Sidereal time

FIGURE 1. Geocentric perspective that shows the annual apparent movement of the Sun by the ecliptic. The point where the Sun passes from South to North of the equatorial plane is the equinox vernal or first point of Aries.

The sidereal time, also called sidereal time, is the time measured by the apparent diurnal movement of the vernal equinox (fig. 1), which approaches, although without be identical, to the movement of the stars. It differs in the precession of the vernal equinox with respect to the stars.

More precisely, sidereal time is defined as the hour angle of the vernal equinox. When the vernal equinox culminates in the local meridian, the local sidereal time is 00.00.

Differences between sidereal time and solar time

FIGURE 2. With the Earth B, culminate simultaneously in the local meridian the Sun and a distant star. When the Earth arrives C culminate again the star, and not the Sun. The star advances the Sun. The Delay of the Sun (DCA) is equal to the advance of the Earth in its orbit (BAC).

Solar time is measured by the apparent diurnal motion of the Sun, and local noon is defined as the time when the Sun is at its zenith (the cast shadow points exactly due north in the northern hemisphere and exactly south in the northern hemisphere). in the southern hemisphere). By definition, the time it takes for the Sun to return to its highest point is on average 24 hours.

However, the stars have a slightly different apparent motion. Over the course of a day, the Earth will have moved a bit along its orbit around the Sun, so it must rotate a little extra angular distance before the Sun reaches its highest point. Instead the stars are so far away that the movement of the Earth along its orbit generates a barely appreciable difference with respect to its apparent direction (see, in any case, parallax), so they return to their highest point in something less than 24 h or solar day. A mean sidereal day lasts about 23 hours and 56 minutes (it is almost 4 minutes shorter than the solar day). Due to variations in the Earth's rate of rotation, the rate of an ideal sidereal clock deviates from any simple multiple of a civil clock. In practice it is taken into account by the difference UTC−UT1, which is measured using radio telescopes, and is stored and offered to the public through IERS and the United States Naval Observatory.

As shown in FIGURE 2, the time between successive culminations is not the same for the Sun as it is for distant stars. As the Earth moves from B to C, the star culminates again but the Sun does not, and it is said that it retards the angle DCA, which is what that it lacks to repeat its culmination. The time corresponding to the arc BC is sidereal time.

Types of sidereal time

The Aries point is not a fixed point, it moves on the celestial sphere subjected mainly to the movement of Precession of the equinoxes and to a lesser extent to the movement of Nutation. If we consider only the movement of precession we will speak of the mean equinox.

• Half-six time

It is the hour angle of the mean equinox. It is a time that passes uniformly, by dispensing with nutation.

If we consider precession and nutation we will talk about the true equinox.

• True Sidere Time

It is the hour angle of the true equinox, and therefore the precession and nutation are taken into account, so it is a time that does not run uniformly.

The difference between the two sidereal times is called the Equinox Equation and is always less than 1.18 seconds.

• Local time (LTS) and Greenwich Side Time

Local values of sidereal time vary according to the longitude of the observer. If we move a longitude of 15º to the east, the sidereal time increases one sidereal hour. Possible differences are due to the accuracy of the measurements. The Greenwich sidereal time is the local sidereal time for an observer located on the Greenwich meridian.

The intervals in Sidereous time (S) and Average time (M) governed by Medium and it has to do with him Universal Coordinated Time (TUC) are related by a constant factor S=M⋅ ⋅ 1,00273790935{displaystyle S=Mcdot 1,00273790935,}.

Relationship between the local Sidereal Time, time angle and straight ascent.

The local time (Tsl or Strike Strike m(th,λ λ ){displaystyle Theta _{m}(th,lambda),}or the local time is the time angle that forms the point Aries with the meridian of the observer. The local time is the straight ascension of a star plus the time angle of that star:TSL=Strike Strike m(th,λ λ )=H+α α {displaystyle TSL=Theta _{m}(th,lambda)=H+alpha ,}

Sidereal time is used in astronomical observatories for the ease it entails in determining which astronomical objects will be visible at a given time. The objects are placed in the night sky using the straight ascension and decline relative to the celestial equator (something similar to the length and latitude on Earth), and when the time of a straight object is equal to its straight ascension, you will find yourself crossing the meridian (H=0{displaystyle H=0}) at the highest point in the sky and will also be the best time to make the observations. Or said in another way: at the moment of the culmination of a star its straight ascension gives us the sidéreous time, or the reverse, known the Sidereal time we have the straight ascension of the star.

As a particular case for Greenwich the Greenwich Side Time, of great importance in astronomy: time angle of the vernal equinox in the meridian of Greenwich. A magnitude that is tabulated in all Anuarios of Astronomy is the Average half-sevent in Greenwich at 0h of U.S. Strike Strike m(0h,Gr){displaystyle Theta _{m}(0h, gr),} and that can be calculated by expression:

• Strike Strike m(0h,Gr)=6h38min45,836s+8640184,542s⋅ ⋅ T+0,0929s⋅ ⋅ T2{displaystyle Theta _{m}(0h, gr)=6h38min45,836s+8640184,542scdot T+0,0929scdot T^{2}}

where T{displaystyle T,} is the number of Julian centuries of 36525 average days passed at midnight of Greenwich since midday in Greenwich on December 31, 1899.

Once the calculation is done, it is transformed to the first round in the range 0-24 hours.

To calculate the Greenwich sidereal time at an hour t U.T., transform the mean time interval t into sidereal time.

• Strike Strike m(th,Gr)=Strike Strike m(0h,Gr)+t⋅ ⋅ 1,00273790935{displaystyle Theta _{m}(th, gr)=Theta _{m}(0h, gr)+tcdot 1,00273790935,}.

To calculate the local TSL time at a geographical location λ λ {displaystyle lambda ,} at an hour t of T.U. just add the length (transformed in time interval) and positive to the east of Greenwich.

• Strike Strike m(th,λ λ )=Strike Strike m(th,Gr)+λ λ {displaystyle Theta _{m}(th,lambda)=Theta _{m}(th,Gr)+lambda ,}

To transform the longitude from degrees to a time interval, a simple comparison is made between 24 hours and 360 degrees of the earth's circumference:

• λ λ =Lorngitud⋅ ⋅ 24/360{displaystyle lambda =Longitudecdot 24/360,}