by alter-ego » Tue Jan 22, 2019 6:38 am
Hey Nitpicker, it's good to hear from you again. I don't often visit the other forums so maybe I've just missed your posts. Anyway, long story short, I was totally missing the discussion (dim bulb last night I guess). I have just a few comments:
Nitpicker wrote: ↑Mon Jan 21, 2019 10:56 pm
Thinking more about this (still without working it all out completely), I think the antisolar point may be somewhat independent of the projection of the umbra at the Moon's distance.
Yes, that's true, and I confused myself by using the antisolar point here. You're right, the antisolar point is totally observer dependent and, in practice, independent of the Earth's shadow.
The antisolar point projects to infinity from the centre of the Sun, through the observer (does it not?). At infinity, it should not exhibit any parallax.
True definition, but except for the Earth's poles, the Sun
does display a varying parallax in the course of a day to any observer. Therefore the observer's antisolar point also changes by the same angle, i.e. as viewed from the sun, the observer's position on the celestial sphere does change by the parallax as the Earth rotates. With all that said,
it's clear the umbral center is the antisolar point for only a geocentric observer where the parallax is zero.
However, the projection of the umbra at the Moon's distance should exhibit the same diurnal parallax displacement as the Moon, I think. But unlike the Moon, the umbra's apparent topocentric motion against the stars forms retrograde loops (assuming the observer is far enough away from the Earth's poles), because the geocentric motion of the Sun is ~12 times slower than the geocentric motion of the Moon.
Yes, both Moon and Earth's shadow (viewed on the Moon) show the same daily parallax motion. Considering motion in right ascension, the threshold lunar orbital period for retrograde loops to begin (when the moon appears to just stop moving and doesn't reverse) is 3x longer, or the Sun's geocentric motion is ~4x slower than that of the Moon.
Hey Nitpicker, it's good to hear from you again. I don't often visit the other forums so maybe I've just missed your posts. Anyway, long story short, I was totally missing the discussion (dim bulb last night I guess). I have just a few comments:
[quote=Nitpicker post_id=289161 time=1548111365 user_id=141578]
Thinking more about this (still without working it all out completely), I think the antisolar point may be somewhat independent of the projection of the umbra at the Moon's distance.[/quote]
Yes, that's true, and I confused myself by using the antisolar point here. You're right, the antisolar point is totally observer dependent and, in practice, independent of the Earth's shadow.
[quote]The antisolar point projects to infinity from the centre of the Sun, through the observer (does it not?). At infinity, it should not exhibit any parallax.[/quote]
True definition, but except for the Earth's poles, the Sun [i]does[/i] display a varying parallax in the course of a day to any observer. Therefore the observer's antisolar point also changes by the same angle, i.e. as viewed from the sun, the observer's position on the celestial sphere does change by the parallax as the Earth rotates. With all that said, [u]it's clear the umbral center is the antisolar point for only a geocentric observer where the parallax is zero.
[/u]
[quote]However, the projection of the umbra at the Moon's distance should exhibit the same diurnal parallax displacement as the Moon, I think. But unlike the Moon, the umbra's apparent topocentric motion against the stars forms retrograde loops (assuming the observer is far enough away from the Earth's poles), because the geocentric motion of the Sun is ~12 times slower than the geocentric motion of the Moon.
[/quote]
Yes, both Moon and Earth's shadow (viewed on the Moon) show the same daily parallax motion. Considering motion in right ascension, the threshold lunar orbital period for retrograde loops to begin (when the moon appears to just stop moving and doesn't reverse) is 3x longer, or the Sun's geocentric motion is ~4x slower than that of the Moon.