Again, as you look out from the front (morning) side of our hurtling planet, you see the Moon, at its last-quarter phase, cross inward over our orbit in front of us. Here for an American location is the morning-twilight scene nearest to the last-quarter moment.
See the end note about enlarging illustrations. The Moon is exaggerated 4 times in size. It is shown at its apparent position for the location on Earth; the arrows are along its path as seen from the center of the Earth, showing the difference made by parallax.
You can see that the Moon will in a few hours pass the point we mark, with a green “steering wheel,” as the direction toward which Earth is driving at this time in its orbit.
How long will it take Earth to reach, or be closest to, that point in space? – that is, the longitude where the Moon is now? I’ve written a small program to find out. The answer on this occasion is 3.98 hours – 3 hours and 59 minutes. That’s about the time it took me to write the program, but I’ll later be able to generalize it for other dates.
If the Moon were magically to stop where it is, at longitude 285.84° around the Sun, Earth would not center it, like a billiard ball propelled by a very exact player, but pass south of it, because it is at a latitude of 0.01° north of the ecliptic as seen from the Sun.
Fred Schaaf drew our attention to this question of the rarity of very close quarter-phase and Moon-latitude coincidences, which we still have to explore more exhaustively.
Saturn is also near the ahead-point, because it was at west quadrature, 90° from the Sun, on July 6. But it is enormously farther away.
Midpoint of the year
Several commenters stated the conundrum in approximately the more accurate way I thought of too late. There is no “middle day” in a leap year.
The midpoint is found by subtracting the Julian date of the start of the year (Jan. 1 0h) from the Julian date of the end of the year (Jan. 1 0h of the next year) and dividing by 2. Common years have 365 days, so the midpoint falls in the middle of a day; leap years have 366 days, so the midpoint falls at the division between two days. You can’t say that there is a “middle day,” unless you regard 0h as part of the day that it starts.
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This weblog maintains its right to be about astronomy or anything under the sun.
ILLUSTRATIONS in these posts are made with precision but have to be inserted in another format. You may be able to enlarge them on your monitor.
One way: right-click, and choose ”View image” or ”Open image in new tab”, then enlarge. Or choose ”Copy image”, then put it on your desktop, then open it. On an iPad or phone, use the finger gesture that enlarges (spreading with two fingers, or tapping and dragging with three fingers). Other methods have been suggested, such as dragging the image to the desktop and opening it in other ways.
Sometimes I make improvements or corrections to a post after publishing it. If you click on the title, rather than on ‘Read more’, I think you are sure to see the latest version. Or, if you click ‘Refresh’ or press function key 5, you’ll see the version change to the latest.