Sidereal time
The sidereal time is used in astronomy and time scale based on the apparent motion of the stars as a result of the rotation of the earth. A sidereal day is the length of time (more precisely: the vernal point ) of the starry sky needed for quite apparent orbit of earth. Compared to the commonly used solar time, based on the apparent orbit of the earth by the sun, the sidereal day is about four minutes shorter than the solar day.
- 7.1 sidereal time at Greenwich
- 7.2 sidereal time at the location of the observer
- 8.1 documents
- 8.2 See also
- 8.3 External links
Definition and properties
The sidereal day is classified as the sunny day in 24 hours. It begins when the vernal equinox passed the meridian of the place of observation and terminates at its next passage. The observer - usually an astronomer at an observatory - excludes the sidereal time to the current view of the sky. The sidereal time is from the right ascension angle - a primary variable for the position of the stars in the sky - derived. A star with for example 15 ° difference in right ascension to the vernal equinox passed the meridian finest hour later than the latter. This fact may indicate briefly so that for example it is 1:00 clock sidereal time. Note, however, that the sidereal time is a bound to the place time. To facilitate comparison over time for observations made at different places, the local sidereal time clocks are set to the sidereal time of Greenwich. The time difference is - the same as the solar time - 1 hour for 15 ° difference in length between the observation locations.
The observation work using sidereal time has the advantage that at the same sidereal time are the stars always in the same direction in the sky. Compared with the ordinary clock is the sidereal time - clock every day about 4 more minutes. After a year, they overhauled the latter and agrees with her briefly in line again.
The general determination of time to Universal Time ( UT) ( sun time ) is carried out in practice by the exact potential observation of star positions. The determined sidereal time is over a set by convention formula (see below) in the corresponding UT converted.
The sidereal time is defined as the hour angle of the vernal equinox. Referring to the mean vernal equinox, one obtains the mean sidereal time. Referring to the true vernal equinox, one obtains the apparent or true sidereal time.
The reason for the continuous growth of the hour angle is called the Earth's rotation. The sidereal time is therefore subject to all short-and long -term irregularities in the Earth's rotation and is therefore not uniformly extending tempo. But it is always a true reflection of the angle of rotation of the earth with respect to the vernal equinox.
Since the vernal equinox moves due to precession against the fixed star background, is a sidereal day (ie one full rotation of the earth with respect to the vernal equinox ) is slightly shorter than one rotation of the earth (ie one full rotation of the earth relative to the fixed star background ). Since the vernal equinox moves per day declined by about 0,137 seconds of arc along the ecliptic, a mean sidereal day by .009 seconds more quickly than one rotation of the earth.
The true vernal equinox differs by the turn variable nutation from Spring Point. Therefore, the apparent sidereal time loses against the ( itself already non-uniform ) mean sidereal time an additional non-uniformity, the main component varies with a period of 18.6 years and an amplitude of ± 1.05 seconds.
However, the hour angle of the vernal equinox is the same for observers who are on the same longitude, for observers at different longitudes different. The derived sidereal time is thus a local time. The sidereal time of Greenwich reference location is the Greenwich sidereal time. It is a very common requirement in calculations. The different types of sidereal time are often referred to by its English abbreviations:
- LAST: local apparent sidereal time, apparent local sidereal time.
- LMST: local mean sidereal time, local mean sidereal time
- GUEST: Greenwich apparent sidereal time, apparent Greenwich sidereal time
- GMST Greenwich mean sidereal time, Greenwich Mean Sidereal Time
The hour angle of the vernal equinox is the counted along the celestial equator from the meridian angle of the vernal equinox. The right ascension of a star on the other hand is counted along the celestial equator from the vernal equinox angle to the star. If the star on the meridian ( that is, culminates the star ), both angles are equal. It follows that at the moment of culmination of a star, the sidereal time is equal to the right ascension of the star.
This can be used to directly determine by observing the Kulminationszeitpunktes the right ascension of the star. That is the reason why the right ascension is often given in units of time rather than in angular units: it is then immediately at the time of culmination read off sidereal time. Vega, for example, has a right ascension of 18h 36m 56s, is thus always culminate at 18h 36m 56s local sidereal time.
On the other hand, by observing the culmination of a star of known right ascension the current sidereal time be determined: if Wega culminates, the sidereal time is 18h 36m 56s (in practice are still corrections for precession, proper motion, parallax, etc. to install ).
Rotation of the star sky
Daily rotation
One can imagine the starry sky as large Uhrscheibe, the counter ( in the northern hemisphere ) rotates once in a sidereal day -clockwise around itself. In this picture disc is marked with a pointer between Polaris and Big Bear. The 24 - hour dial (out of 23, 0, 1, ...) is fixed on the horizon. The pointer has rotated 15 ° further ( scale 0 °, 15 °, 30 °, ... ), a sidereal hour has passed. For a solar time hour, he must continue to rotate slightly.
Annual rotation
On a carryover from the sun, rotating around the North Star Dial one finds a very slow rise of the pointer. The pointer circled it once a year: 30 ° ( range 0 °, 15 °, 30 °, ...) in about a month ( scale 06, 07, 08, ...).
The picture was taken in early July (paragraph 07) 2:00 clock. Two hours later (about 4:00 clock ) is further hiked the Big Dipper to point 4. A month later, in August (paragraph 08) it is located at 2:00 clock already at the point 4
Sidereal and solar day
The solar day as the basis of the commonly used solar time lasts slightly longer than the sidereal day because the sun is slightly slower than the star - also apparently - to the earth moves. The reason is again the own motion of the Earth, namely their annual trip around the sun.
The sidereal day is approximately 1/365 ( length of the year equal to 365.2422 days ) is shorter than the solar day. Measured at the 24 hours of the solar day is the sidereal day is 23 hours, 56 minutes and 4.091 seconds long. The sidereal day is itself divided again within 24 hours, his hours in 60 minutes and his minutes in 60 seconds.
Due to the nutation of the earth the vernal equinox varies with a period of about 18.6 years. Accordingly, we distinguish the true sidereal time, which results from direct observation, and the mean sidereal time, which is exempt from these fluctuations. The difference between true and medium sidereal time is a maximum of about 1.1 seconds.
Sidereal time and stargazing
Knowing the sidereal time facilitates the observation of stars considerably. In observatories to use clocks that show the sidereal time. You go in sync with the current stars in the sky. At a fixed location every star passage has a fixed sidereal time by a certain amount or direction and can therefore be registered immovable in an observation schedule after Stardate. It should be noted that the possible nocturnal observation period runs through the schedule once a year.
The sidereal time is like the True Solar Time local time. As with the True Sun Time 12 clock ( noon) is when the sun passes through the local meridian, is for star time is 0 clock, when the vernal equinox is in the local meridian. The sidereal time to standardize on a time zone would be absurd. On the contrary: Stardate contained in yearbooks for a day applies to a specific longitude. It must be converted to the longitude of the place of observation in order to work profitably with it can ( 4 minutes per sidereal degrees west ).
The difference between the local sidereal time of a place to sidereal time at Greenwich, the longitude of that place immediately following, see celestial navigation. One measure of this local sidereal time thus corresponds to either a location or a time measurement - depending on whether the sidereal time at Greenwich time of observation or the longitude of the observing site is known.
Sidereal time and right ascension
For the sidereal time applies:
- The sidereal time is the hour angle of the vernal equinox.
- Sidereal time θ, and hour angle τ and right ascension α of a star are linked by the relation τ = θ - α.
- The sidereal time in one place is the right ascension of that heavenly body that just culminates ( τ = 0).
On the day of the autumnal equinox True solar time and sidereal time are approximately the same, because a star near the vernal equinox culminates at midnight, when the modern 24 -hour count starts.
Sidereal time and UT
The hour angle of the sun is the true solar time. It is directly observable and is displayed by sundials. However, due to the tilt of Earth's axis and the ellipticity of the Earth's orbit, the true solar time runs unevenly ( Main article: equation of time ). To obtain a measure of time liberated from the equation of time, is considered instead of the true solar called fictitious mean sun, an imaginary point which is at a constant speed along the celestial equator (not the ecliptic ) runs. The hour angle of this point is not the equation of time subject to local mean time. The location of the fictitious mean sun on the celestial equator can not be determined by observation but only by invoice.
In 1896, the following determined by Simon Newcomb expression was determined for the right ascension of the fictitious mean sun as binding under an international agreement:
In this case, the number of Julian since Greenwich mean noon (12h UT) has elapsed on 0th January 1900 centuries, each 36525 mean solar days. The linear term of the equation indicates the speed of the fictitious mean sun with respect to the mean vernal equinox of the date, the quadratic term takes into account the fact that the präzessionsbedingte movement of the vernal equinox currently slightly accelerated.
The world time UT was defined as the Greenwich hour angle of the fictitious mean sun plus 12 hours ( the addition of 12 hours is necessary because of the meridian passage of the fictitious mean sun is to take place by 12 clock UT, her hour angle is at this moment but 0h ). The hour angle of an object is but equal to the hour angle of the vernal equinox minus the right ascension of the object, and the hour angle of the vernal equinox, in turn, is by definition nothing more than the sidereal time. The relationship between universal time UT and Greenwich sidereal time is:
As given by Newcomb right ascension of the fictitious mean sun is related to the mean vernal equinox of the date that occurs here sidereal time is Greenwich Mean Sidereal Time.
Each 12 clock UT Greenwich sidereal time is the same as RU ( since this is the Kulminationszeitpunkt the fictitious mean sun with the right ascension RU). Therefore RU can also be regarded as the date the corresponding 12h UT Greenwich sidereal time. It follows the 1900 to 1984 used term for Greenwich Mean Sidereal Time: is the time 0h UT of each day, the corresponding Greenwich Mean Sidereal Time
Here grows TU, starting from the date 1900.0, successively in increments of 1 / 36525th For the particular so for 0h UT sidereal time are still the interval since 0h UT sidereal hours to add ( see below).
With the introduction of improved astronomical constants in the year 1984, this formula has undergone a revision. The relationship between GMST and UT1 has been redefined as
This is TU = dU / dV 36525 and since 1 January 2000, 12h UT1 (JD = 2451545.0 UT1 ) elapsed UT Days: dU = ± 0.5, ± 1.5, ± 2.5, ± 3.5, ...
The equations above establish a connection between the sidereal time and universal time UT. Although UT would actually derive their definition in the course of the sun, it was derived, in practice, these formulas from the observed meridian passages of stars, ie the sidereal time. Star passages can be much more precise than watching the position of the extremely bright and the instruments warming sun. This definition of UT1 was valid until 2003. Since then UT1 no longer on the sidereal time, but determined the newly introduced " Erdrotationswinkel ".
Before the irregularities and the long-term slowing of the Earth's rotation has been detected, the sidereal time and deduced from their UT were considered strictly uniform time scale. At the beginning of the 20th century, astronomers discovered that the two scales non-uniformly ran and had to introduce new, uniform time scales. The derived from the Earth's rotation time scales such as UT are also referred to as " civil time " and are increasingly switching from regular time scales such as Ephemeris Time, Atomic Time, etc. from ( Main article: Delta T).
Calculation of Sidereal Time
The formulas can of course also be used to calculate the sidereal time of known UT.
Sidereal time at Greenwich
To do this, first determine the Julian date JD for the time 0h UT on the desired date ( on a 5 -ending number). Then calculate T:
And thus the Greenwich Mean rating time 0h UT, in the time or degree measure according to need:
To determine the Sidereal Time GMST for any time of the given date we multiply UT UT with 1.00273790935 and add the result to the previously calculated sidereal time for 0h UT.
Sidereal time at the location of the observer
An observer on the longitude λ has yet to convert his local sidereal time:
The angle LMST is possibly yet to be put on the main value (0 ° -360 ° ), and converted into the time scale.