Perturbation (astronomy)

# Perturbation (astronomy)

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Encyclopedia
Perturbation is a term used in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

in connection with descriptions of the complex motion of a massive body which is subject to appreciable gravitational effects from more than one other massive body.

Such complex motions of a body can be broken down descriptively into component parts. First, there can be the hypothetical motion that the body would follow, if it moved under the gravitational effect of one other body only. Expressed in other terms, such a motion could be regarded as a solution of a two-body problem
Two-body problem
In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. Common examples include a satellite orbiting a planet, a planet orbiting a star, two stars orbiting each other , and a classical electron orbiting an atomic nucleus In...

, or as an unperturbed Keplerian orbit
Kepler orbit
In celestial mechanics, a Kepler orbit describes the motion of an orbiting body as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space...

. Then, the differences between that hypothetical unperturbed motion and the actual motion of the body can be described as perturbations, due to the additional gravitational effects of the additional body or bodies. If there is only one other significant body, then the perturbed motion can be called a solution of a three-body problem
Three-body problem
Three-body problem has two distinguishable meanings in physics and classical mechanics:# In its traditional sense the three-body problem is the problem of taking an initial set of data that specifies the positions, masses and velocities of three bodies for some particular point in time and then...

: if there are multiple other significant bodies, the motion can represent a higher case of the n-body problem
N-body problem
The n-body problem is the problem of predicting the motion of a group of celestial objects that interact with each other gravitationally. Solving this problem has been motivated by the need to understand the motion of the Sun, planets and the visible stars...

.

Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

at the time of formulating his laws of motion
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...

and of gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

already recognized the existence of perturbations and the complex difficulties of their calculation. Since Newton's time, several techniques have been developed for the mathematical analysis of perturbations, and they can be divided into two major classes, general perturbations and special perturbations. In methods of analysing general perturbations, general differential equations of motion are solved, usually by series approximations, to give a result which is usually in terms of algebraic and trigonometrical functions, and can be applied generally to many different sets of conditions. Historically, general perturbations were investigated first. 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.

Most systems that involve multiple gravitational attractions present one primary body which can be regarded as dominant in its gravitational 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). Then, the other gravitational effects can be treated as causing perturbations of the hypothetical unperturbed motion of the planet, or the satellite, around its respective primary body.

In the Solar System, many of the perturbations are made up of periodical components, so that the perturbed bodies follow orbits that are periodic or quasi-periodic for long periods of time – such as the Moon in its strongly perturbed
Lunar theory
Lunar theory attempts to account for the motions of the Moon. There are many irregularities in the Moon's motion, and many attempts have been made over a long history to account for them. After centuries of being heavily problematic, the lunar motions are nowadays modelled to a very high degree...

orbit, which is the subject of lunar theory
Lunar theory
Lunar theory attempts to account for the motions of the Moon. There are many irregularities in the Moon's motion, and many attempts have been made over a long history to account for them. After centuries of being heavily problematic, the lunar motions are nowadays modelled to a very high degree...

.

Planets cause periodical perturbations in the orbits of other planets, a fact which led to the discovery of Neptune
Discovery of Neptune
Neptune was mathematically predicted before it was directly observed. With a prediction by Urbain Le Verrier, telescopic observations confirming the existence of a major planet were made on the night of September 23, 1846, and into the early morning of the 24th, at the Berlin Observatory, by...

in 1846 as a result of its perturbations of the orbit of Uranus
Uranus
Uranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus...

.

On-going mutual perturbations of the planets cause long-term quasi-periodic variations in their orbital elements. Venus
Venus
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...

currently has the orbit with the least eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...

, i.e. it is the closest to circular
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....

, of all the planetary orbits. In 25,000 years' time, Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

will have a more circular (less eccentric) orbit than Venus.
The orbits of many of the minor bodies of the Solar System, such as comet
Comet
A comet is an icy small Solar System body that, when close enough to the Sun, displays a visible coma and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet...

s, are often heavily perturbed, particularly by the gravitational fields of the gas giant
Gas giant
A gas giant is a large planet that is not primarily composed of rock or other solid matter. There are four gas giants in the Solar System: Jupiter, Saturn, Uranus, and Neptune...

s. While many of these perturbations are periodic, others are not, and these in particular may represent aspects of chaotic motion. For example, in April 1996, Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

's gravitational influence caused the period
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...

of Comet Hale-Bopp
Comet Hale-Bopp
Comet Hale–Bopp was perhaps the most widely observed comet of the 20th century, and one of the brightest seen for many decades...

's orbit to decrease from 4,206 to 2,380 years, a change that will not revert on any periodical basis.

In astrodynamics
Astrodynamics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation. It...

and the case of man-made satellite
Satellite
In the context of spaceflight, a satellite is an object which has been placed into orbit by human endeavour. Such objects are sometimes called artificial satellites to distinguish them from natural satellites such as the Moon....

s, orbital perturbation may be a consequence of atmospheric drag or solar radiation pressure.

• Nereid
Nereid (moon)
Nereid , also known as Neptune II, is the third-largest moon of Neptune. It has a highly eccentric orbit. Nereid was discovered by Gerard Kuiper in 1949 and was the second moon of Neptune to be discovered.- Discovery and naming :...

one of the outer moons of Neptune with a high orbital eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...

of ~0.75 and is frequently perturbed
• Osculating orbit
Osculating orbit
In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space is the gravitational Kepler 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 In astronomy,...