Quote:
Originally Posted by Rockin Robbins
The answer is that the full moon MUST be 180 degrees opposite the sun. Therefore, if the sun sets at 6:30 pm, the full moon MUST rise at that time.
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Must it? Take a look at
this image. The Moon is 100% illuminated, but the elongation (apparent angle from the Sun) is only 177°25'51"...over two and a half degrees less than 180°. How is this possible?
You may have noticed that the equation I posted earlier for finding the separation angle or elongation contained two types of variables. "GHA" or Greenwich Hour Angle, and "Dec" or Declination. GHA is similar to longitude - it's a measure of the distance of a body from the Greenwich meridian in the horizontal axis. Unlike longitude, however, GHA is only measured westward, through 360°. Declination is similar to latitude. It's a measure of the distance of a body from the celestial equator (an extension of the Earth's equator out into space) in the vertical axis. Finding the elongation of a body is not as simple as subtracting one GHA from another. Declination must also be taken into account.
Also apparent in the previous image is the time which the [100%] full Moon will set on this date at this location (July 9th, 2017 at 45°N, 0°E): 04:37 UTC. Now, have a look at
this image. It shows that the Sun, at the same location on the same date, rose at 04:28 UTC. IOW, the Sun and the full Moon are both in the sky at the same time. There is a nine minute window between when the Sun rises and the Moon sets.
Nine minutes may not seem like much, but consider this: the Earth rotates through 360° in [roughly] 24 hours
*. That means that for each second, the Earth rotates 15 arc seconds. That causes celestial bodies to appear to change position by 15" each second. So, when determining longitude from the position of a celestial body, an error of 4 seconds of time equates to an error of 1 nautical mile of longitude. That means that an error of nine minutes of time equals an error of
135 nautical miles of longitude. That's about two thirds of the distance from New York City to Washington D.C. (At the equator. Differences in longitude become smaller with regard to absolute distance as latitude increases toward the poles.)
As for the statement that "Reality ALWAYS trumps math."...well, I almost don't even know where to begin responding to that. Spherical trigonometry is how navigation is actually done,
in reality. And not just celestial. Math is a tool which allows us to predict reality with very high precision. It's how the almanacs and sight reduction tables are generated, it's at the heart of how GPS works, and it even helps us understand reality itself through theoretical and experimental physics (a topic which you alluded to in your previous post). You even used it yourself in describing how the Moon changes position relative to the Sun. Without math, things like modern navigation, astronomy and physics would not be possible. Again, just because you haven't taken the time to understand it doesn't invalidate it in any way.
Now, your synopsis of how celestial navigation works is fairly good. Well, that's how "modern" celnav is supposed to work, generally. However, that's not how celestial navigation was
actually done for the majority of the time it was used before the introduction of GPS, Loran and other methods of fixing one's position. The concept of "circles of position", or more practically, "lines of position" (LOPs) was a fairly late comer in the history of navigation. Most often, the navigator would stick to the routine of longitude by time sight in the morning, latitude by noon sight and another longitude by time sight in the evening. Longitudes and latitudes would be "run up" to each other to produce a "fix".
We can debate the finer points of celnav until the cows come home. But, although I don't claim to be an "expert" in
any field, I'm asking you to trust that I just might be a little more knowledgeable in this one than most people. I'm not saying that you're completely wrong. You seem like a relatively intelligent person. I'm just saying that, whatever is causing DaveR's problem, whether it's SH's model or perhaps a bit of understandable confusion on his part...I might be uniquely suited to ascertain exactly what is causing it and what can be done to remedy the situation. In the end, our collective enjoyment of these sims is what we all have in common, for whatever reason. I'd just like to contribute what I can to that end. Besides that, this is a relatively complex subject and this thread (or even this forum) may not be the place to get into such technicalities.
*We haven't even gotten into the difference between UTC, UT1 and the fact that the Earth's rotation is slowing, causing us to have to insert "leap seconds" into UTC to keep our clocks in step with "actual" solar time.