Equinox

Equinox (from Latin aequus "equal" and nox "night" ) or equinox (also day - and - night - same ) are named in the year in which the last possible day and night of equal length, the two days. The equinoxes mark the beginning of the calendar astronomically defined seasons of spring and autumn.

In astronomy, the date of the equinox is determined in more detail about the unit day out and given as exact to the second stage. It is that moment when the sun sets the equator in the spring or in the fall point happened, and with the beginning of this season is then defined astronomical.

Both these exact times and the respective positions of the passed Spring and autumn equinoxes, also abbreviated hot spot.

• 3.1 Astronomical beginning of spring and autumn, true equinox
• 3.2 equinoxes

• 4.1 True equinox and mid- equinox
• 4.2 vernal equinox and the fall point
• 4.3 Äquinoktiallinie
• 4.4 vernal equinox as the coordinate origin
• 4.5 migration of Äquinoktialpunkte
• 4.6 The equinox of celestial coordinate 4.6.1 equinox and epoch
• 4.6.2 Standardäquinoktien
• 4.6.3 Katalogäquinoktium and dynamic equinox
• 4.6.4 Conversion from one equinox to another 4.6.4.1 Conversion equatorial coordinates in kart. coordinates
• 4.6.4.2 rotations with the aid of a rotation matrix
• 4.6.4.3 Calculate the equatorial coordinates of the Zieläquinoktiums

Definitions

As equinox are on the northern hemisphere of the earth received the following issues may refer to:

Time points

• An equinox - the calendar day on which the Sun crosses the Earth's equator, and thus begin the spring or fall Primaräquinoktium - crossing from the south to the north, the beginning of spring
• Sekundaräquinoktium - crossing from north to south, beginning of autumn

• Spring Equinox: exact time beginning of spring to the 20-21. March
• Autumnal Equinox: exact time of autumn start to the 22-23. September

Places in the sky

• A Äquinoktialpunkt - the point on the ecliptic where the Sun is at true equinox: Vernal equinox and
• Fall point

• First point of Aries and
• Balance point.

Equinox as the beginning date for determining and religious festivals

In some calendar systems is the spring equinox of the beginning of the year and one of the main festivals of the year, such as Nowruz (literally " Neulicht ") of the astronomical solar calendar and the Iranian Bahai calendar. Rosh Hashanah, the Jewish New Year, is not identical to the same autumn, but is dependent on (before to after). Analog is the case with the Jewish Passover and the Christian Easter, always take place after the spring equinox.

Equinox as the beginning of season

Astronomical beginning of spring and autumn, true equinox

The exact definition is:

• Apparently means taking account of aberration and nutation.
• Geocentric means of a (hypothetical) observer in the center of the Earth as seen.

The definition is independent of the location of a real observer; the equinoxes occur worldwide at the same time one ( but different in different time zones corresponds times ).

These times fall to within a few seconds along with the times, where the center of the solar disc crosses the celestial equator, where the sun so from the southern to the northern sky half ( ecliptic longitude 0 ° ) or from the northern to the southern sky -half ( ecliptic longitude 180 °) changes. The time difference results from the fact that it actually is the focal point of the Earth- Moon system, which moves in the average Earth's orbital plane around the Sun as the Earth itself this focus circles ( "true orbit of the earth " ), and thus in the is usually slightly above or below this level. From a geocentric observer from, so the sun does not exactly on the ecliptic ( ecliptic and has a non-zero width ). It also happens not exactly the spring or autumn, crossing point before or after it has reached the ecliptic longitude of these points the equator. This time difference makes a few seconds.

Because the average duration of one revolution of the earth around the sun based on the spring equinox (tropical year) with approximately 365.2422 days, just under six hours longer than the duration of the calendar year overhead with exactly 365 days, the date of the equinoxes of calendrical specified shifts a common year to the next at a later time to about six hours. With the insertion of February 29 in a leap year there is an earlier to about 18 hours, compared to last year time for the Äquinoktialzeitpunkt. The following details of the equinoxes are rounded to minutes ( at the beginning of the four seasons see also table in the article seasons).

Equinoxes

The equinoxes are the shortened indicated on the calendar dates of the Astronomical commencement of spring or autumn. In the northern hemisphere spring in March and autumn begins in September. In the southern hemisphere it is the reverse happened.

The Sun crosses the celestial equator at the Equinox, so stands to this day around the time of the equinox vertically above the Earth's equator. Day and night are then everywhere on earth about the same length as one half of the daily path of the sun above ( diurnal arc ), the other is below the horizon. Everywhere on earth therefore the sun sets on this day almost exactly in the east and sets in the west (see the rising point).

In Astronomy spherical celestial objects treated are simplified and the extension of the sun wheel is initially disregarded, as well as atmospheric influences. Because of atmospheric refraction of sunlight and the reference to the first or last ray of sunshine but actually have the time periods of sparse day and night of equal duration, but the night is the appointment of a " equinox " is shorter by a few minutes (see below Equilux ).

Are the solstices, ie the days on which the sun reaches its greatest distance from the celestial equator and is perpendicular on one of the turning circle of the earth between the equinoxes. The two equinoxes and the two solstices in a year each represents the beginning of astronomical seasons

Equilux

With " Equilux " means a calendar day, would be on the on the earth's surface with ideal (mathematical) horizon, the exposure duration, measured between the first ray of sunshine in the morning and the last ray of sunshine in the evening, exactly twelve hours; This definition thus refers to the edge of the sun, not its center. The date of Equilux therefore not covered for the date of the equinox ( " Equinox "), but takes place a few days before the primary or after Sekundäräquinoktium during the year. In contrast to the erdmittelpunktbezogenen and thus the equinoxes the same world Equilux date beyond each depends on the latitude of the location. For the 40th parallel, it is around March 17 and September 26, for the fifth degree of latitude to the 25th February and the 15th of October.

The sun rises, when its upper edge above the horizon line is visible, that is, before its center appears. The sunset occurs after the solar disk center is apparently dropped below the horizon, when the last ray of sunlight of the upper edge of the sun disappears. Compared with a point-like viewing the Sun's middle order is in addition a one half diameter arc of the sun ( about 0.25 ° or 16 ' minutes of arc ). In addition, the refraction of light caused by the Earth's atmosphere each an apparent increase of the solar disk (by about 0.6 ° or 34 '). This extension of the bright day at the expense of the night by a total of just under seven minutes ( 1.7 °, 1 ° corresponds to 4 minutes) is taken into account in determining the Equilux.

Equinox as the coordinate origin

True equinox and mid- equinox

The true Äquinoktialpunkte are the actual points of intersection of the celestial equator with the ecliptic:

• The passage through the vernal equinox defines the astronomical beginning of spring;
• The passage through the autumn point defines the astronomical beginning of autumn.

The mean Äquinoktialpunkte however, are fictitious. They are intended to reflect only the long-period orbital motion, so no short-term disturbances are taken into account (for example, nutation and aberration) in their determination. Therefore, the average Äquinoktialpunkte from the actual may vary by several hours.

• The mean vernal equinox is the " first point of Aries ," named after the constellation Aries.
• The mean fall point is the " balance point ", named after the constellation Libra.

The usual symbol for the Aries point, which is of outstanding importance in celestial mechanics, or ♈ (U 2648 ). He is the coordinate zero point for ecliptic coordinates and equatorial coordinates and several other basic astronomical sizes. His English name is first point of Aries.

Vernal equinox and the fall point

Also, the Spring and Autumn period itself, ie those points on which the sun (in the above sense) is at the time of the equinox before the background of fixed stars, called the equinoxes. Discriminating in clear language, they are also referred to as " Äquinoktialpunkte ".

The vernal equinox (also first point of Aries ) is the point on the imaginary celestial sphere, in which the sun on their projected onto this ball path, the ecliptic, on the way from south to north of the celestial equator intersects ( RA = 0 h ).

Accordingly, the autumn period ( also balance point) of the point on the imaginary celestial sphere, in which the sun on their projected onto this ball track the celestial equator on its way from north to south through cuts ( RA = 12h).

At an angle of 90 ° to the vernal equinox and autumn each point of the summer point are ( RA = 6 h) and the winter period ( right ascension = 18 h), in which the sun is at the summer solstice.

Äquinoktiallinie

The connecting line between the two positions of the Earth at the time of an equinox is called Äquinoktiallinie. This line is so right through the sun shining through, extending them beyond the Earth's orbit by the Äquinoktialpunkte. It is perpendicular to the Solstitiallinie.

Vernal equinox as the coordinate origin

In the context of astronomical coordinate systems, the term equinox always never called the vernal equinox, the fall point. The vernal equinox is used both for the equatorial as for the ecliptic coordinate system as the zero point, are counted by the out right ascension or ecliptic longitude (east positive). Although the vernal equinox is not directly observable and anmessbarer point, but its location can always be determined from appropriate observations calculation.

Migration of Äquinoktialpunkte

The gravitational forces of the sun, moon and the other planets try to pull the equatorial bulge of 23.5 ° inclined to the ecliptic plane earth in this level, and so the earth with respect to the ecliptic " erect ". However, the earth does not focus on yourself; rather, the Earth's axis deviates due to the moment of inertia, while retaining its angle of inclination of the side, so that the direction in which it is inclined, in about 25,800 years, even going through a full 360 °. The perpendicular to the axis of the earth 's equatorial plane taking part in this movement, so that the Äquinoktialpunkte run as intersections of the equatorial plane and the ecliptic plane in 25,800 years, once around the ecliptic. This movement of the earth's axis or the Äquinoktialpunkte is called precession (Latin for " Pioneering ").

The Äquinoktialpunkte shift this year by about 50 arc seconds in a westerly direction along the ecliptic. This effect is so great that it stands out over an observation period of a few decades, and therefore was already known in ancient times.

The precession superimpose additional periodic influences; they are caused by the inclination of the orbit of the moon, which is inclined by 5 ° 9 ' to the ecliptic, the continuously shifting line of nodes of the lunar orbit and periodic variations in the displacement of the axis of rotation of the earth. These various periodic fluctuations that performs the Earth's axis in addition to the precession, are summarized in astronomy, the term nutation. The drift of the Äquinoktialpunkte along the ecliptic, therefore, does not take place completely uniform, but with slightly periodically fluctuating velocity.

Note: The Strasbourg Münsteruhr contains a part that represents this precession.

The equinox of celestial coordinate

The migration of the Äquinoktialpunkte particular consequence that the zero points of the above astronomical coordinate systems are not fixed in space but move slowly with the vernal equinox along the ecliptic. For example, taking the ecliptic longitude of a star without proper motion in one year by 50 arc seconds and in 100 years by 1.4 °. The coordinates of a celestial object change so without this corresponds to an actual motion of the object. In its statement, therefore, must always of time, ie the position of the vernal equinox, are given, to which the coordinates refer. This point in time (not to be confused with one of the equinoxes ) is also called equinox and is year number, possibly with fraction specified. Of importance to observations are the coordinates for the equinox of the observation time point (eg 2005.432 ), known as the equinox of date.

The conversion of coordinates between different equinoxes is a frequently encountered task.

Equinox and epoch

Must not be confused with the equinox, the term of the era. The age refers to the actual time of observation or an operation: the equinox, the coordinate system in which it is measured.

Standardäquinoktien

Catalogues of celestial objects are based on so-called Standardäquinoktien usually. These are coordinate systems that are related to specific points in time and are also called standard epochs. The timings are set to change every 25 year. Previously, the time difference was between two eras standard Bessel 25 years ( approximately 9131.055 days ), today there are 25 Julian years ( 9131.25 days ). This Standardäquinoktien are denoted by a year and a B or J before. These are:

Example: The star Arcturus has at different times, the following provisions related to various equinoxes equatorial coordinates right ascension and declination:

The change of coordinates for various epochs, but the same fixed equinox ( J2000.0 or J2050.0 ) reflects the proper motion of the star. The difference of the coordinates for the same period but different equinox is due to the precession. Appropriate to the equinox of date coordinates include the influence of both the proper motion and the precession.

For calculations, it is often advantageous to ignore the influence of the periodic nutation on the motion of the equinox and to refer to a fictional uniformly moving equinox ( nutation must then of course be subsequently added to the results again). It then is the mean equinox, while the true equinox contains the influence of the nutation.

Katalogäquinoktium and dynamic equinox

The exact location of the equinox has to be as well as the position of the equator and the ecliptic determined by observation. To this end, appropriate observation material is very carefully evaluated occasionally. The result is, for example, a star catalog, specify its coordinates information as accurately as possible the position of the stars relative to the desired equinox. These coordinates represent the coordinate system for practical use, and represent a fundamental system, can refer to the other position measurements. If, for example, the coordinates of a star determined by its distance is measured by appropriate fundamental stars, then found his coordinates refer automatically to the equinox of the fundamental system. The equinox, which is derived from catalog positions ( as the intersection of the hour circle of right ascension zero with the equator ), the Katalogäquinoktium. The embodied by the fundamental system equinox never falls due to unavoidable measurement inaccuracies completely exactly with the actual equinox. For high accuracy requirements, therefore, the catalog shall indicate on its Katalogäquinoktium the measurements refer. If the equinox derived exclusively from planetary observations ( the angular momentum vector of the Earthmoving Equipment for example, is perpendicular to the ecliptic plane and allows these to be determined), we obtain a dynamic equinox.

Conversion from one equinox to another

The following conversions transform equatorial coordinates from one equinox to another. The proper motion of astronomical objects is not taken into account. Procedure:

Conversion equatorial coordinates in kart. coordinates

Α with right ascension and declination δ is valid for

Rotations with the aid of a rotation matrix

The rotation matrix is derived from the superposition of three rotations ζ to the values ​​obtained with polynomials angle, z, and θ:

This means the matrix multiplication:

Calculate the equatorial coordinates of the Zieläquinoktiums

Conversions between Standardäquinoktien

For the Standardäquinoktien B1875, B1900, B1950, B1975 and J2000 following matrices are:

Example

For the conversion of B1950 after J2000, the values ​​apply, and; hence the matrix

Results. This means for the matrix multiplication:

For example, the celestial equinox B1950 applies:

And from this