How does the lunar cycle affect the equinox in the Muslim Hijri calendar?

[Klarkaaaa15]

Hello, I found this question on the Internet and I would like to ask for help, if anyone knows the answer to it?

At what time of day at the autumnal equinox can we observe the third quarter moon on the western horizon?

 

[Baluncore]

Welcome to PF.

At what time of day at the autumnal equinox can we observe the third quarter moon on the western horizon?

The time will be at your local moon-set closest to the instant in time of the equinox.

Go to https://www.heavens-above.com
Set up your time and location.
Go to Astronomy, Sun, and read the date and time of the Autumn equinox.
Back out to main menu.
Go to Astronomy, Moon, and set the date and time of the equinox.
Then read off the time that the Moon sets, which is always towards the West.

The phase of the Moon, as it sets on the equinox, will be different depending on the year.

 

[Klarkaaaa15]

Okay, thank you very much.

 

[Baluncore]

At what time of day at the autumnal equinox can we observe the third quarter moon on the western horizon?

It becomes an easier problem if we rewrite the question. "At what local time of day, (in the two weeks either side of an equinox), do we observe the third quarter moon on the western horizon"?

Firstly, on days near an equinox, the Sun rises and sets at close to 6AM and 6PM.

The lunar first-quarter and third-quarter occur when the moon is half illuminated, because then it is 6 hours ahead of or 6 hours behind the Sun. The local time of moon-rise in the East, or moon-set in the West, must then be close to 12 midnight or 12 noon.

A third-quarter moon rises at midnight, then sets at midday, 12 noon. The third-quarter Moon will not be noticed setting by many people, due to the bright midday sunlight.

The answer to the question is therefore about midday, 12 noon.

 

[Baluncore]

Searching for the source of this question leads to the "sciencemadefun" website where it is suggested that the equinoxes are related to the phases of the moon.
Science Experience "Equinox - Oreo Phases of the Moon".
https://sciencemadefun.net/downloads/oreo_phases_moon.pdf
At the end of page 4 is written: "The moon phases are directly affected by the equinoxes because of the position of Earth to the Sun. During the autumnal equinox, the Moon phase is the Third Quarter Moon. During the Spring equinox, the Moon phase is the First Quarter Moon."

I disagree. Can the phases of our moon really be locked to the equinoxes ?
The lunar phases repeat on average every; 29.530575 days.
The equinoxes on Earth repeat every; 365.25636 days.
Therefore, there are (365.25636/29.530575=) 12.368752 lunar cycles per year.
12.368752 is not an integer, nor is it a simple fraction.
That shows that the phase of the moon cannot be locked to the equinoxes.

What is the approximate period for it to get even close to repeating ?
After 19 years, it will come within 1 hour of being synchronous.
After 15,265 years, it will come within 1 minute of being synchronous.

In the Muslim Hijri calendar, the months start on the day of the new moon, but then in that system, the equinox has the more variable date.