An extraordinary guest article by John Pahl.
I love looking at the night’s sky, following the movement of the Moon and stars across the sky. The problem is that I live in London, where all too often clouds close in for days on end. But I’ve worked out a way to keep track of the phases of the moon, just by looking at the tidal Thames.
The gravitational field of the moon pulls on the Earth’s oceans, causing tides that rise up towards the Moon and on the opposite side, as in this very much not to scale figure:
This can be seen in the tidal Thames, where every day the river rises and falls twice, reaching high and low points called high water and low water, as in this plot:
Note this plot and the data used in this post are all taken from the Port of London Authority (PLA) web site: http://www.pla.co.uk/Safety/Tide-Tables. The times and heights are likely to be different where you live, but the same principles should apply.
In this example day, the 3rd September 2020, the times of high water at Tower Bridge were 02:31 and 14:38 (all times GMT: to get to BST just add one hour). If I go back to August and plot the times of high water, they make a pattern a bit like this:
There can be seen to be a regular pattern of the high water being a bit later each day. We could make a similar plot of low water times, though higher water is more visible.
This pattern is due to the Moon travelling around the Earth once every 27.3 days, so each day the high water is on average about 53 minutes later. As the Moon moves around the orbit, it’s phases change, the most obvious of which are the new Moon and the full Moon. These connect the position of the Moon to the Earth and Sun as in the following figures:
Note that when the Sun, Earth and Moon line up like this, the combined gravitational forces make the tides even bigger than normal, the so-called spring tides. So these spring tides, when the Moon is full or new, will occur at the same time of day each time they come round, as they relate to the geometry of the Earth, Sun and Moon.
In theory they should come at midday and midnight, but there is typically a lag in the tides due to friction and inertia, so they actually are slightly behind where the Moon is:
So rather than happening at midday on the day of the full or new Moon, the high water on the day of the full or new moon occurs just after midday and the highest high water of the month a day or two later.
On our plot of the time of the high water in August, the full Moon was on the 3rd August and new Moon on the 19th, as shown here:
It can be seen that the time of high water on those days was around 14:00 hours. This is typical, though it can vary, as shown by the plot below of the daytime time of high water on the day of the new or full Moon during 2020:
The time varies slightly as the orbit of the Moon isn’t a simple circle but an ellipse, where the Moon travels faster when near its perigee (closest point in the orbit to the Earth) and slower when near its apogee (furthest point from the Earth).
But it does mean that if I look at the tidal Thames and keep track of when high water is, I can deduce something about the position and phase of the moon.
In this example, based upon the records for central London, in particular Tower Bridge, if the high water is around 14:00, then the Moon must be either full or new. We can extend this to create a tide clock, as described in the book “The Book of Tides” by William Thomson:
It’s quite hard to work out whether a high-water at 14:00 means the Moon is full or new just by looking at the river, but hopefully it won’t be necessary if we can remember the previous month, as the Moon will be full (or new) at roughly the same date.
Note the predicted tide height and times can vary slightly due to the weather, in particular from a low pressure system, and raising the Thames Barrier will change everything by stopping the incoming or outgoing tides.
There is a bit more information that can be deduced by looking at the tide height. If you plot the height of the highest high water through 2020, it looks a bit like this:
That’s showing a clear pattern – but what does it mean?
The answer comes from plotting another variable on this graph, namely the distance from the Earth to the Moon:
It can be seen that the highest high water for the full and new Moons is when the distance to the Moon is at its lowest. This makes sense, as gravity falls off as an inverse to the distance squared, meaning it is strongest when the distance is lowest.
Hence by looking at the tidal Thames it’s possible to work out not just the phase of the Moon but also whether it is near its apogee or perigee.
So next time my early afternoon run down Putney Embankment is stopped by the Thames flooding into the streets, I’ll be able to say that the Moon must have just been either new or full and must be near it’s perigee, and if full look out for a super Moon that evening.
Unless, of course, it is cloudy, again!
Thank you John. Very impressive work. There is a tenaciousness about this article that reminded me of John Harrison of chronometer fame!
Learn more about John Pahl’s writing at noctilucents.com