Perturbation (astronomy)

Vector diagram of the Sun's perturbations on the Moon. When the gravitational force of the Sun common to both the Earth and the Moon is subtracted, what is left is the perturbations.
The perturbing forces of the Sun on the Moon at two places in its orbit. The blue arrows represent the direction and magnitude of the gravitational force on the Earth. Applying this to both the Earth's and the Moon's position does not disturb the positions relative to each other. When it is subtracted from the force on the Moon (black arrows), what is left is the perturbing force (red arrows) on the Moon relative to the Earth. Because the perturbing force is different in direction and magnitude on opposite sides of the orbit, it produces a change in the shape of the orbit.

In astronomy, perturbation is the complex motion of a massive body subject 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]

Introduction

The study of perturbations began with the first attempts to predict planetary motions in the sky. In ancient times the causes were a mystery. Newton, at the time he formulated his laws of motion and of gravitation, applied them to the first analysis of perturbations,[2] recognizing the complex difficulties of their calculation.[3] Many of the great mathematicians since then have given attention to the various problems involved; throughout the 18th and 19th centuries there was demand for accurate tables of the position of the Moon and planets for marine navigation.

The complex motions of gravitational perturbations can be broken down. The hypothetical motion that the body follows under the gravitational effect of one other body only is typically a conic section, and can be readily described with the methods of geometry. This is called a two-body problem, or an unperturbed Keplerian orbit. The differences between that and the actual motion of the body are perturbations due to the additional gravitational effects of the remaining body or bodies. If there is only one other significant body then the perturbed motion is a three-body problem; if there are multiple other bodies it is an n-body problem. A general analytical solution (a mathematical expression to predict the positions and motions at any future time) exists for the two-body problem; when more than two bodies are considered analytic solutions exist only for special cases. Even the two-body problem becomes insoluble if one of the bodies is irregular in shape.[4]

Plot of Mercury's position in its orbit, with and without perturbations from various planets. The perturbations cause Mercury to move in looping paths around its unperturbed position.
Mercury's orbital longitude and latitude, as perturbed by Venus, Jupiter and all of the planets of the Solar System, at intervals of 2.5 days. Mercury would remain centered on the crosshairs if there were no perturbations.

Most systems that involve multiple gravitational attractions present one primary body which is dominant in its effects (for example, a star, in the case of the star and its planet, or a planet, in the case of the planet and its satellite). The gravitational effects of the other bodies can be treated as perturbations of the hypothetical unperturbed motion of the planet or satellite around its primary body.

Other Languages
Deutsch: Bahnstörung
eesti: Häiritus
Ελληνικά: Πάρελξη
hrvatski: Perturbacija
Bahasa Indonesia: Perturbasi (astronomi)
latviešu: Perturbācija
lietuvių: Trikdymas
polski: Perturbacja
português: Perturbação
русский: Пертурбация
srpskohrvatski / српскохрватски: Perturbacija
українська: Пертурбація
中文: 攝動