The Moon: plotting the dates and time of a full moon

This exercise started as I was sitting on the back of a motorbike tootling down a country road when Namwan said that the moon was full … I said, hmm, your eyesight is better than mine but it doesn’t look quite full to me!

Being the sort of person I am I got home and started to review the dates and times of full moons. I announced that the moon will be full on 31st August! Well, that was wrong as I had misread a table and the moon was full on 31st August LAST year. It will be full tomorrow, 21st August 2013. OK, so we clarified that point.

I went to this site, following a google search and downloaded the dates and times of full moons for the period 1st January 2005 to 31st December 2013:

The data were not in the least bit friendly from a spreadsheet point of view and despite trying to concatenate and formatting cells and all sorts of things, I ended up hard coding all 111 bits of data to produce this chart:



Now, I know nothing about the mathematics of astronomy except that I expected to see a regular curve falling out of these data … and it didn’t. In reality, my original curve was a lot wilder than the above! I checked my typing and found some errors, I went to other sites and found different dates and times. I thought I should try to correct this work sheet to present a consensus chart but in the end realised I shouldn’t do that. After all, since I know nothing, how could I judge what to accept and what to reject except by way of deciding what looked good?

My problem with the above chart is the range either side of the 55th data point: the middle of 2009. It just doesn’t look right to me.

I moved on and after a difficult search for more data, I found loads of sites where people were happy for me to pay them to give me an Excel formula that would help me to predict the dates and times of full moons. I didn’t need any of that! I eventually found the dates, times and Julian Days from 1st January 1900 to 31st December 2099. I drew three charts from these data:




The above chart comprises all of the data I got from this web site: One bit of luck came my way with this chart too: in addition to days, months, years and times, this data series included Julian Days which are defined as follows:

The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Greenwich Mean Time, with Julian day number 0 assigned to the day starting at noon on January 1, 4713 BC proleptic Julian calendar (November 24, 4714 BC in the proleptic Gregorian calendar). For example, the Julian day number for 1 January 2000 was 2,451,545


What this means is that instead of worrying about all of the formatting work I did earlier, I could simply use the Julian format of, for example, 2,434,318.47 for 1st November 1952 … decimalised values!

I then prepared this table as the basis for my graphs, just as I had done with the first, error ridden, data set, above:



You can see the calendar and the Julian Days. To prepare the graphs I assigned the number 1 to the first full moon, 15th January 1900, number 2 to the second full moon and so on. The Diff column is the key to this whole exercise and it shows the difference in days between one full moon and the next, to two decimal places. That is, for example, there was a difference of 29.78 Julian Days between our first and second full moons. When these Numbers (X) and Differences (Y) are plotted on the graphs, this is what you see, above.

That first chart from this data series was far too full of data to demonstrate the full moon cycle adequately so what I did was to split the data into batches of 20 years: 1900 – 1920, 2000 – 2020 and so on; and I have shown the graphs for these two periods below:





You should be able to see that the data curves are smoother and more consistent than the first graph I was able to draw and present and I believe that these data are more consistent and accurate.

That’s it: when you sit me on the back of a motorbike and tell me that the moon is full, look what happens!