that of the Sun.


General perturbation methods are preferred for some types of problems, as the source of certain observed motions are readily found. This is not necessarily so for special perturbations; the motions would be predicted with similar accuracy, but no information on the configurations of the perturbing bodies (for instance, an orbital resonance) which caused them would be available.[4]

Special perturbations[edit]

In methods of special perturbations, numerical datasets, representing values for the positions, velocities and accelerative forces on the bodies of interest, are made the basis of numerical integration of the differential equations of motion.[6] In effect, the positions and velocities are perturbed directly, and no attempt is made to calculate the curves of the orbits or the orbital elements.[2]


Special perturbations can be applied to any problem in celestial mechanics, as it is not limited to cases where the perturbing forces are small.[4] Once applied only to comets and minor planets, special perturbation methods are now the basis of the most accurate machine-generated planetary ephemerides of the great astronomical almanacs.[2][7] Special perturbations are also used for modeling an orbit with computers.

Formation and evolution of the Solar System

Frozen orbit

Molniya orbit

one of the outer moons of Neptune with a high orbital eccentricity of ~0.75 and is frequently perturbed

Nereid

Osculating orbit

Orbit modeling

Orbital resonance

Proper orbital elements

Stability of the Solar System

Bate, Roger R.; Mueller, Donald D.; White, Jerry E. (1971). . New York: Dover Publications. ISBN 0-486-60061-0.

Fundamentals of Astrodynamics

Moulton, Forest Ray (1914). (2nd revised ed.). Macmillan.

An Introduction to Celestial Mechanics

Roy, A. E. (1988). Orbital Motion (3rd ed.). Institute of Physics Publishing.  0-85274-229-0.

ISBN

P.E. El'Yasberg:

Introduction to the Theory of Flight of Artificial Earth Satellites

(by Aldo Vitagliano) predictions for the position/orbit/close approaches of Mars

Solex

Sir George Biddell Airy's 1884 book on gravitational motion and perturbations, using little or no math.(at Google books)

Gravitation