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Lunar Parallax exercise

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About this observation
Observer
Peter Anderson
Time of observation
08/03/2012 - 11:00
Object
Moon
Observing location
Brisbane, Australia
Equipment
CelestronCPC11 at F10 prime focus
Exposure
Each image 1/200sec 100 ISO Canon 300D on 8th& 9th March 2012
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Many years ago I read an item by Patrick Moore that because of their location, northern hemisphere observers had a slightly better view of far northern regions of the Moon as southern hemisphere observers did for the far southern regions.  He specifically gave an example of an observer in England and one in South Africa, being at similar longitudes, but separated by close to 90 degrees of latitude, observing at the Moon at the same time. He stated that their viewpoint would be slightly different.

The Moon is 27% the diameter of the Earth, and subtends an angular diameter of half a degree, so by rough calculation - dependent upon the orientation of the Earth, the difference in viewpoint between the two stations mentioned would be around one degree or slightly more. How much difference would this make for practical purposes? A degree is 30km on the lunar surface but it would be incredibly foreshortened on the lunar limb. Still the profile would be subtly changed and  features very near the north or south limbs would be very slightly better or worse oriented for viewing and interpretation.

So I considered how I might seek to investigate Patrick Moore’s example.  I decided that I could use the rotation of the Earth over six hours to provide a similar movement but in the East-West direction. I live in Brisbane at 27.5 degrees south latitude so, unlike high latitudes, the physical movement of the Earth in its rotation during the period of of six hours is significant especially if the Moon was on the meridian midway between observations. It all fell into place. I would image the east and west limbs of the full moon at 9pm and 3am when it had sufficient altitude for detailed imaging. I had a choice and decided that near equinox when the Sun and Moon both rose near true East and then set near true West would simplify things. Since March was then only some weeks away, the full Moon near the March equinox was chosen.

Then I considered some of the other factors.  The Moon’s orbit is not circular. In fact its distance from the Earth varies in a proportion of around 7:8.  When it is closer and under a greater gravitational pull from the Earth, it travels faster laterally across the sky. The reverse occurs when it is further away. Since it keeps one face to us and its rotation period remains constant, this means as the month progresses we first see a little more around one limb and then around the other.  Because its orbit is inclined 5 degrees we also see a little over each of the polar regions alternately. The effect is called libration and allows us to see 59% of the total of the Moon’s surface. Looking at the tables of libration, the east-west and north-south movements are overlaid and effectively go through the whole cycle each lunation or lunar month. An examination of the tables indicated that this effect would only be a fraction of the movement I was seeking to record over the 6 hours time span, so for practical purposes I could disregard it.

And so I set up to take the photographs.  The first at 9pm was only 80 minutes after full moon and both east and west limbs were nicely illuminated. By 3am though, the terminator had moved on and the limb on the west facing side was lost as the terminator advanced. No matter, I would concentrate on the other one and continue taking a few photos all around the limb.

When I came to examine the images, I realised that the changed perspective was very tiny indeed. Perhaps a mountain or feature on the very limb presented a slightly different outline...but I had inadvertently stumbled upon a similar effect which was somewhat more obvious in the northern and southern polar regions. This was unexpected and had nothing to do with the rotation of the Earth in the six hours that had elapsed but rather the motion of the Moon itself.

As we know from our viewpoint the sun moves north or south at a fairly fast rate as it passes the equinoxes in March and September. By contrast near the solstices in mid-summer and mid-winter the Sun is virtually stationary in declination. However the Moon traverses the whole sky in a month and goes through this whole cycle from north to south in the course of this monthly orbit, so travels thirteen times faster than the Sun. This means that over the several days around full moon near the March and September equinoxes, when its declination is changing at the maximum rate, the Moon will move 4 or even 5 degrees in declination in each 24 hour period.  On the date I had chosen it moved 5° 29’. In six hours this is a 1.37° which was more than the figure I had set out to achieve.

And so my result reveals a definite, but still very slight, effect on the far northern and southern polar areas of the Moon. The images show the northern limb area and craters marked ‘a’ and ‘b’ are clearly better presented in the right hand (later) image as the Moon tracked south presenting the the northern limb at a slightly better angle.

In summary, the effect over this short period of six hours is extremely slight and certainly not worth the effort except as a demonstration. Nevertheless the movement is detectable, and in this case the Moon’s position had changed, and not that of the observer on the Earth (the London and Cape Town example). However the effect was just the same though it was the Moon that had moved south, and not the observer.

I also learned a lesson. The Moon is a moving target, and there are many factors that need to be taken into consideration.  Finally, it did prove Patrick Moore’s rather obvious assertion, but not quite in the way I had intended.

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