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I found it mentioned in ancient Arabic astronomic book Kitāb al-Amwāl by Ibn Qutaybah (889 AD)

Cresent can't be seen in the morning in the east in front of the sun and in the evening i the west behind the sun in the same day

ولا يمكن أن يرى الهلال بالغداة فى المشرق بين يدى الشمس، وبالعشىّ فى المغرب خلف الشمس فى يوم واحد.

Is this information valid for all locations and dates

Sun and Moon have very near orbits and both daily apparent motion (east-west) but moon has apparent retarding motion (west-east) could this retarding motion make the sun catch the moon in the first day of lunar month?

could this happen in normal (non polar) latitudes?

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  • $\begingroup$ This will be quite a "sophisticated task" to answer in a reasonable amount of space; "be seen" and "in the same day" and "all locations" and "all dates" are all open to some amount of interpretation. Circa 4.5 billion years ago the Moon was a lot closer and moved more quickly (length of day was different too), and there could have been really tall mountains, and one can look through a long tube the way some people do to see Venus in the daytime. How long is a day at the south pole? Is it possible to constrain at least some of those four phrases to allow for a science-based answer? Thanks! $\endgroup$ – uhoh Aug 12 at 3:39
  • $\begingroup$ Of course if one is like @JamesK and only answers the title and ignores "Is this information valid for all locations and dates?" then its easier. $\endgroup$ – uhoh Aug 12 at 3:55
  • $\begingroup$ @uhoh might simplify that response to "do you want a visible crescent or just a physical rising & setting of the moon?" :-) $\endgroup$ – Carl Witthoft Aug 12 at 15:39
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It's possible, but it's not very impressive.

This month (August 2020 New Moon) from, say central Asia (I used Aral for my simulation on Stellarium) The moon rises at 05:48 local time (UTC+5) and the sun a few minutes later at 06:01

Of course you can't see the moon rise, it is the day of the new moon and it is invisible.

Then in the evening, the sun sets at 19:51 and the moon sets at 20:28. Again, it is not visible at this time. (I've not accounted for atmospheric refraction here, which will change the times but not the example.)

This doesn't happen from all locations every month, it just depends on whether the sun passes the moon during the day or during the night, I'd venture a guess that in any particular month, half the world will have the moon rise before, and set after the sun on the date of the new moon. 

So this isn't valid for all locations. If you were in America, then the moon would pass the sun during the night: on one day the moon would rise and set before the sun, the next day it would rise and set after the sun.

Its is also not valid for all dates at a single location. It is possible that the New moon in September might pass the sun during the day when viewed from America, but not from Asia (though I haven't checked)

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To answer your title question ("can moon rise before sun and set after it in the same day"), the answer is "yes," but the caveat is "barely."

The basic reason is that a solar day is approximately 24 hours. The equivalent "lunar day" (the moon returning to the exact same spot in our sky) is approximately 50 minutes longer. So, as long as the moon rises 49 minutes or less before the sun rises, then it will technically set after the sun by 1 minute or more. So, it basically happens during a new moon.

Because it happens during a new moon, it will be almost impossible to see with the unaided eye, if impossible, period. You would have to know pretty much exactly where to look, and look just before the sun rose, and just after the sun set, for it to be visible, otherwise the sky brightness would be too much for you to see it.

To answer other parts of your question, this happens at some time during the year pretty much everywhere on Earth, and the ≈+50 minutes that the moon takes to return to the same spot in the sky versus the sun does not depend on the lunar phase. It would happen for approximately half the planet every new moon (for the other half of the planet, the exact time when the moon is least full will be during that part of the planet's night). You also have to the sun and moon rise and set, so if you are some place on Earth where that does not happen, then this won't happen (such as in the arctic or antarctic circles during their summer, or during their winter, you would have to get it on an equinox).

These numbers will vary slightly based on where the moon is in its orbit (aphelion vs perihelion will change that +50 minute number), local viewing conditions will affect your ability to see the crescent, as will where the moon is relative to lunar nodes (if the moon is on a node when it's new, you get a solar eclipse; if the moon is farthest from a node during a new moon, the crescent will be very slightly more visible).

So, the text you quote is not correct from a technical standpoint. From a practical standpoint of the ability for someone more than a millennium ago to know exactly where and when to look, and even a modern person's ability to view it without an aid, then the text could be considered effectively correct simply due to the limits of the human visual system.

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    $\begingroup$ Thanks for taking the time and space to address several interesting aspects of the question! $\endgroup$ – uhoh Aug 13 at 2:57
  • $\begingroup$ At best the crescent moon will be within about 12.5 degrees of the sun. – Wayfaring Stranger 10 mins ago $\endgroup$ – Wayfaring Stranger Aug 16 at 15:56
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There is another fact that the previous answers did not consider.

Once in ~18.6 years, the Moon reaches its maximum declination of roughly 28°36' (the Earth inclination of 23°27' plus the lunar orbit inclination of 5°9'). This means that at latitudes larger than (90°- 28°36') = 61°24' it becomes circumpolar (the get a "midday moon" even if they are below the polar circle).

At latitudes lower than 61°, on that day the Moon will indeed rise and set, but much further north (south in the Southern Hemisphere) than the Sun. If this happens close to the Summer Solstice for that hemisphere, the phenomena described by the previous answers will be more than "barely" visible.

Take for instance what will happen in Edinburgh (Scotland, L=56°N) on 25th June 2025. The waning crescent Moon will rise at 03:45, 43 minutes before the Sun, and set as waxing crescent at 23:07, 55 minutes after it (local times). On the same day in Palermo (Italy, at just L=38°N!) the same will happen, with the waning Moon anticipating the sunrise by 33 minutes and setting 35 minutes after the sunset.

So not only it is possible to see the quoted phenomenon from mid-latitudes, but the intervals between sunrise/sunset and moonrise/moonset can be much larger than those quoted by Stuart Robbins. However, such events are rare.

A little extra: because of the same considerations, it is indeed possible to see the FULL Moon both before dawn and after dusk on the same day even at latitudes much farther away from the poles. For instance, take what will happen on 22 June 2024 in Puerto Montt (Chile, at just L=41°30 S): the Full Moon will rise 35 minutes before the Sun sets and set 47 minutes after the Sun rises, being visible for the whole night. This is in some sense the opposite of what your question was about.

Ciao!

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