Calculating Direction Using the Moon – Part 1

Like the other celestial bodies (stars, sun and planets) the moon appears to move through the sky from a roughly easterly to a westerly direction, however if studied carefully it will be observed that the moon doesn’t move at quite the same speed as everything else. This is readily apparent if it’s position to a clearly recognisable star or planet is monitored over successive nights.  This blog will attempt to explain how and why the moon’s movements are different and in Part 2, we will see how with that knowledge the moon can be used to determine direction.

To start with it helps to work out what the sun and stars are doing first.

The largest causal factor for the movement of heavenly bodies through our sky is a result of the earth spinning around its north-south axis anti-clockwise. It takes approximately 24 hours to make one complete revolution………and a bit!  This “bit” is because the earth is simultaneously  orbiting the sun whilst rotation on its axis. If we take any location (Greenwich is as good as anywhere) and say that at midday the sun is at it’s zenith. The next day the earth will have moved over 1.6 million miles around its orbit of the sun so that it will have to have to rotate about an extra 1 degree for the sun to reach its zenith over Greenwich the following day at midday.  This means that the sun appears to move through the sky at about 15  degrees per hour or 1 degree every 4 minutes.

It is however slightly more complicated than that.  The earth’s orbit around the sun isn’t circular, it’s an ellipse and this means that the speed at which the earth orbits the sun varies depending on which part of the orbit we are at.  We actually move faster at the part of the orbit when we are closest to the sun (perihelion) than at the point when we are furthest away. This can cause a difference of up to + or – 7 minutes between noon on your watch and solar noon, when the sun is at it’s highest.

                          Elliptical orbit of the Earth around the Sun (not to scale)

Also the earth’s rotational axis is tilted with respect to the plane of its orbit around the sun. It is currently tilted at an angle of 23.4 degrees. This tilt is what gives us our seasons and also varying day lengths in summer and winter (see part 2 for the explanation) but it also has an effect on solar day length, almost up to 10 minutes at the half points between solstices and eqinoxes.

The tilted rotational axis of the earth (not to scale)

So the combined effects of both of these these factors can cause the actual time that the sun is at its zenith to be up to 15 minutes before or after midday as shown on a watch.

Graph showing the effect of the speed we orbit the sun (dashed line) and the tilt of the earths axis (crossed line) and the combined effect of both (solid line) on the difference between watch noon and when the sun is at its highest through out the year. X axis is in minutes. Positive numbers are when the sun reaches its zenith before noon on a watch.

The 24 hours that we use for time keeping purposes is simply an average over the year, and even then it is just a little bit out requiring us to have an extra day added in every 4 years …. leap year.

The stars are much further away, so on a day to day basis there position relative to the earth doesn’t change but because our day length is calculated from our relationship to the sun the appear to rise 4 minutes earlier every day.  This is simply caused by that extra 1 degree of rotation made to keep our clocks and the sun in sync. So if our clocks were set to sidereal (star) time the day would be 23 hours and 56 minutes long.  This is what gives us summer and winter constellations, the stars may well be there at other times of the year but the light from the sun makes them invisible.

The net effect is that the stars will also appear to move almost the same speed as the sun just a tiny bit faster 0.04 of a degree an hour…too little to notice.

The planets are all orbiting the sun on there own orbits and so appear to wander through the sky relative to the stars over a period of time, the speed and direction will vary according to the planet.  As a general rule they move quite slowly and over the course of a night their position relative to the background of the constellations is unlikely to perceptibly change.

So now to the moon.

The moon, actually orbits the earth and does so in a direction opposite to the spin of the earth.  It’s orbit takes 28 days. To help visualise this, imagine we could stop the world spinning. The moon would rise in the west and then be visible in the sky for 14 days before setting in the east and then not being visible again until 14 days later.

Now start the world spinning again, 361 degrees every 24 hours in the opposite direction.  The combined effect is for the moon to now appear to move from east to west through the sky but just a little bit slower than everything else, so instead of moving at around 15 degrees an hour through the sky like the sun, stars and planets it is moving at 14 degrees and 30 minutes per hour. Not a lot different but enough to be detectable.  This means each day at any particular time the moon will be about 12.2 degrees behind where it was the day before and relative to the sun and stars.  This is why the moon rises about 50 minutes later each successive day (this is also why high tide times are about 50 minutes later each day).  It is also why we get the phases of the moon.

We only see the moon because from our vantage point it is reflecting light from the sun towards us like a big spherical mirror.

To understand what is happening imagine a new moon.  This is normally considered the beginning of a lunar cycle and it is where the moon is in the same part of the sky as the sun and therefore as all the light is reflected back towards the sun so we cannot see it.  24 hours later the sun (and the stars) will (to all intents and purposes), be roughly where they were the night before. The moon however will now be lagging behind by 12.2 degrees. This may give enough of an angle to see the thinnest crescent of a waxing moon.  Certainly by the following day when the moon is now 24.4 degrees behind the sun you will then have a distinct  crescent.

Each day the moon will carry on lagging behind so that by around 7 or 8 days it will appear with half of its surface lit up, this is known as a quarter moon (it’s a quarter of the way through the cycle).  It carries on lagging and growing, now called a waxing gibbus until after another week the moon is now lagging so far behind the sun it is completely opposite and so now we see it completely lit up as a full moon.  After this point it is still effectively lagging by the same amount each day but it appears that it is catching up with the sun and the part lit up starts to decrease (wane) through waning gibbus, three quarter moon and waning crescent until eventually after 29.5 days it has lagged so far behind it is back where it started.

Approximate phases of the moon on a daily basis as observed from earth

In the next blog we will take all of that understanding and show how you can use it to calculate direction.

 

Kev Palmer

References

“The Natural Navigator” by Tristan Gooley

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