The assumption in the top diagram is that the Sun is basically infinitely far away, so that a line toward the Sun from Alexandria would go in the same direction in space as a line toward the Sun from Syene. But the lines to the Zenith from Syene and Alexandria would go in different directions. . .and how much different, the 7 degrees bit, permits you to determine what percentage of the way around the Earth it is from Alexandria to Syene. 1st quarter the following Saturday. The Moon is a bit farther away during an annular eclipse. We'd have solar eclipses every time the Moon was new if the Moon's orbit coincided with the ecliptic.
Solar eclipses are only apparent to people who are in or near the very narrow path of the shadow.
A Full Moon Rises as the Sun sets, so roughly 6 p.m. A Moon that is transiting about sunset is about 90 degrees to the east of the Sun in the sky so it must be 1st quarter. The Moon is moving prograde among the stars faster than Venus, so as they both set the separation between them increases. Back to Astro 100 problem page.