Notes on Time

Local Sidereal Time (LST)

Local Sidereal Time is defined by the motion of the celestial sphere.  The sidereal rotation rate of the Earth is 23 hours 56 minutes 4 seconds so that LST moves forward 24 hours per sidereal rotation.  The LST is defined as the Hour Angle of the Vernal Equinox (alpha=0, delta=0).  Also, the Right Ascension (measured in hours of angle) of objects crossing the meridian also equals the LST.

The LST can be related to the Right Ascension (RA) and the Hour Angle (HA) of any object:
LST = RA + HA

Apparent Solar Time

The Sun is an obvious time-keeping tool.  Sundials are constructed to measure the position of the Sun relative to the meridian.  Thus, the hour angle of the Sun is tied directly to time.  When the Sun has an hour angle of  +1 hours = 15 degrees,  it is one hour to the west of the meridian (i.e., 1 hour post-meridian = 1 pm).  Time also can be measured using the anti-meridian below the horizon.  When the Sun has an hour angle of +6 hours relative to the anti-meridan we call it 6 am. 

Throughout this class we shall use 24-hour clocks.  Thus we use 13:00 for 1 pm.
It makes it quite simple to compute the aparent solar time (ast) by measuring the hour angle of the Sun relative to the meridian.
ast = 12 hours + HA_sun

One can relate LST to ast
LST = RA_sun + ast - 12 hours

It is clear that the LST runs faster every day because the RA of the Sun increases from 0 at the vernal equinox.

Mean Solar Time

The actual time between meridian crossing is not exactly the same every day.  Although very close to 24 hours, some days the time between meridian crossing is shorter or longer by several seconds.  Two factors combine for this effect: (1) the tilt of the spin axis causes motion along the ecliptic and the celestial equator to be at different angles throughout the year (2) the Earth has an eccentric orbit so that the speed of the Earth changes and causes the speed of the Sun along the ecliptic to change.

To keep the day as a standard unit of time, we define a mean solar day as the AVERAGE time between meridian crossings.  Thus, 24 hours is set equal to this average time.
The mean solar time (mst) can be related to the apparent solar time (ast) with the equation of time (eqT).

mst = ast - eqT
ast = mst + eqT

One can relate mst to LST with this formula:
LST = RA_sun + mst + EqT - 12 hours

Universal Time and Longitude

A worldwide time standard has been chosen based on the standard for longitude.  The Royal Observatory in Greenwich, England is set at 0 degrees longitude.  Thus, we define the mean solar time to be Greenwich Mean Time (GMT) or Universal Time (UT) as the time standard for the world.  There is a simple relationship between mean solar time (mst) at any longitude (lambda) and the Universal time (UT).  This relation measure longitude in hours of angle, East as positive, West as negative.

mst = UT + lambda

Standard Time Zones

The world is divided into time zones that mostly run north to south and typically differ by hour increments relative to Universal Time.  Time zones are approximately 15 degrees east to west unless national and political divisions supercede (e.g., China is all one time zone, most of western Europe is one hour ahead of UT).  Glassboro is close to 75 degrees west longitude, so its mean standard time is extremely close to Eastern Standard Time (within 30 seconds).

Note:  During daylgiht savings time, clocks are set an hour ahead of standard time.  Thus 1pm (13:00) EDT is actually Noon (12:00) EST.