We know that the Earth revolves about its axis once every 24 hours.  In other words, the Sun completes its apparent revolution of 360^o in 24 hours.  This means that the Sun crosses each of the 360 meridians of longitude once every 24 hours.

So, in 1 hour, the Sun appears to move 15^o,

in 4 minutes, it appears to move 1^o,

in 1 minute it appears to move 15′,

in 4 seconds it appears to move 1′.

From this, it becomes obvious that there is a direct relationship between arc and time such that 1 hour of time equals 15 degrees of arc.

For example, if the difference between Greenwich Mean Time (GMT) and Local Mean Time is three hours, then the difference in longitude must be 3 x 15^o.  If local mean time is ahead of GMT then the  longitude must be east of the Greenwich Meridian and if local time is behind GMT the longitude must be west.

i.e.  GMT Least, Longitude East

        GMT Best. Longitude West

It is important not to confuse local mean time (LMT) with standard time or zone time.  LMT is the mean time along a single meridian of longitude whereas standard time is a time adopted for convenience sake within a country or region and may encompass a very wide area.  In the case of zone time, a zone covers a range of 15^o of longitude and the time within that zone is the LMT of its center meridian of longitude.

In a survival situation, there is only one time of the day that you can be sure of the actual local time at your position and that is at midday.  This is because, at midday, the Sun momentarily lies over your meridian of longitude.  We know that at midday, the Sun is at its highest altitude and we can use this knowledge to calculate our longitude in the following way.  (This method assumes that you have the equipment listed in the post ‘Astro navigation in a survival situation’).  (This equipment includes a watch set to GMT).

Note.  Survivors on land could tell when it is noon by making a survival sundial.

We must be careful here to make the distinction between ‘mean time’ and ‘apparent time’.  The sun that we see in the sky is the ‘True Sun’ not the theoretical ‘Mean Sun’ which  simply provides us with a convenient regular time system that we use to overcome the variations in the movement of the true sun.  So when we see the sun reach its highest altitude, we know that it is ‘apparent noon’ but this may differ by a few minutes from ‘mean noon’.  However, in a survival situation, an error of a few minutes is acceptable, especially since the altitude of the sun changes very slowly as it approaches is zenith.  To summarize, in a survival situation, we can assume that ‘apparent noon’ and ‘mean noon’ coincide.

It is also worth distinguishing between Greenwich Mean Time and Universal Time in case there is any confusion about this.  The term Universal Time (UT) was adopted internationally in 1928 as a more precise term than Greenwich Mean Time because GMT can refer to either an astronomical or a civil day.  However, the term Greenwich Mean Time persists in common usage to this day and is generally considered to be synonymous with the term Universal Time.

Method:

1. Use a clinometer to calculate when the Sun is at its highest altitude with the aid of a filter of smoked glass to protect the eyes.
2. When the Sun reaches its highest altitude, note the time in GMT and make a note of the altitude reached.
3. Calculate your longitude as shown in the following examples.

Example 1:  If it is midday local time and the time GMT is 07.45, then local time must be 4 hours and 15 minutes ahead of GMT.

Therefore, longitude = [4 x 15^o] + [(15 ÷ 60) x 15^o]

= 60^o + 3.75^o

= 63.75^o

= 63^o 45’ East (GMT least, longitude east).

Example 2:  If it is 17.50 GMT when  it is midday local time, then  local time must be  5 hours and 50 minutes behind GMT.

Therefore, longitude  = [5 x 15^o] + [(50 ÷ 60) x 15^o]

=  75^o + 12.5^o

=  87.5^o West   (GMT best, longitude west).

Fixing you Lat and Long.  If you note the highest altitude reached by the Sun at midday, as recommended in the method above, you can use this information to also calculate your latitude.  In this way you will be able to establish a Lat and Long fix of your position.

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