time

Learning Objectives

  • Understand the different types of time and their functions.
  • Understand how to convert between different times.
  • Use the almanac to locate standard time.
  • Apply time calculations to different scenarios.

Types of Time

Universal Time (UT)

  • Definition: The International Reference for time, measured through Greenwich at the Prime Meridian.
  • Relation to GMT: Same as Greenwich Mean Time (GMT).

Local Mean Time (LMT)

  • Definition: The mean ‘solar’ time specific to a location on Earth.
  • Variability: Changes with longitude.

Zone Time

  • Definition: A time representation where every 15° of longitude roughly equals one time zone (360°/24 hours).

Standard Time (ST)

  • Definition: Applied in cases where countries span several time zones or utilize fractional time zones.
  • Reference: Found in an almanac.
  • Assumptions: At sea, we use zone time; in port, we use standard time.

Standard Time Zones of the World

  • Each time zone is represented by zones typically every 15° longitudinally.
  • UTC and Time Zone Calculation: To obtain local time from UTC, add the zone time number; to obtain UTC from local time, subtract it.
  • Example Locations by timezone include:
    • United States: Seattle, Chicago, New York
    • Europe: France, Germany, UK
    • Australia: Sydney, Melbourne

Converting Between Local Mean Time (LMT) and Universal Time (UT)

Longitude in Time (LiT)

  • Definition: A value that relates the Earth's rotation (360° corresponds to 24 hours).
  • Conversion Formula:
    Longitude in Time (LiT)=Longitude15°h\text{Longitude in Time (LiT)} = \frac{\text{Longitude}}{15° \text{h}}

Converting Formulae

  • From LMT to UT:
    UT=LMT−LiT (East)/+LiT (West)\text{UT} = \text{LMT} - \text{LiT (East)} / + \text{LiT (West)}
  • From UT to LMT:
    LMT=UT+LiT (East)/−LiT (West)\text{LMT} = \text{UT} + \text{LiT (East)} / - \text{LiT (West)}

Conversion Examples

  1. Example Calculation for 15th May 06:24 LMT, Longitude 066° 28.0' E:
    • Calculate LiT:
      LiT=066°28.0′E15=04:26\text{LiT} = \frac{066° 28.0' E}{15} = 04:26
    • Calculate UT:
      UT=15/06:24−04:26=15/01:58\text{UT} = 15/06:24 - 04:26 = 15/01:58
  2. Example Calculation for 1st March 14:02 UT, Longitude 121° 05.0' W:
    • Calculate LiT:
      LiT=121°05.0′W15=08:04\text{LiT} = \frac{121° 05.0' W}{15} = 08:04
    • Calculate LMT:
      LMT=14:02+08:04=05:58\text{LMT} = 14:02 + 08:04 = 05:58

Converting Between Zone Time (ZT) and Universal Time (UT)

Conversion Formulae

  • From ZT to UT:
    UT=ZT−ZN (East)/+ZN (West)\text{UT} = \text{ZT} - \text{ZN (East)} / + \text{ZN (West)}
  • From UT to ZT:
    ZT=UT+ZN (East)/−ZN (West)\text{ZT} = \text{UT} + \text{ZN (East)} / - \text{ZN (West)}

Example Calculation 29th June 04:24 ZT, Longitude 164° 38.0' E:

  1. Calculate LiT:
    LiT=164°38.0′E15=10:59\text{LiT} = \frac{164° 38.0' E}{15} = 10:59
  2. Calculate Zone Number (ZN):
    ZN=11\text{ZN} = 11
  3. Calculate UT:
    UT=04:24−11=17:24\text{UT} = 04:24 - 11 = 17:24

Crossing the International Date Line (IDL)

  • To cross the IDL eastbound, subtract one day (24 hours); the same day reoccurs on the other side.
  • To cross westbound, add 24 hours, advancing the calendar date.

Standard Time in Terrestrial Navigation

  • Sources: Standard time can be tracked in an almanac.
  • Lists Provided:
    • Locations fast on UTC (primarily east of Greenwich).
    • Locations keeping UTC.
    • Locations slow on UTC (west of Greenwich).

Standard Time Calculations

  1. For Vienna, Austria on 25th August at 18:00 UT:
    • Standard Time = UTC + SN(+)
    • ST=18:00+01:00=19:00\text{ST} = 18:00 + 01:00 = 19:00
  2. For Reykjavik, Iceland on 1st Nov at 22:20:
    • ST=22:20\text{ST} = 22:20 (No SN)

Calculation of Universal Time (UT)

  1. For Colombo, Sri Lanka on 1st Feb at 15:24:
    • ST=UTC−SN(+)=15:24−06:30=08:54\text{ST} = \text{UTC} - \text{SN(+)} = 15:24 - 06:30 = 08:54
  2. For Alabama, USA on 6th June at 08:14:
    • 08:14+0500=13:1408:14 + 0500 = 13:14

Chronometers

Definition and Usage

  • Chronometer: An instrument designed for accurate timekeeping, found on a ship's bridge.
  • Time Keeping: Maintained on Universal Time.
  • Error Adjustments:
    • If chronometer is slow, add the error.
    • If chronometer is fast, subtract the error.
Example Chronometer Calculation
  • Chronometer Time = 11:42:41
  • Chronometer Error = 00:00:41 (fast)
  • Actual Time: 11:42:00

Accurate Universal Time Calculation

  • Example Data: 1998 Jan 03 / 09:27 ZT, Longitude: 28° 53' S, 035° 49' E
  • Calculate:
  1. LiT: LiT=035°49′E15=02:23\text{LiT} = \frac{035° 49' E}{15} = 02:23
  2. Zone Number: ZN=2\text{ZN} = 2
  3. Universal Time: UT=ZT−ZN=09:27−02:00=07:27\text{UT} = \text{ZT} - \text{ZN} = 09:27 - 02:00 = 07:27
  4. Adjusted Time: UT=Chronometer Time+Chronometer Error=07:22:38+00:04:48=07:27:26\text{UT} = \text{Chronometer Time} + \text{Chronometer Error} = 07:22:38 + 00:04:48 = 07:27:26

Applying to Celestial Navigation

Example Date/Time: 1998 October 15 / 09:59

  • Assumed Position: 56° 06' N, 025° 07' E
  • Chronometer Time: 07:56:13
  • Chronometer Error: 00:02:49 slow on UT.
  • Calculations:
  1. LiT: LiT=025°07′E15=01:40\text{LiT} = \frac{025° 07' E}{15} = 01:40
  2. Zone Number: ZN=2\text{ZN} = 2
  3. Universal Time: UT=extZT−extZN=09:59−02:00=07:59\text{UT} = ext{ZT} - ext{ZN} = 09:59 - 02:00 = 07:59
  4. Adjusted Chronometer: UT=Chronometer Time+Chronometer Error=07:56:13+00:02:49=07:59:02\text{UT} = \text{Chronometer Time} + \text{Chronometer Error} = 07:56:13 + 00:02:49 = 07:59:02
  5. GHA and LHA of the Sun as per the provided positions.
    • Increment calculated based on observations.
    • Corrections made to included data.