Calculate the Moon's Synodic Period from a graph

[TFM]

Homework Statement

Calculate the Moon's Synodic Period

Homework Equations

N/A

The Attempt at a Solution

I am supposed to plot a graph of Time(y-axis) against Phase (x-axis), where phases is not a sin curve but a straight line, because we are adding upwards, ie from a new moon to ful is from 1/8 -> 8/8, then it goes back down, but the phase plotted continues to go up, from 1 1/8 -> 2, and so on, giving a nice straight line. Now we are supposed to plot a straight line through the data, which I have done in Excel, and it has given me a gradient of 0.0713.

Can anyone give me any clues how you are supposed to get the period from this?

Thanks in advanced,

TFM

 

[Carid]

The Synodic period is, we read, the time between two full moons.

Any chance of seeing that graph of yours?

 

[TFM]

Okay I have attached a copy of my Graph. It features the sin wave graph, as well as the straight line graph, plotted on the same axies.

TFM

 

[Carid]

TFM,

Consulting internet gives us a value of 29.5 days for the synodic period.

Looking at your graph I'm a bit at a loss to to how we can derive this value.

If we start from the 240 value on the X axis which you say represents the phase, this would correspond to 30 full moon periods. Trace a line up to the curve and turn left. We meet the Y axis roughly at a value of 17. Now the question is what does this value mean?

Also your blue sine curve at the bottom seems to be going forwards and backwards in time. A very interesting property but not one observed when looking at the moon.

If I assume you've got time along the X axis (as we usually do) and phase up the Y axis then I'm still not much clearer. I think we need some units on both these axes so we know what the graph is trying to represent.

 

[TFM]

The Day (a Julian Date version) goes along the x-axis, and the Phase Fraction goes along the Y-Axis.

The Sin curve is the fractions, and it oscillates between 0 and 1 in 1/8 sizes. The Straight Line is the same, but the phase increases, this is what we was told to do:

Determined purely from phase observations
– Convert date to day number (2008 Feb 1 12:00 = 32.5)
– Convert phase to be monotonically increasing
– Fit straight line to obtain synodic period and error

TFM

 

[TFM]

I think I have worked a way to calculate the Synodic Period, but it doesn't seem to use the line:

The Synodic Period is basically the tiome between one full moon and the next. I have 10 consecutive new moon to new moon. And we have a time for that duration, using this, I can get a synodic period of 28.53, not quite right, but quite close, but the only trouble is it doesn't really use the graph...?

We also have to work out the sidereal period, using a similar graph, but with Ecliptic Longitude in degrees along the y-axis, now this graph has a gradient of 13.15, which, if you double it gives a value of 26.3, which again is close to the value I have found of 27.3

Does this seem right?

TFM

 

[Carid]

TFM,

Two points. I'm still in the dark as to what you are listing on the Y axis.

If the 10 lunar synodic cycles (80 lunar 1/8 phases) takes 285.3 days along the X axis, what does this correspond to on the Y axis if we go via the straight line curve? It seems to point to the number 19.

Your synodic period value of 28.53 days has a >3% error when compared with the official value of 29.5. Any idea where the error has come from?

 

[TFM]

TFM,

Two points. I'm still in the dark as to what you are listing on the Y axis.

[\quote]

The Y axis is basically just the phase, so if the sin plot was on its own, it would go from 0 to 1 in 1.8 intervals, however, we were ytold to keep the value going up, so after the first full moon, 1, instead of the value going back down to 0, we had to add on, so when the moon went back down to 7/8, we had to plot it as 1 1/8, 5/8 went to 1 3/8, and so on

If the 10 lunar synodic cycles (80 lunar 1/8 phases) takes 285.3 days along the X axis, what does this correspond to on the Y axis if we go via the straight line curve? It seems to point to the number 19. [\QUOTE]

well the 19 is the number of half cycles, see above note.

Your synodic period value of 28.53 days has a >3% error when compared with the official value of 29.5. Any idea where the error has come from?

This is actually good value for the error, the synodic plot comes from my personal observations of the moon phase, so the value would be x/8 plus or minus 1/8 - since it can be difficult to accurately see what fraction the moon is in, sometimes they look very similar. An error of 2/8 corresponds to 0.25, which is very close to 0.3 you stated, especially when I sometimes have a full moon lasting two days in a row!

 

[Carid]

TFM,

Seems you have sorted it out.
Personally I would have counted in 1/8 phases up the Y axis not half cycles!
Good reasoning for the cause of your error but it still works out as one day per lunar cycle and taken over ten months that seems rather a lot to be out. I can accept that you are a day or two out on the first observation and a day or two out on the last observation, but in between you know the number of days and the number of lunar cycles.

 

[TFM]

See, I thought it would have been best to keep the sin wave version, and then try and fit a sin curve on that, okay, not easy to do, but would have been easier to figure out.

Personally I would have counted in 1/8 phases up the Y axis not half cycles!

I probably would have done that, or in whole cycles, but that is just the graph Excel gave me from the data.


Thanks,

TFM

 

[Carid]

TFM,

Excel is a good slave and a bad master!