# Ecliptic

Seen from Earth, the sun appears to move relative to the background stars over the course of the year. In fact, the earth moves around the sun. Both movements have the same direction. After a little over 365 days, a closed orbit has passed.

In the narrower sense, the ecliptic is the apparent , i.e. H. denotes the orbit of the sun seen from the earth against the background of the fixed stars . In general, the ecliptic is a plane (the ecliptic plane ) in which the sun and (more or less) all planets lie. On the celestial sphere , the ecliptic is a great circle .

The observation of the ecliptic took place in early antiquity. Not during the day, but at twilight the position of the sun can be seen on the background of the stars and constellations . The sun passes through a fixed sequence of 12 constellations (according to the earlier classification) or 13 constellations (according to the current classification) each year. An approximately 20 degree wide zone around the ecliptic is called the zodiac , in which the orbits of the moon and all planets run. The constellations of the zodiac are called the signs of the zodiac .

The northern and southern ecliptic poles are the two points of intersection of the celestial sphere with a straight line perpendicular to the ecliptic plane that goes through the center of the earth.

Ecliptic as a geocentric projection of the sun's positions onto the celestial sphere . The inclination of the ecliptic is the angle ε between the ecliptic plane and the equatorial plane.

A plane different from the ecliptic plane is the equatorial plane . It arises when the circle enclosed by the earth's equator (determined by the daily rotation of the earth around its own axis ) is expanded in all directions without limit. The circle in which this plane intersects the celestial sphere is the celestial equator . While the ecliptic (plane) is determined by the (annual) orbit of the earth around the sun, the equatorial plane is determined by the (daily) rotation of the earth around its own axis. The angle at which both planes are inclined to one another is called the inclination of the ecliptic .

## etymology

The name ecliptic ( lat. Linea Ecliptica , the Eclipse delivered listening Line ') is derived from the Greek expression ἐκλειπτική [τροχιά] ekleiptikē [Trochia] for, concealing [orbit]' (to ἔκλειψις ékleipsis , leaving, absence, (sun / moon -) Darkness'), see also eclipse as covering ( occultation ). With ékleipsis equal to absence, disappearance, eclipse it is expressed that earth, moon and sun are together on a straight line in the ecliptic plane when a solar or lunar eclipse occurs.

## introduction

The sun describes two different apparent paths in the sky:

• As a result of the earth's rotation around its own axis, the fixed star sky and the sun in front of it appear to rotate around the earth from east to west over the course of a day. This leads to the apparent daily movement of the sun relative to the horizon , the day arc .
• As a result of the earth's annual orbit around the sun, the position of the sun in relation to the fixed star sky gradually shifts. It passes through the twelve ecliptic constellations in one year .

The orbit of the annual apparent movement of the sun relative to the fixed star sky is the ecliptic. Your course can be z. B. by noting the positions of the sun on a celestial globe that have been determined over the course of a year . It is practically irrelevant from which location on earth the observations are made, since the sun is very far away in relation to the size of the earth and the observation angle therefore remains almost the same.

## The ecliptic plane

The orbits of the planets around the sun are roughly in the same plane. This abnormality is explained by the formation of the planetary system from a protoplanetary disk .

Heliocentric considers the orbits Earth , the sun on an in-ecliptic path .

On closer inspection, it is not the earth that runs on this orbit around the sun, but the common center of gravity of earth and moon (which is still in the interior of the earth, but not in its center). Therefore, from a geocentric point of view , the sun does not move exactly on the ecliptic across the sky, but its ecliptical latitude fluctuates in the monthly rhythm by about ± 0.7 "around the mean value 0.

The ecliptic plane serves as a reference plane for location information in the solar system ( ecliptic coordinate system ).

## The obliqueness of the ecliptic

The earth's axis , the earth's axis of rotation , is not perpendicular to the plane of the earth's orbit , but forms an angle with it of currently 66.56339 °. Thereby, the plane includes the equator of the earth or of the celestial equator with the ecliptic plane is currently an angle of 23.43661 ° (23 ° 26 '11.8 ") a, the inclination of the ecliptic or obliquity is called (lat. Obliquus , wrong') .

The term earth inclination reflects this angle as viewed from the ecliptic plane on the earth, the perspective of the ecliptical coordinate system .

The skewness of the ecliptic is one of the ten most important basic quantities in astronomy and geodesy for the definition of coordinate systems and for calculations. It is usually referred to by the Greek letter ε (epsilon) . Due to the gravitational influences of the other bodies in the solar system, it changes over long periods: within around 40,000 years it varies between 21 ° 55 'and 24 ° 18', i.e. by over 2 °.

### The seasons

While the earth orbits the sun , the direction of its axis in space remains almost unchanged, if one disregards the long-period effects described above. As a result, the northern hemisphere is slightly more inclined towards the sun from March to September and the southern hemisphere from September to March . In the course of the year, the angle of incidence of the sun's rays and the duration of the bright day change , which creates the seasons .

## The zodiac

A representation of constellations of the northern sky and the twelve 30 ° sections of the zodiac in old star maps , such as here the Uranographia by Johannes Hevelius  (1690), takes the “stable” ecliptic poles as the center.

While the earth's orbit lies in the ecliptic plane and the sun seems to travel along an orbit along the ecliptic every year from the orbiting earth, the orbital planes of the moon and the other planets are inclined at different degrees in relation to the ecliptic plane . Their apparent orbits therefore run within a few degrees wide strip around the ecliptic, the zodiac or zodiac. Since ancient times this has been divided from the spring equinox to the east into twelve equal sections (each 360 ° / 12 = 30 °), the signs of the zodiac . These have their names from the ecliptic constellations, but their location does not match them. In astrology the positions of the sun, moon and planets are described in relation to the signs of the zodiac.

## The precession

Constellation Little Bear with Polaris , depicted in the tip of its tail near the circle on which the northern celestial pole in a Platonic year orbits the northern ecliptic pole ( Uranographia von Hevelius , 1690)

The two ecliptic poles form the centers of two circles on which the north and south celestial poles move in the course of a Platonic year of around 26,000 years due to the precession of the earth's axis .

Since the shape of the earth differs from a sphere ( earth ellipsoid ), the tidal forces of the moon and sun cause a torque that tries to straighten the oblique earth axis and thereby changes its direction. As with an inclined top , the earth's axis, the extension of which shows the two celestial poles, therefore describes a precession movement and wanders around the ecliptic poles on a cone shell with an opening angle of 2ε. These ecliptic poles are drawn on more precise star maps - the northern one is in the constellation Dragon , by definition at right ascension  18 h (with a declination of 90 ° −ε, currently around 66 ° 34 ′), the southern one in the constellation Swordfish at 6 h .

Because of the great mass of the earth of almost 6 · 10 24  kg, the “earth top ” is very sluggish, the earth axis needs about 25,700-25,800 years for a cycle of precession ( Platonic year ). Today's Pole Star only takes on its role temporarily.

 The path (orange) of the celestial north pole around the ecliptic pole (red), for which it takes about 26,000 years; around the year (+) 2000 it is near the Pole Star . The very bright star below is Vega . The path of the South Celestial Pole around the Ecliptic Pole, which takes about 26,000 years. Around the year (+) 2000 it is close to Polaris Australis . The extremely bright star in the picture is Canopus .

## history

For the early astronomers , the orbit of the moon , which can be observed directly in the night sky, and the rising and setting of the stars with the greatest luminosity were obvious; the connection between the ecliptic and the apparent orbit of the sun was not yet recognized. However, inspired by solar and lunar eclipses , which are dependent on the position of the moon in relation to the ecliptic orbit, corresponding myths have been developed. Early Chinese astronomy speaks of a heavenly dragon devouring the moon and sun. Early Indian astronomy knows the demon Rahu , who devours both stars. Such and similar myths led to the name dragon points for the lunar nodes .

The ancient Egyptian conceptions of the sky, however, related with a mythological background, among other things, to dean stars and were based on their heliacal sighting. The concept of the zodiac, developed in Mesopotamia , was not adopted until the Hellenistic period . There the observation of the stars had already started in the Old Babylonian Empire . But it was not until the Assyrian period (1200–630 BC) that ideas were developed that are close to the ecliptic. The data collection of the MUL-apin texts contains the idea of ​​the four seasons, in which the sun runs through different constellations and thus moves in a crooked circle. In the Persian period (539–326 BC) the division of the ecliptic into the 12 signs of the zodiac was created. This development is documented by hundreds of Babylonian cuneiform tablets , on which astronomical series of measurements are recorded in Babylonian numerals with details of ecliptic-related positions.

With the geocentric worldview of the philosophy of antiquity , the movements observed in the sky were understood in such a way that the sun, which sets in the west , moves around the earth on a rotating sphere when it returns to the east at night . This shell with the sun, similar to a spherical surface , also shifts against that of the fixed stars, so that the sun faces the stars that appear 12 hours later. With this idea, the shift of the starry sky, already known from star observation, could be brought into harmony with the observation that the sun seems to orbit the earth within one year with respect to the stars , on the orbit called the ecliptic - according to today's understanding as geocentrically related apparent Move. Based on this worldview, several Greek philosophers dealt with the ecliptic and the signs of the zodiac on it. Anaximander (6th century BC), Pythagoras (6th century BC), Oinopides (5th century BC) and Eudoxus of Knidos (4th century BC ) are particularly known through surviving writings or mentions by later authors . Century BC). Then in the middle of the 2nd century the scholar Claudius Ptolemy wrote a comprehensive account of astronomical knowledge. In this work, the Almagest , he defines the ecliptic as a great circle on the sphere and creates a number of - also trigonometric - calculations, e.g. B. a table of skewness (the ecliptic).

In Europe, a division of the ecliptic into twelve equal sectors was introduced during antiquity. In India, on the other hand, the lunar orbit was traditionally divided into 27 nakshatras (stations of the moon) according to star groups along the ecliptic . This number corresponds to the rounded number of days in a sidereal month (27.32 d), with which the moon usually rises every day in a different house. The system already handed down in Yajurveda (around 1000 BC) is widespread in Asia; It is controversial whether it was preceded by a system developed by Chinese astronomers.

Already in pre-Islamic times, the division into Nakshatras was also known in the Arab world, and was transformed into the system called Manazil al-Qamar (moon houses), which divides the ecliptic into 28 moon houses according to star groups. After the formation of powerful caliphates , however, educational centers and libraries were set up where the Greek astronomical texts were translated into Arabic . In particular, Claudius Ptolemy's Almagest was translated at the end of the 8th century and gained great influence. The works were not only received, but also developed further. For example, the values ​​transmitted by Ptolemy for the skewness of the ecliptic were improved by Arab astronomers ( Al-Battani , 9th century).

The early Middle Ages offer a number of astronomical texts. Most of them are excerpts from late antique collections (mainly Macrobius Ambrosius Theodosius and Martianus Capella ). Only later authors such as Georg von Peuerbach and Regiomontanus (both mid-15th century) deal with the ecliptic. Finally, Copernicus specifies in his work Commentariolus (chapter De motibus, qui circa Solem apparent ): The axis is inclined by about 23 1/2 degrees. The center of the earth remains on the level of the ecliptic (translation by Hans Günter Zekl , abbreviated). Since about the turn of an era know astronomers that the Earth's axis to precess , but the well-known today worth 25,700 to 25,800 years ago was found in the 13th century. It was only in the Middle Ages that one suspected that, in addition to its direction , the inclination of the ecliptic would change . At that time it was assumed that its angle would assume all values ​​from 0 ° to 90 ° over the course of the millennia. It was not until the 16th century that it became clear that the fluctuation range is much smaller; Copernicus assumed changes in the ecliptic inclination between max. 23 ° 52 ′ and min. 23 ° 28 ′ off, only around 24 ′.

## Fluctuation of the earth's axis and the ecliptic skew

Skewness of the ecliptic for the years −8000 to +12000
Skewness of the ecliptic for the years 1800 to 2200

The angle of the ecliptic inclination also changes over long periods due to the mutual gravitational influences of the bodies in the solar system . Therefore, ε varies between about 21 ° 55 'and 24 ° 18' within about 41,000 years. In addition to the fluctuations in the eccentricity of the earth's orbit (100,000 years) and precession (25,780 years), this effect contributes to the formation of the Ice Ages (as one of the factors of the long-term, regular, naturally occurring climatic fluctuations called Milanković cycles ):

As a first approximation for the mean ecliptic inclination is given:

ε 0 = 23 ° 26 ′ 21.45 ″ - 46.8 ″ T ,

where T denotes the numerical value of the time in Julian centuries since epoch J2000.0 (January 1, 2000 12.00  TT )
(in epoch J2000.0 the ecliptic has the direction (0, sin (ε), cos (ε))) .

So in 2014 the skew of the ecliptic is:

23 ° 26 '14.9 "= 23.43747 °.

The value of the mean ecliptic skewness is superimposed by the effect of nutation in an order of magnitude of Δε = ± 9.21 ″ (nutation in skewness) .

### Table of ecliptic inclination

−3000 to +3000
year Crookedness year Crookedness
−3000 24 ° 01.6 ′ 0 23 ° 41.7 ′
−2500 23 ° 58.7 ′ +500 23 ° 38.0 ′
−2000 23 ° 55.6 ′ +1000 23 ° 34.1 ′
−1500 23 ° 52.4 ′ +1500 23 ° 30.3 ′
−1000 23 ° 49.0 ′ +2000 23 ° 26.4 ′
−500 23 ° 45.4 ′ +2500 23 ° 22.5 ′
0 23 ° 41.7 ′ +3000 23 ° 18.6 ′
+1600 to +2200
year Crookedness
+1600 23 ° 29.5 ′
+1700 23 ° 28.7 ′
+1800 23 ° 27.9 ′
+1900 23 ° 27.1 ′
+2000 23 ° 26.4 ′
+2100 23 ° 25.6 ′
+2200 23 ° 24.9 ′

You can already see from these 6 out of 40 millennia that the change accelerates from −2.9 ′ to −3.9 ′ over 500 years, because the sinking sine wave becomes steeper until the 5th millennium ( mean ε = 23 ° 06 Around the year 4300).

### Measurement of the skewness of the ecliptic

The ecliptic skew is best determined by precisely measuring the midday elevations of the sun (e.g. with the meridian circle ), which is repeated at different times of the year. The declination  δ of the sun is obtained from the elevation angle by taking into account the geographical latitude , atmospheric refraction and various calibration sizes of the telescope .

The time course of the declination δ between the limits + ε and −ε gives ε at the mean point in time of the observations. Here, δ is used as a sine-like function of ε and the length λ.

### Calculations

#### From Leonhard Euler to Laplace

The cause of the changes in the ecliptic skew are the other 7 planets , whose orbital planes differ from that of the earth by 1 ° ( Jupiter , Uranus ) to 7 ° ( Mercury ). They exert torques on the earth because of its flattening (deviation from the spherical shape 0.3353%, diameter at the equator about 43 km larger than between the poles).

Leonhard Euler succeeded in the first theoretical calculation of this change in ecliptic skewness ε in 1754. As a result of his analysis, he obtained the rate of change dε / d t of ecliptic skewness as −47.5 ″ / century, from which he obtained the value for 1817 for the Skew predicted the value ε = 23 ° 27 ′ 47.0 ″. When the masses of the planets were more precisely known, Joseph-Louis Lagrange repeated Euler's calculations in 1774, from which he got −56.2 "per century and for 1817 the value 23 ° 47 '48.0". In 1782, with an improved theory, he came to −61.6 ″ / century, whereas Jérôme Lalande in his astronomy tables around 1790 showed the rate of change −33.3 ″ / century. and received the value 23 ° 47 ′ 38.9 ″ for 1817.

These considerable differences between such outstanding mathematicians prompted Pierre-Simon Laplace (1749–1827) to carry out an even more thorough analysis, which resulted in a range of ± 1.358 °. It deviates from today's value by only 0.6 ° (in 20 millennia). The Mannheim astronomer Friedrich Nicolai - a student of Carl Friedrich Gauß - calculated the rate of change dε / d t = −49.40 ″ / year for 1800 . Other famous celestial mechanics also researched the course of this fundamental quantity , and Urbain Le Verrier published the theoretical formula in 1858

${\ displaystyle \ varepsilon = 23 ^ {\ circ} \ 27 '\ 31 {,} 83' '- 47 {,} 594' '\ T-0 {,} 0129' '\ T ^ {2}}$

where the time in Julian centuries counts from 1850.0. Le Verrier was the first to notice that its value of −47.6 ″ / Jh. the observed value of about −45.8 ″ / century. easily contradicted. ${\ displaystyle T}$

#### From Newcomb (1895) to space travel

Towards the end of the 19th century, the generally accepted value was that of John Nelson Stockwell (1873), namely ± 1.311379 ° or −48.968 ″ / century. Later a price was advertised for this problem , for which Paul Harzer calculated all secular orbital disturbances of the eight planets in 1895 . In order to take into account the perihelion rotation of Mercury (which was still inexplicable before Albert Einstein ) , he assumed a special mass distribution in the sun and received 47.499 "(or 0.14" less without the correction). In the same year, Simon Newcomb developed his theory of fundamental astronomy and used observations from many famous observatories . Its values, used until around 1970, are:

${\ displaystyle \ varepsilon = 23 ^ {\ circ} \ 27 '\ 08 {,} 26' '- 46 {,} 844' '\ T-0 {,} 0017' '\ T ^ {2}}$    ( the time in Julian centuries from 1900.0).${\ displaystyle T}$

A recalculation by Eric Doolittle in 1905 only deviated from this by 0.07 ″, which was not much higher than the measurement accuracy of ε at that time. The quadratic polynomial in T is only to be understood as an approximation , since the ecliptic skewness changes periodically . Around 1960 a period of 41,050 years was assumed.

#### Current state of theory

Today, the planetary masses are known about 100 times more precisely thanks to interplanetary space probes - and therefore also the long-term changes in ecliptic skewness . In 1970 J. Lieske calculated their secular trend as follows:

${\ displaystyle {\ frac {\ mathrm {d} \ varepsilon} {\ mathrm {d} t}} = - (46 {,} 841 '' \ pm 0 {,} 006 '') / \ mathrm {cent. }}$

From all suitable observations back to the time of Leonhard Euler (see above) the value ε = 23 ° 27 ′ 47.1 ″ is obtained for 1817 - which deviates from the values ​​of the astronomers of that time by only 0.5 ″.

In 1984 the reference epoch J2000.0 was used:

${\ displaystyle \ varepsilon = 23 ^ {\ circ} \ 26 '\ 21 {,} 4056' '\ pm 0 {,} 0005' '}$

The difference to the 1970 system is 0.008 ″ below the standard deviation at that time .

Axel D. Wittmann published a compensation calculation in 1984 that is based on around 60 of 230 historical solstitial observations, which he reduced again. In addition to a 3rd degree polynomial, he also received a formula with a sine term:

${\ displaystyle \ varepsilon = 23 ^ {\ circ} \ 26 '\ 44.89' '\ -0 {,} 856033 ^ {\ circ} \ cdot \ sin (0 {,} 015306 \ cdot (T + 0 { ,} 50747))}$
( the time in Julian centuries since J2000.0)${\ displaystyle T}$

The Astronomical Almanac introduced the following formula in 1984, which was also adopted by the IAU :

${\ displaystyle \ varepsilon = 23 ^ {\ circ} \ 26 '\ 21 {,} 448' '\ -46 {,} 8150' '\ T-0 {,} 00059' '\ T ^ {2} +0 {,} 001813 '' \ T ^ {3}}$
decimal
${\ displaystyle \ varepsilon = (23 {,} 4392911111-0 {,} 0130041667 \ cdot T-0 {,} 000000164 \ cdot T ^ {2} +0 {,} 0000005036 \ cdot T ^ {3}) ^ { \ circ}}$
( the time in Julian centuries since J2000.0)${\ displaystyle T}$

In 1986 Jacques Laskar gave a formula that was valid in the period J2000.0 ± 10,000 Julian years. The greatest deviation between the years +1000 and +3000 is about 0.01 ″ and a few arc seconds at the validity limits:

{\ displaystyle {\ begin {aligned} \ varepsilon & = 23 ^ {\ circ} \ 26'21 {,} 448 "- 4680.93" \ U-1 {,} 55 "\ U ^ {2 } +1999 {,} 25 '' \ U ^ {3} -51 {,} 38 '' \ U ^ {4} -249 {,} 67 '' \ U ^ {5} \\ & \ quad -39 {,} 05 '' \ U ^ {6} +7 {,} 12 '' \ U ^ {7} +27 {,} 87 '' \ U ^ {8} +5 {,} 79 '' \ U ^ {9} +2 {,} 45 '' \ U ^ {10}, \ end {aligned}}}
where denotes the numerical value of the time in Julian decades since J2000.0.${\ displaystyle U = T / 100}$

## literature

• Andreas Guthmann: Introduction to celestial mechanics and ephemeris calculus. BI-Wiss.-Verl., Mannheim 1994, ISBN 3-411-17051-4 .
• John David North : Vieweg's History of Astronomy and Cosmology. Braunschweig / Wiesbaden 1997.
• BL van der Waerden : Adult Science. Basel / Boston / Stuttgart 1980.

Commons : Ecliptic  - collection of images, videos and audio files
Wiktionary: Ecliptic  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. https://www.spektrum.de/lexikon/astronomie/ekliptik/94
2. ^ John David North: Viewegs history of astronomy and cosmology , 1 prehistory
3. ^ John M. Steele : Observation and Predictions of Eclipse Times by Early Astronomers , Dordrecht / Boston / London 2000, p. 176
4. ^ Alfred Forke : The World-Conception of the Chinese , New York 1975, p. 1998
5. John David North: Vieweg's history of astronomy and cosmology , 2 Ancient Egypt, pp. 8-11
6. BL van der Waerden: Adult Science , p. 78
7. BL van der Waerden: Adult Science , p. 124
8. BL van der Waerden: Adult Science , pp. 258–261
9. ^ Translation by Karl Manitius , First Book, Sixteenth Chapter
10. George Thibaut : Astronomy, Astrology and Mathematics in Outline of Indo-Aryan Philology and Antiquity , Strasbourg 1899, p. 12
11. George Thibaut: Astronomy, Astrology and Mathematics , p. 13
12. ^ Daniel Martin Varisco: Medieval Agriculture and Islamic Science , Seattle / London 1994
13. ^ John David North: Vieweg's history of astronomy and cosmology , 8 Der Ostliche Islam , pp. 122–126
14. John David North: Vieweg's history of astronomy and cosmology , 8 Der Ostliche Islam , pp. 126-128
15. ^ Hans Günter Zekl: Nicolaus Kopernikus: Das neue Weltbild , Hamburg 1990, p. XLVIII
16. ^ Ernst Zinner : Origin and expansion of the Copernican teaching , Munich 1988, Peuerbach, Regiomontan
17. ^ Nicolaus Copernicus: De revolutionibus , 1543, 2nd book, 2nd chapter or 3rd book, 10th chapter.
18. Andreas Guthmann: Introduction to celestial mechanics and ephemeris calculation. 1994, p. 160.
19. Axel D. Wittmann: On the Variation of the Obliquity of the Ecliptic , in: Mitteilungen der Astronomischen Gesellschaft , Vol. 62, p. 201
20. ^ Astronomical Almanac for the year 1984, Washington, DC, 1983. pp. 26
21. ^ J. Laskar: New Formulas for the Precession, Valid Over 10000 years , Astronomy and Astrophysics, 157 (1986), 68