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 + HAsun
One can relate LST to ast
LST = RAsun + 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 = RAsun + 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
Note: During daylgiht savings time, clocks are set an hour ahead
of standard time. Thus 1pm (13:00) EDT is actually Noon (12:00)