The Moon will reach its first-quarter position, where it looks like a D, on May 23 (at about 11 by Universal Time).
Here is the after-sunset scene closest to the quarter phase moment
The Moon is exaggerated 4 times in size.
The point we mark as the “antapex of Earthh’s way” – that is, the direction away from which we are traveling – is about where the Moon is. We were there – how long ago?
The “Moon’s orbit” and “Moon as Signpost” sections of the Astronomical Companion explain that the Moon at first quarter is crossing Earth’s orbit outward, therefore behind us, therefore is seen from the rear or evening side of our planet, and is back along our orbit at the position in space where Earth was 3.5 hours ago – approximately.
Fred Schaaf, in 2008, took up this theme and “thought of checking for close co-incidences of First Quarter and Last Quarter Moons with the times that the Moon passes through the ascending node and descending node of its orbit”, because only when a quarter phase coincides closely with a node passage can we truly say that the Moon, being in the ecliptic plane, is at a position in space where the Earth just was or soon will be.
Fred in 2026 noticed that there was to be a coincidence of this kind on May 23. He explained it in the astronomy column he writes for The Press of Atlantic City<%>, New Jersey; called it a “rare” coincidence, and promised that in his next column he would tell his readers how rare such coincidences actually are.
He had hoped to be able to get this calculated information from an expert, who, however, was unavailable at the time. I offered to try to write a program (I call it phnod.for), found myself spending more days on it than I had expected, but it gives me a new tool for myself.
“How rare” depends on what timespan of years you cover, and what span of hours you choose as “coincidence”.
Here are some results. The last two columns are the time in hours from node to phase; and distance to the Moon in ER (Earth-radii). Earth travels about 16.8 ER per hour.
Hi Guy, from Sydney we get a close conjunction of the moon with Regulus at 4.41pm about 16 mins before sunset. So by 5.30 the pair should be easy to the naked eye but it will be a test to see it in binoculars earlier. By 9.10 pm it is first quarter with the moon still nearly 30 degrees elevation.
And of course the “D shape” is appropriate only for northern hemisphere viewers. Those of us in the southern hemisphere see a “C shape”. I remember being taught about the phases of the moon in science classes at school. We were given the mnemonic COD for the Latin verbs Crescere (to increase/grow) and Decrescere (to decrease/wane).
Very cool Guy!
Whoops! Lunar eclipse March 3.
When the waxing or waning quarter Moon is close to the Moon’s ascending or descending node, the Sun is about halfway from one eclipse season to the next. In 2026 there was a solar eclipse February 17 and a solar eclipse March 3. By ecliptic longitude the Sun will be 90 degrees from the Moon’ nodes on May 25, two and a half days after the waxing quarter Moon. There will be a solar eclipse August 12 and a lunar eclipse August 28. The Sun will again be square the Moon’s nodes on November 17, just five minutes after the waxing quarter Moon. (All dates are by UTC.) Now I’m curious why the November coincidence is so much closer, and why both the May and November coincidences coincide with the waxing quarter Moon … . Astronomy is full of rabbit holes!
I was aware of these points, wanted to limit toil for the day, and intend to do more and put it into a webs page pn the subject, under the “Astronomical Miscalleny”.
https://www.universalworkshop.com/astronomical-calendar-any-year/
Thank you, I’m looking forward to it. I hope my comment didn’t seem to imply that you had overlooked anything. There is always more to say about anything astronomical.
Congratulations on finishing your new program.
Twas also a good idea to include ER so one can calculate how many hours ago the Earth was where the moon is now. (Or for last quarter moons, how many hours ago the moon was where we are now).
Calculations would be close but not exact since the Earth travels faster at perihelion and slower at aphelion.