Calculating Direction Using the Moon – Part 2

In Part 1 we looked at the speed the sun, stars, planets and the moon appear to move through the sky and the reasons behind them.  In part 2 we will look in a bit more depth at the sun’s trajectory through the sky and then how we can use this information together with the information of the moon’s position relative to the sun to calculate direction.

So we said in part one that heavenly bodies appear to rise in an easterly direction and set in a westerly direction. For the sun it only actually rises exactly due east and sets exactly west on the Spring and Autumn Equinoxes.  At other times of the year it can rise and set almost 45 degrees out from, either north or south.  This is because of the tilt of the earth. As already mentioned the rotational axis of the earth is tilted at a 23.4 degrees which results in the northern hemisphere being tilted towards the sun during our summer (June-Aug) and the Southern Hemisphere tilted towards it during our winter (Nov-Jan).

This gives us our seasons but also our varying day length.  So in the summer, as we in the UK are tilted towards the sun, the bulge of the earth creates less of a shadow, blocking the sun, meaning the sun rises around 4am and will actually rise almost north-east. It then passes in a big arc through the sky reaching its zenith around 1pm (BST) and then continue westwards eventually setting almost north west at about 10pm.

In the middle of winter, around Christmas, we in the UK are tilted away from the sun and so now the bulge of the earth creates a shadow obscuring the light and the sunrise at this time of year is after 8am and the sun rises at nearly south-east and then sets before 4pm roughly south west.

In between around the equinoxes when it does rise in the east and set in the west we have roughly 12 hours of night and 12 hours of day and depending whether or not we are on Greenwich Mean Time (GMT) or British Summer Time (BST) sunrise will be at around 6 or 7am and sunset at 6 or 7 pm.

The sun’s trajectory through the sky as viewed from the UK (not to scale)

If we start to now think about the relationship between the sun and time we can now start to see a pattern emerging. If we always work to GMT, the sun is North East at 03.00, East at 06.00, South East at 09.00 then in the afternoon South West at 15.00, West at 18.00, and North West at 21.00.  This gives us approximate directions for the sun which change by 45 degrees every three hours, and if we fill in the gaps then at 12.00 the sun will be half way between South East and South West i.e. South and therefore North at 00.00 or midnight.  This sort of makes sense, if we think back to part 1 when we said that the sun moves 15 degrees an hour.  Just remember that the movement is 15 degrees along the suns trajectory through the sky and not along the horizon so this method of calculating the suns position is not accurate.  For an accurate method of using the sun to determine direction see the blog on Shadow Sticks.

The approximate position of the sun at different times of the day (working on GMT)

So with this information, provided we know the time we can deduce the approximate bearing  of the sun even if it is dark and we cannot actually see it, simply by multiplying the time (on GMT and using a 24 clock) by 15.

 From the information in the previous blog we can now also deduce what day of the lunar cycle we are in from simply looking at the moon.

And we also know from the first blog,  that the moon lags behind the sun by 12.2 degrees each successive day of the cycle.  So we now have all the information we need to calculate the moon’s bearing by substituting all the information into the following equation;-

Bearing of the moon = (Time x 15) – (Day of lunar cycle x 12.2) 

So let’s start with an easy example.  It’s a winter night at 9pm and you see a moon that looks like this;-

It looks like a quarter moon so it’s around day 7 in the lunar cycle so putting all the numbers into the equation.

• Bearing of the moon = (21 x 15) – (7 x 12.2)
• Bearing of the moon = 315- 85
• Bearing of the moon = 230 degrees

If you think about it the sun will be around North West at that time and a quarter moon is around 90 degrees behind the sun, so South West which is 225 degrees…close enough!

In our experience the method can be variable in its accuracy, on some occasions it is spot on whilst at other times it can be up to 10 degrees out.  This can be for a variety of reasons. Firstly we have already discussed that the position of the sun as determined by time is not completely accurate, add to that the differences between when the sun is at its highest and noon as determined by your watch, these differences will apply throughout the day so if it at its at the extreme of 15 minutes, that alone will give you a 4 degree error.

Then consider your position relative to Greenwich, the difference between Kent and Cornwall is over 5 degrees but both are on GMT.

The other really important factor to consider is that the lagging between the moon and the sun is continuous not incremental. New moons and Full Moons etc. happen at precise time on an assigned day, and determining the exact phase to less than a day is beyond mos peoples ability.  So in the above example calculation, we estimated that the moon was 7 days into it’s cycle. If it was exactly 7 days it would  be 7 x 12.2 behind the sun but if it’s say 7 days and 6 hours (which we would not be able to precisely estimate) then it would actually be an additional 3 degrees behind.

The First Quarter moon would actually occur at 7 days 9 hours and 7 minutes after the New Moon!

Like with all methods of natural navigation as long as you are aware of the limitations if the method then it won’t cause problems. So on the next clear night, get out there and have a practice.

Kev Palmer

References

“The Natural Navigator” by Tristan Gooley

“Finding Your Way Without Map or Compass” by Harold Gaty

Thanks to Jo Logan for coming up with the original algebraic equation