Ecliptic

The ecliptic (Latin linea Ecliptica ' Eclipse Relevant line ', from Greek ἔκλειψις, ékleipsis ' absence, disappearance, darkness ') is the apparent path of the sun in the course of a year before the fixed star background. Seen from Earth, in geocentric projection, the ecliptic forms on the celestial sphere an imaginary great circle. Its county line defines a plane of the ecliptic, the ecliptic plane or Ekliptikalebene; it is compared with the equatorial plane defined by the celestial equator is inclined at an angle as obliquity of the ecliptic ε ( obliquity or even Erdneigung ) and are currently about 23.4 °.

In the heliocentric picture the earth orbits the sun on an in- ecliptic orbit. On closer inspection, are for " sun" and " earth " to be assumed mean body celestial mechanics instead of the actual celestial body, so the "earth" of the Earth-Moon center of gravity.

  • 4.1 Etymology and early concepts
  • 4.2 From Antiquity to Leonhard Euler and Laplace
  • 4.3 The obliquity of Newcomb (1895 ) to aerospace
  • 4.4 Current status of theory
  • 5.1 Table of the obliquity

Obliquity of the ecliptic

The axis of rotation of the Earth, Earth's axis is not perpendicular to the plane of Earth's orbit, but is inclined at an angle of about 66.56 degrees. This currently includes the ecliptic plane with the plane of the equator of the earth or the celestial equator at an angle of 23.4385 °, the obliquity of the ecliptic or obliquity is called (from the Latin obliquus " wrong "). The term Erdneigung is this angle below the view from the ecliptic plane to the earth again, the perspective of the ecliptic coordinate system.

The obliquity of the ecliptic is one of the ten most important basic sizes of astronomy and geodesy to define coordinate systems and for calculations in astronomy and geodesy. It is usually by the Greek letter epsilon ε respectively.

Ekliptikpol

Since the Earth deviates from the spherical shape, the tidal forces of the moon and sun cause a torque that tries raise up the inclined axis of the earth. The Earth's axis that points to the celestial poles, thus describes how an obliquely running children gyro to precess on a cone with opening angle 2ε around the Ekliptikpole around. This Ekliptikpole drawn on precise star charts; the northern Ekliptikpol is located in the constellation Draco, by definition, at right ascension 18 h (with a declination of 90 ° minus ε, currently around 66 ° 34 '), in the constellation of the southern swordfish at 6 h

The " Erdkreisel " is very slow because of the large mass of earth of just 6.1024 kg, and the earth's axis need for a round about 25700-25800 years ( a Platonic Year ). Today's so-called polar star takes his role so only temporarily.

Fluctuation of the Earth's axis and mean obliquity

The angle of obliquity changes the periodicity of long gravitational influences of the body in the solar system. Therefore, ε varies within 40,000 years between approximately 21 ° 55 'and 24 ° 18'. This effect contributes next to the eccentricity ( 100,000 years ) and the precession ( 25,780 years ) to the formation of the ice ages when ( as one of the factors in the long term, regular, naturally occurring climate fluctuations that can Milankovitch cycles is called ):

As a first approximation, for the mean obliquity ε0 = 23 ° 26 ' 21.45 " - 46.8 " * T where T is the time specified argument in Julian centuries since the epoch J2000.0, is thus:

Ecliptic latitude of the sun

Strictly speaking, the Ekliptikalebene is not exactly the orbital plane of the earth, but that of the barycenter ( center of mass) of the Earth and Moon ( Earth-Moon center of mass), so to speak, as a double planet circling the sun.

Therefore, the geocentric sun is not running (calculated from the center of the earth ) exactly in the ecliptic ( ecliptic latitude β = 0), but it has a small ecliptic latitude: Superimposed is the value of the mean obliquity on a monthly basis by the effect of the nutation of the order of Δε = ± 9.21 " ( nutation in obliquity ). In the nutation in obliquity are approximately ± 0.7 " included by the variations of the Earth around the Earth-Moon center of gravity and even smaller fluctuations of the true sun around the barycenter of the solar system.

The ecliptic longitude ( λ in the image, from 0 ° to 360 °) approximately follows Kepler's laws plus the nutation in length. This aspect is discussed in detail below average length of the earth in the article Tropical year.

Seasons and obliquity

As the Earth orbits the Sun once a year, the position of its axis in space remains almost unchanged, with the exception of the long-period effects described above. This has, in the months from March to September in the northern hemisphere a little more to the sun, in the months of September to March but the southern hemisphere. This variable angle of incidence of the sun rays and the associated change in day length are the causes for the change of seasons.

The stronger the ecliptic angle, the more pronounced are the seasons - and the differences between the winter in the northern and southern hemispheres. The latter has harsher winter (July to September) than the north, because in July the earth their sonnenfernsten point ( aphelion ) passes. However, since the " line of apsides " ( aphelion - perihelion ) also shifts long-period, it is sufficient a relatively small regional climate change, that a kind of " cold wave " escalates. This may have an impact on the ice ages. For if the earth more than usual covered by ice, radiates this heat back into space more sun and cools even more out.

History to the ecliptic Research

Etymology and early concepts

The name " ecliptic " is derived from the Greek feminine adjective ἐκλειπτική [ τροχιά ] ekliptikí [ trochiá ], the masking [ orbit ] ' (of έκλειψη éklιpsi literally, overlay, masking, effacement '; εκλειψις ekleïpsis, darkness, blackout '; compare Eclipse / occultation ): eclipses come before namely only when the new or full moon near ( partial eclipse ) or very near ( total or annular eclipse ) is the ecliptic.

For the early astronomers the moon's orbit was intuitive the priority - because the immediate observable - rail line, but the ecliptic, path of the dragon ' that swallows the dragon points, the Moon's Nodes, the sun or moon.

The relationship between the ecliptic and the apparent path of the sun only came later. Due to the geocentric view of the ancients understood that the sun does not independently wanders on the nightly return to the east beneath the earth, but on a sphere exactly opposite to the stars, who are at the respective place of the sun 12 hours later. Thus, the already known from the stargazing annual parallax of the star sky could thus be linked to the sun on the ecliptic in one year, the earth orbits ( according to current understanding, of course, as the apparent geocentric motion).

The area on either side of the ecliptic, extending the apparent movements of the sun, moon and planets within which is called the Zodiac or Zodiac. The fixed stars with respect to the celestial sphere practically motionless and form, as seen from the Earth, the constellations. Twelve of the thirteen constellations that are intersected by the ecliptic, were used as the basis of the calendar calculation of the ancient astrologers as a sign of the zodiac. Due to the precession of these and the constellations are the same since the designation of the zodiac signs but not any more congruent, but at about 30 °, so moved a zodiac sign. From about 4000 to 1500 BC, the vernal equinox was running through the constellation Taurus where he also happened to the Golden Gate of the ecliptic, which is formed by the two distinctive star cluster of the Pleiades and Hyades.

The division of the ecliptic into twelve equal signs of the zodiac came during ancient times. So the scale was long considered part of Scorpio. In India, the lunar orbit, and thus the ecliptic, however, in 27 or 28 lunar mansions ( nakshatras ) was divided, a system which has also been adopted by the Arabs ( al - Qamar Manazil ) and the Chinese. On the other hand, the ancient Egyptians divided the ecliptic into 36 deans.

From ancient times until Leonhard Euler and Laplace

One of the most important astronomers of the golden age of Islam was Muhammad Ibn Jubayr al - Battani ( 858-929 ). He determined, among other things, the obliquity of the ecliptic and the equinox. Since around the turn of time, astronomers know that the Earth's axis precesses, but the now known value 25700-25800 years was found only in the 13th century. The fact that in addition to their direction is also changing the obliquity of the ecliptic, you guessed until the Middle Ages. It was thought at that time that her Angle takes all values ​​from 0 ° to 90 ° over the millennia. It was only in the 16th century it became clear that the range of variation was much lower. Copernicus went from a maximum variation of 24 ' (max. 23 ° 52' min. 23 ° 28 ').

The cause of the changes ( see table above) are the other seven planets, their orbital planes differ from that of the Earth by 1 ° (Jupiter, Uranus ) to 7 ° (Mercury). They practice because of the flattening of the earth on it torques (deviation from the spherical shape 0.33530 % or 21 km).

The first theoretical calculation of this change in ε succeeded Leonhard Euler in 1754. The result of his analysis was dε / dt = -47.5 " / century, from which he ε = 23 ° 27 ' 47.0 for the year 1817 " forecast. When the masses of the planets were known more accurately, Joseph -Louis Lagrange in 1774 repeated Euler's calculations, from which he " 23 ° 47 48.0 per century, and for 1817 the value ' " was -56.2. In 1782 he came with an improved theory to -61.6 " / century, while Jérôme Lalande in 1790 in his astronomy panels -33.3 " / century and 23 ° 47 ' 38.9 " received.

This still considerable differences between such outstanding mathematicians led Pierre- Simon Laplace (1789-1827) to a more thorough analysis, which was followed by a fluctuation range of ± 1.358 °. It differs from the present value of only 0.6 ° ( in 20 thousands ) from. The Mannheim astronomer Friedrich Nicolai - a student of Carl Friedrich Gauss - calculated for the year 1800 dε / dt = -49.40 " / century also other famous sky mechanics explored the course of this fundamental size, and Urbain Le Verrier published in 1858 the theoretical. formula

( Counted in Julian centuries from 1850.0 ). Le Verrier noticed but the first that his -47.6 " / century the observed value of about 45.8 " / century slightly disagreed.

The obliquity of Newcomb (1895 ) to aerospace

Towards the end of the 19th century, the generally accepted value of those of John Nelson Stockwell (1873 ), namely ± 1.311379 ° and -48.968 " / century later was a prize has been awarded for this problem, for the Paul Harzer 1895 all secular perturbations of the 8 major planets calculated. To account for (before Albert Einstein still unexplained ) perihelion of Mercury this, he took part in a special mass distribution in the sun, and received 47.499 "(or without the correction 0.14 " less). That same year, Simon Newcomb developed his theory of fundamental astronomy and used observations of many famous observatories. His values ​​used until about 1970 are:

A recalculation of Eric Doolittle 1905 aside from it only by 0.07 " from what was not much more than the former measurement accuracy of ε. The quadratic polynomial in T is, however, intended only as an approximation, since the obliquity changes periodically. By 1960, they took it to 41,050 years.

Current status of theory

Today we know through the interplanetary space probes, planetary masses about 100 times more accurate. 1970 J. Lieske calculated the trend for:

From all appropriate observations to back to time Leonhard Euler (see above ), we obtain for ε 1817 = 23 ° 27 ' 47.1 "- what the values ​​of the former astronomers only 0.5 " deviates.

1984 we went to the reference epoch J2000.0 on:

The difference to the system in 1970 is 0.008 "under the former standard deviation.

Axel D. Wittmann published in 1984 a compensation bill, which is based on approximately 60 of 230 historic Solstitialbeobachtungen and were re- reduced by it. He was next to a 3rd degree polynomial and a formula with a sine link:

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

Jacques Laskar 1986 is a formula that in the period J2000.0 ± 10,000 Julian years ( ie ± 100T ) is valid. The largest deviation between the years 1000 and 3000 is about 0.01 " and the validity limits of a few arc seconds:

Measurement of the obliquity of the ecliptic

The obliquity is best determined by precise afternoon highs at the meridian circle of the sun, which are repeatedly measured at different seasons. From the elevation angle is obtained by considering latitude, atmospheric refraction ( refraction) and calibration of various sizes of the telescope declination δ and from the ecliptic lengths λ of the sun.

By the timing of the declination δ between the limits ε and - ε are obtained ε to the middle time of the observations. Here, δ is taken as the sine -like function of ε and the length λ; latter is related to the Kepler laws. However, the perturbations of these correlations are not negligible.

Our present analysis and computer methods allow such calculations - among other things by simulation of the planetary orbits by numerical integration - much faster and more accurate than at times of Newcomb. Nevertheless, it has only around 1980 and around 2000, the IAU fundamental constants must adapt to the latest results.

Table of obliquity

You can see already from these 6 of 40 millennia, that the change by 500 years of -2.9 ' to -3.9 ' accelerated because the sinking sine wave until the 5th millennium steeper ( mean value is ε = 23 ° 06 ' around the year 4300 ).

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