Local Sidereal Time and the Celestial Sphere

Second Authors (in no particular order):  Eric, John, Mee, Daniel

When astronomers study celestial bodies, it is important to find them in the first place.  Fortunately, there is a coordinate system that allows them to do so.  Let's define the coordinates.

Wikipedia

Celestial Equator:  As the name suggests, the celestial equator is the equator of the celestial sphere.  It is a projection of the Earth's equator into space.

Right Ascension (RA):  The right ascension is the first of two coordinates of the equatorial coordinate system and is the equivalent of longitude on the celestial sphere.  It can be measured as an angle, or on a 24 hour timescale (00:00 to 24:00 instead of 0 to 2π).  Starting at the Meridian (the line perpendicular to the celestial equator that the sun crosses at noon on the vernal equinox), the RA increases eastward.

http://upload.wikimedia.org/wikipedia/en/a/a6/Sidereal_Time_en.PNG

Declination:  The other coordinate, the declination is the equivalent of latitude and is measured in degrees north or south of the celestial equator.

Sidereal vs Solar Time
When one is asked how long a day is, the typical answer will be 24 hours.  This is approximately the length of a mean solar day, which is the apparent time it takes the sun to circle the celestial sphere.

When mapping distant stars, however, using solar time becomes problematic, since it appears to take about 4 minutes less for other stars to circle the celestial sphere.  As such, objects outside our solar system follow what is called sidereal time.  Instead of 24 hours, one sidereal day is about 23 hours, 56 minutes long.  The 4 extra minutes of a solar day are due to the fact that the earth revolves around the sun.  The local sidereal time (LST) the current right ascension of the meridian, and is 00:00 at noon on the vernal equinox.  How do we calculate the LST throughout the year?  Let us examine this with some examples.

To find the LST at midnight on the vernal equinox, we add 12 hours to 0:00.  The LST is thus 12:00.

What is the LST 24 hours after the vernal equinox?  00:00 + 24:00 gives us an LST of 00:04.

What is the current LST?  I am writing this at about 1pm (20:00 UT) on Friday October 7, 2011, which is 4832 hours after the vernal equinox, or 201 sidereal days + about 21 hours.  Thus, the LST at the moment is about 21:00 in UT, or 05:00 in PST.  The LST at midnight tonight will be 11 hours later, making the LST 01:00.

Sunset on my birthday will be 5580 hours after the vernal equinox, so the LST will be 19:00.

The differences between solar and sidereal days account for the apparent annual "rotation" of the celestial sphere.