I invented my own phrase for a sky gazing experience; "Perfect Full Moon" It is something that I think most people could observe perhaps 1 or 2 times in a lifetime. I define it as follows. Each lunar month, the time of full moon is an instant. At that instant, there will be one place seeing moon rise at the same time as sunset, and another place (180 degrees away) seeing moon set at the same time as sunrise. Actually it is not two points but a great circle. The great circle is close to loci of longitude but not exactly. The two points are places where the great circle falls close (+1 one nautical minute) to a city with a recognizable name. Often, the perfect full moon great circles do not intersect any populated place. Lots of things can prevent you from seeing it. Clouds, no view of horizon, etc, but the biggest factor is not knowing when and where to expect it. I would like to make up a table of places and dates to expect perfect full moons. My question: What astronomical tables, or web sites might help me calculate that table? I think that I need a table of time/date/lat/lon of where the moon it at zenith at the instant of full moon. Then using that point, I need to plot an equatorial great circle where that point is the pole. I tried it a year ago using Stellarium software on my PC plus Google Earth and a spreadsheet. It was very tedious and error prone. I should also ask; has anyone beaten me to is and already calculated the perfect full moon table?
If sun, moon and earth are aligned in the way you describe, you do not get a full moon, you get a lunar eclipse. Most of the time, the moon is a bit "below" or "above" the point of a perfect alignment, so your great circle gets reduced to two points. In general, the great circle where the angles are the same will be quite far away from the poles - up to 23°, depending on the season. There are tons of websites and programs that can determine the time of full moon and the time of sunrise/set. Note that +-1 nautical mile won't make any visible difference for an observer on earth.
Seems to me that those two instants are not the same instant. Places 180 degrees apart don't experience sunrise/sunset at exactly the same time nor do they see moonrise/moonset at exactly the same time, so sunrise/moonset at one location does not correspond exactly to sunset/moonrise at 180 degrees around the Earth.
Thank you MFB. After contemplating your comment, I realize that there will be two great circles, not one. One circle normal to the earth-sun axis and the other normal to the earth-moon axis. The two circles intersect in two points as you say. That makes seeing a perfect full moon an even rarer event and suggests that there may be latitudes from which it is never visible (perhaps latitudes >23 degrees?). Also thanks to PHINDS. I'm sure that you're right. My simplistic thinking about geometric models is inadequate. That's why I'm seeking tables. Further thinking makes me focus on tables of sunrise/set moonrise/set times. I need to pick a location and search for occurrences of ABS(sunset-moonrise) time difference less than a threshold. If those tables include the real life complexities, I don't need to make any (probably incorrect) geometric models. My GPS chart plotter gives me times for sunrise/set moonrise/set at any point on the globe for any date. It must have an algorithm, or a curve fit. Since all brands seem to have this feature, I guess that they must have gotten the algorithm from a public source. Can anyone help point me to that source?
Whoops. Found the algorithms. I should have tried harder before posting the question here. Thanks for helping to clarify my thinking.