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:
  $\text{Longitude in Time (LiT)} = \frac{\text{Longitude}}{15° \text{h}}$

Converting Formulae

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

Conversion Examples

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

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

Conversion Formulae

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

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

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

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(+)
   • $\text{ST} = 18:00 + 01:00 = 19:00$
2. For Reykjavik, Iceland on 1st Nov at 22:20:
   • $\text{ST} = 22:20$ (No SN)

Calculation of Universal Time (UT)

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

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: $\text{LiT} = \frac{035° 49' E}{15} = 02:23$
2. Zone Number: $\text{ZN} = 2$
3. Universal Time: $\text{UT} = \text{ZT} - \text{ZN} = 09:27 - 02:00 = 07:27$
4. Adjusted Time: $\text{UT} = \text{Chronometer Time} + \text{Chronometer Error} = 07:22:38 + 00:04:48 = 07:27:26$

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