A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 Jan 21, 13:21 -0800
Tony, you wrote:
"It took me quite a lot of thinking to comprehend that while the part of ecliptic, where the Sun is now, is currently very deep under the equator - the opposite part of ecliptic is by the same amount above the equator. Plus Moon's ~5° on top of it."
Heh. Yep! One of the unfortunate things about jumping straight to the spherical trigonometry is that these basic things can slip right by. The Full Moon during any month and the Sun are always on opposite sides of the sky, give or take some degrees. Both travel on or near the ecliptic, and when there has been a recent lunar eclipse, you know that the Moon is quite close to the ecliptic. So a January Full Moon matches a July Noon Sun in terms of maximum altitude and general progress across the sky.
In June, when you see the Full Moon in the evening, note how low it hangs in the sky... Note how its brightness is somewhat muted and for a long stretch of the night its color is bit yellow-tinted by low altitude absorption in the air. Its light casts long beams that extend under overhanging foliage and illuminate our living spaces. It's nice, right? Then contrrast that with the December Full Moon. It rides high like the Sun in summer. Its light is undiminished and bluer thanks to passing more nearly overhead. It shines down on us, doesn't illuminate beneath low-hanging foliage and only barely lights up our homes. It's harsher. The summer moon is pleasant. The winter moon is harsh. And finally consider how these strictly astronomical differences have impacted literature and the arts....
Finally, some key geometry. You want to know the meridan passage altitude of some celestial object. You know your latitude and that body's declination. The key to this is to remember that the celestial equator is the zero of declination, and to remember that the celestial equator runs across your sky from exactly due east, climbing up at an angle away from vertical that is equal to your latitude, then reaches a maximum altitude of 90-latitude, and sets again exactly due west with the same inclination. All declinations get added on (up or down) from the celestial equator. So on the meridian at 39°N, for example, if I know that some planet has declination of 10°N, I can immediately say that the max altitude (on the meridian) will be 51+10 or 61°. In that same latitude, knowing that the Sun's dec ranges from 23.5 S to 23.5 N, I can easily determine that the range in altitude is from 51-23.5 to 51+23.5, or from 27.5° to 74.5°.
BTW, yes, it's quite normal to over-estimate altitudes above 45°. And anything about 70° feels like straight up ...until you check properly by looking up a pole or a building corner for a better vertical.