Time and Hour Angles

1. Hour Angle and Time
2. Example 1 - Local time and UT from Standard Time
3. Example 2 - Standard Time from UT

Hour Angles

Time is determined by the HOUR ANGLE of the Sun. The angle is measured in hours, minutes and seconds just in same way as right ascension.

Hour angle is defined as the angle of the Sun from the local MERIDAN measured along the celestial equator in the westerly direction. As the Earth rotates this angle increases by 15 degrees every hour. The Hour Angle ranges from 0 to 24 hours. EXAMPLE: 10 am local time has the sun 2 hours east of your local meridian. This is 22 hours west of that meridian hence the Hour Angle is 22 hours.

The local meridian is a reference line on the celestial spherer that stretching from the north celestial pole to the south point of the local horizon. The sun is on the local meridian at noon local time.

Types of Time

There are several types of time to be discussed.

1. Standard Time = Hour Angle of the Sun at the STANDARD MERIDIAN for the local TIME ZONE. Each Time Zone is about 1 hour wide (15 degrees of longitude) and near the center of the zone is the meridian of the zone. The longitude of this meridian is always a multiple 15 degrees of longitude.
2. Local Time = Hour angle of the Sun as seen from your location
3. Universal Time (UT) = Hour angle of the Sun at zero of longitude (Greenwich, UK)

The diagram below shows the relationship between the various types of time. Because they are located at different longitudes, the angle of the Sun is different at Greenwich, your location and the standard meridian of your time zone.

The diagram below gives more detail and shows the Hour Angles associated with the various types of time.

If your location is west of Greenwich (ie. your longitude is a West longitude) then Universal Time is later tnan Local Time by your longitude measured in hours. Your Standard Time is earlier than UT by the longitude (again in hours) of the standard meridian of your time zone.

The relationship between local and standard time depends on the difference between your longitude and that of the standard meridian of your time zone (SMTZ). If you are located east of SMTZ then the Local time will be later than the Standard Time, while if you are located west than local time is earlier.

EXAMPLES

EXAMPLE - 1: Calculate Local Time and Universal Time from the Standard Time.

• Standard Time = 7:45 pm July 5
  On the 24 hour clock it is 19:45 hours on July 5
• Longitude of Location = 126 degrees West

1. Standard Time Zone Meridian = 120 degrees West (120 degrees = 120/15 = 8 hours)
   (Pacific Standard Time or Time Zone U - see Observer's Handbook on Time)
2. Universal Time is 8 hours later than Pacific Standard Time. Thus UT = 19:45 + 8:00 = 27:45 hours.
   This places the UT the next day and the time is then 3:45 am July 6
3. Longitude difference from standard meridian of time zone = 126 - 120 = 6 degree west
4. Standard Time will be (6 deg * 4 min/deg) 24 minutes later than at the standard meridian.
5. Local Time is 24 minutes earlier than Standard Time. 7:45 pm - 0:24 = 7:23
   7:23pm Local Time on July 5.

EXAMPLE - 2: Calculate the hour angle of the Sun if you know UT. Also determine the Standard Time.

• UT = 18:29 hours (6:29 pm at Greenwich)
• Local Longitude = 50 degrees East

1. Standard Time Zone = 45 degrees East (45/15 = 3 hours later than Greenich) Time Zone C.
2. Standard Time = 18:29 + 3:00 = 21:29 hours = 9:29 am
3. Location is (50 - 45) 5 degrees east of the Time Zone meridian.
4. The local time is ( 5 deg * 4 min/deg ) 20 minutes later than Standard Time.
5. Local Time (12 hour clock) = 21:49 - 12:00 = 9:49 am
6. Hour Angle of the Sun = 21:29 + 0:20 = 21:49 hours
   This places the Sun ( 24 - 21:49 ) 2:11 hours or (2 hr* 15deg/hr + 11 min/(4min/deg) ) 32.8 degrees East of the local celestial meridian