Elongation (astronomy)

The elongation referred to in the astronomy of an observer watched angular separation of two celestial objects. In general, the observer standing on the ground, and the elongation describes the observed (apparent) distance from the sun of a planetary.

The elongation is measured east or west of the sun each from 0 ° to 180 °. Western elongation means that the object is going on in the sun and can be seen in the morning sky; in eastern elongation happens after the sun and can be observed in the evening sky.

The Problem of Definition

There are two different definitions of elongation in use:

• The center of the earth seen from ( " geocentric " ) spherical angular distance between a planet and the sun, measured along the plane in which the planet, the earth and the sun are. so R ... geocentric position vector from the Earth to the Sun g ... geocentric position vector of the Earth to the planet This angle is compared with the phase angle in the triangle Earth Planet - sun, and we have:
• The difference between the geocentric ecliptic lengths of the planet and the sun. λ ... geocentric ecliptic longitude with

For ecliptic objects and large angular distances is the difference between the two definitions, except for the sign is small. However, the planet is seemingly close to the Sun, the angle values ​​may differ according to both definitions.

The elongation is one of the classic angle of observational astronomy and has been used for Leonhard Euler. The name is a Latin scientific education to ex - and Latin longus, long ', also Engl. means the elongation, elongation, length change ' ( rheol., tech., med ), but is in astronomy in mind, deflection ' is used ( an orbiting celestial body about its center ). So you are at the greatest elongation, ie the maximum angular distance that a planet can have if you look at it from outside its orbit.

The elongation is particularly suitable for the perturbation theory because they simply parameterizes the influence of the other bodies in the system, and is found as such the end of the 19th century in the planetary theory of Hill and Newcomb as the Moon Theory by Brown ( ILE ). However, these theories neglected the existing, albeit small ecliptic latitudes of the sun and the planets, so spherical and ecliptic angular distance fell into each other. As a path element in the lunar theory by Brown - Eckert ( j = 2) we pass to the Delaunay parameters for the mean elongation, which is measured as a broken angle ekliptikal from the sun to the moon nodes, and from there into the lunar orbit plane to the moon.

A careless use of the term elongation in the literature has then led to this unsatisfactory situation definition. The first - ecliptic - definition is used for example by the Astronomical Almanac, the second - spherical - among others, the Annuaire du Bureau des Longitudes, the third - a broken angle - in the lunar theory, but what played hardly any role to the development of modern computer Astronomy: Relevant computational accuracy, and visual precision to control these were achieved only in the 80s.

Problems makes the deviation in actual calculations of the exact time points of conjunction and opposition, whose classical definition is. Taking a planet for a terrestrial observer apparently behind the sun over ( conjunction), or in front of her (passage), he pulls due to the inclination of its orbit to the ecliptic passing above or below the Sun's middle. The elongation according to the second definition takes always at a certain time the value zero, as must the geocentric lengths of planet and sun in the process necessarily coincide once - when solar and planetary center lie in a plane normal to the ecliptic. The elongation according to the first definition, however, only decreases to a certain minimum value, and then increase again - namely the angular distance at the moment of closest approach. Only then would take the value zero if the planets center would run exactly through the center of the solar disc - what exactly does not occur in nature. The same applies to the opposition of a planet: The elongation according to the second definition always takes a moment for the value of 180 ° on when they change from west to east. Elongation according to the first definition does not reach this value in the rule.

Therefore, there are still differing data in the literature for the two aspects. Usually the conjunct ( geocentric - ekliptikal ), or even (ie geocentric - equatorial) specified functions, which indeed are exact zero, but do not describe the exact moment of maximum area, but elsewhere with ( geocentric or topocentric - spherical) or in relation to the lunar theory ( broken ekliptikal / rail system ), which typically have no zeros. Caused confusion, the particular case passes of the moon near the node, ie in the criteria of a solar eclipse.

We noticed the error only failed since zeros Search due to today's high calculation accuracy, or otherwise expressions over the angular distance in computer programs is produced crashes because an exact zero appeared where none had should. Therefore, the reference plane is in more recent publications specifically mentioned, or the term elongation is avoided, the new moon theory about ELP2000 speaks explicitly of argument instead, elongation ' - with, argument ' as an expression of celestial mechanics for non-specific, closer to explanatory parameters. In older literature, is often not easy to find out which definition is based.

Greatest elongation

While the planet (or other celestial bodies ) outside the Earth's orbit are (upper planets), can stand in opposition and thus an elongation reach up to 180 °, which does not apply to planets and other celestial bodies, whose orbit is inside the Earth's orbit (lower planets). Objects within the Earth's orbit can stay only 90 ° within a range of ± naturally. Venus has a greatest elongation of only 47 °, 28 ° and Mercury. The exact value will fluctuate, in astronomical yearbooks times and degrees of the greatest western or eastern elongation are usually given.

Example: Mercury reached on 11 August 1990 greatest angular distance from the sun (ie, 27 ° 25 ') by 21 clock UT, the greatest distance in geocentric longitude (27 ° 22'), but already by 15 clock UT.

Observation practice

The elongation is crucial for the visibility of an object. However, it is not always a great elongation synonymous with good visibility. So Mercury is in summer and autumn in our part not observable at its maximum eastern elongation in the evening sky, and in the spring and winter at its greatest western elongation in the morning sky, even though these be larger than the largest eastern elongations in winter or spring and the largest Western elongations in summer or autumn, because in our latitudes the ecliptic during the summer and autumn in the evening and in winter and spring flat on the morning of the horizon and Mercury already goes down during bright twilight, or rises only during bright twilight.

The Venus does not reach its best visibility to the greatest elongation: In her contribution by the fraction of the illuminated disc ( light level ) due to the proximity to the ground is already relevant. The greatest elongation but only about 53% of the disk are illuminated, and it reaches its maximum brightness about five weeks before / after maximum elongation.