Moon local time calculator - v. 2.3.3
What time is it on the moon?

by Luca Cassioli 2019

Moon data calculated for time:
Earth Local:
Earth UTC: -
Illuminated percentage: -
Phase percentage: -
Moon age: -
Phase name: -
Sunrise selenographic longitude(1): -
Sunset selenographic longitude: -
Colongitude: -(*)
Phase from colongitude: -

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Vikram landing site (Chandrayaan 2): Lat, Lon = 70.90267°S , 22.78110°E, or -70.90267, 22.7811 (use Lon, Lat, Alt = 22.7811, -70.90267, 1737 for NASA Horizons)
Yutu 2 landing site (Chang'e 4): Lat, Lon = 45.4446°S , 177.5991°E, or -45.4446, 177.5991 (use Lon, Lat, Alt = 177.5991, -45.4446, 1737 for NASA Horizons)
Beresheet crash site: Lat, Lon = 32.5956°N, 19.3496°E, or 2.5956, 19.3496 (use Lon, Lat, Alt = 19.3496, 2.5956, 1737 for NASA Horizons)


(1)
See picture below

(*) All data in the table are based on this value.

(**)
Midnight: 00:00
Sunrise: 06:00
Noon: 12:00
Sunset: 18:00

(***)
00:00 = New Moon (Phase = 0%)
06:00 = First quarter = sunrise (Phase = 25%)
12:00 = Full Moon (Phase = 50%)
18:00 = Last quarter = sunset (Phase = 75%)


Credits
Calculate colongitude: http://www.inconstantmoon.com/calt_topo.htm
Calculate Moon phase: https://github.com/mourner/suncalc (modded to add Moon phases strings)
Draw moon phase: https://codepen.io/anowodzinski/full/ZWKXPQ
Calculate Moon Reference Time and Local Moon Time: Luca Cassioli (see below for algorithm) - cassioli at libero dot it
Moon reference systems image: Luca Cassioli, public domain, no copyright - cassioli at libero dot it

Local Moon time alogorithm
A lunar day lasts 29.53 Earth days.
An Earth day lasts approximately 24 hours.
Moon age is calculated as "days since last new moon".
Moon phase is ratio between Moon age and lunar day length.
Hence frome moon phase value you can calculate "moon time":
Sun as seen from Moon surface rises and sets just like on Earth, just much more slowly; but if it rises and sets, then we have a sunrise, a noon, a sunset and a midnight. But from midnight to midnight, 29.53 days pass rather than 24 hours. To get a raw, intuitive idea of how long it is until sunrise or sunset, I created definitions "Moon Reference Time" and "Moon Local Time", or "Selenotime".
If it's 17:30, it's half a selenhour to sunset (18:00).
What is this for? To get a quick&dirt idea of how long shadows are on surface.

At 06:00 (sunrise) objects will cast longest shadows;
At 12:00 objects will not cast any shadow;
At 18:00 they will cast longest shadows;
From 18:00 to 06:00 it's night. From 06:00 to 18:00 it's daylight.

But you may also need to know exactly how long it is in Earth days/hours to sunrise or sunset: this can be calculated from "colongitude", or "selenographic West longitude of sunrise terminator w.r.t. Moon prime meridian, which points approximately points toward Earth". Adding 90° to colongitude you get how many degrees sunrise terminator moved from last new moon; divided by 360° and multiplied by lunar day length 29.53 you get moon age, which is how many days passed from last new moon; correlating this angle to longitude of any point on surface you can determine angular distance (and hence time distance) of point from last/next sunrise and last/next sunset.
Calculations starting from colongitude and from Moon phase value should give same results, but for some reasons calculations of Moon data za href="https://the-moon.us/wiki/Colongitude">is not always precise, so you can see slight differences (some 1%) in data.
Colongitude appears to be a very disregarded moon data on internet: the only SW capable of calculating it which I was ablew to find is this by T. Wesley, without source code.
Moon local time is instead something which just does not exist anywhere (at least after 2 months looking for it on Google). But with Moon Race started again in 2018, and with Lunar Reconaissance Orbiter flying over Moon surface and shooting 30cm/pixel images, knowing when a lander on the Moon is visible when LRO passes over it could be useful to somebody. Hence this page.
You can also use this other page to plot distance of LRO from any point on Moon surface (not just altitude).


Useful pages
Prime meridians UAI definitions for some celestial bodies:

Version 2.3.4 - 9 august 2020