We know that the Earth revolves about its axis once every 24 hours. In other words, the Sun completes its apparent revolution of 360o 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 15o,
in 4 minutes, it appears to move 1o,
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 minute of time equals 15 minutes of arc.
If we have two accurate clocks, one calibrated to GMT and the other calibrated to local time, then it is an easy matter to calculate our longitude from the difference between the two times. (In fact, we could manage with just one clock because we know that noon, local time is when the Sun is at its highest altitude).
For example, if the difference between GMT and local time is three hours, then the difference in longitude must be 3 x 15o. If local time is ahead of GMT then the local longitude must be East of the Greenwich Meridian and if local time is behind GMT the longitude must be West.
Example: If it is 18.00 GMT when it is 09.20 local time on the same day, then local time must be 8 hours and 40 minutes behind GMT.
Therefore, Long = – [(8 x 15o) + (40 ¸ 60 x 15o )]
= – [120o + 10o] = -130o = 130o West
However, if we had no way of knowing the time in GMT, we would be in the same situation as mariners were before John Harrison invented the chronometer in the 18th. century. They had to navigate the oceans without a reliable method of calculating their longitude.
A full exposition of this topic can be found in the book Astro Navigation Demystified
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