Before you decide where to put your EME dish, you of course want to know the place that will give minimal obstruction between your dish and the moon.
Once you have determined the location of that place, it is where your dish should be located.
The azimuth of moonrise and moonset and the height of the moon at any particular azimuth depends on the lunar declination and your latitude.
Lunar declination varies over time, with several intertwined cycles with periods of 27.2 days, 6 months, and 18.6 years.
So you need to know the range of declinations over these cycles, you need to know your latitude, and then you can calculate the range of azimuths that will occur for moonrise and moonset at your location, and you can also calculate the minumum elevation of the moon for any particular azimuth. Once you know this information, you can do a site survey of your QTH and the optimal location for your dish will become clear.
If you wish, you can read a bit about lunar declination here.
But you don't need to read about lunar declination if you don't wish to. I've created a spreadsheet that will give you all the information that you need to figure out where to place your dish once you've done a site survey for your QTH. You can download the spreadsheet here.
An illustration of that spreadsheet is below. It is based on the equation sin(D) = sin(L)*sin(H) + cos(L)*cos(H)*cos(AZ) where D = Declination, L = latitude, H = Height, and AZ = Azimuth, all in radians.
Near the top of the spreadsheet you enter your latitude in decimal degrees, as well as an estimation of the elevation of the horizon in degrees for both moonrise and moonset. I generally begin with these two elevations set to zero; they can be adjusted once you see the range of azimuths subtended by moonrise and moonset and then survey your site over that range of azimuths to determine your horizon's actual elevation over that range of azimuths.
Just below that section of the spreadsheet are two cells where you can enter the declination for moonrise and moonset and then see the azimuth for moonrise and moonset for those declination values. This section was used by me when I was checking the accuracy of the spreadsheet. This section is not needed for siting your array/dish, and you can ignore it.
Once you have, as described above, filled in the cells for your latitude and the estimated elevation of the horizon at moonrise and moonset, then the azimuth for moonrise and the azimuth for moonset will be calculated for representative declination values from the greatest possible negative declination value to the greatest possible positive declination value. The cells containing the results for these calculated azimuth values are colored yellow and displayed next to the headings "MOONRISE" and "MOONSET", respectively:
Below these tables is a section labeled "ARBITRARY AZIMUTH" where you can enter an arbitrary azimuth value. When you enter an arbitrary
azimuth value, then the moon elevation that will occur at that azimuth for the full range of possible declination values will be displayed. This is useful for determining if a potential obstruction at a
particular azimuth will in fact present a problem with EME from your location.
At the bottom of the spreadsheet, you can also enter both an arbitrary azimuth and an arbitrary declination and you will be given the moon
elevation that occurs at your location for that combination of values. I used this section for checking the accuracy of the spreadsheet calculations, and you can ignore this portion of the spreadsheet.
This spreadsheet is a LibreOffice spreadsheet, so you need LibreOffice or OpenOffice to run it. LibreOffice is free and open-source and is available at: https://www.libreoffice.org/
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