“Lunar Time”

Published 2021‑02‑14 at 01:20 UT by Pierre Paquette

As the third manned Moon mission, Apollo 13, was getting ready for launch, an unusual watch was introduced on the market by Helbros Watches: A “Moon Watch.” Designed in collaboration with Dr. Kenneth L. Franklin, astronomer at the Hayden Planetarium, it indicated time not in years, months, days, hours, minutes, and seconds, but in lunations, lunes, lunours, centilunours, and millilunours.

Here’s the little I managed to glean on the subject.

Measuring Lunar Time

In the late 1960s and (very) early 1970s, the Moon was the big rage. With the first manned lunar mission, Apollo 11, successfully placing two men on our natural satellite and bringing them back safely, every dream was allowed. The next steps were to not only send more astronauts, but even to install permanent Moon bases and eventually build cities on it. While the dream may, sadly, have faded from the collective unconscious of humans, it remains in the head of a few visionaries such as Elon Musk and some mentions of it have slipped on screen, for example in Star Trek: First Contact (1996):

COCHRANE: What, you don't have a moon in the twenty-fourth century?

RIKER: Sure we do. It looks a lot different. There are fifty million people living on the moon in my time. You can see Tycho City, New Berlin, even Lake Armstrong on a day like this.

Eventually, someone wondered how to measure time on the Moon: The 24-hour system used everywhere on Earth wouldn’t make sense, as the Sun is up for about 14.75 days at a time. A new system had to be devised. The most obvious was to use lunations—the time between one new moon and the next, which may be compared to a lunar day—and to divide them up. As one lunation is equal to 29.530587981 Earth days (29 d 12 h 44 min 02.8016 s), the most logical division was by 30: In Franklin’s system, these divisions are the lunes and are equal to slightly less than one Earth day. Each lune is in turn divided in 24 lunours equivalent to slightly less than an hour each. Then, in breaking with the centuries-old sexagesimal system, Franklin chose to divide each lunour in 100 centilunours of 10 millilunours each.

Helbros Watches started manufacturing special timepieces that used this system: One watch was given to United States President Richard Nixon, but apparently, very few other units were sold. One may only suppose that Earth-bound humans didn’t find it necessary to spend what must have been a good amount of money in order to get a watch that served no practical purpose on our planet.

Very little information is available on the exact correspondence of “lunar time” with Earth time. The only reference I found online was in an article published in the New York Times for April 8, 1970, which mentioned two data basepoints:

The Apollo 13 astronauts are scheduled to land on the moon at 45 centilunours past 22 lunours in the ninth lune of the 585th lunation, according to Dr. Kenneth L. Franklin, astronomer at the Hayden Planetarium.

To earthlings, that’s 9:55 P.M. Eastern standard time on April 15, 1970.

[. . .]

As the news conference ended at precisely 3 centilunes [sic] past 8 lunours in the first lune of the 585th lunation (11 A.M. yesterday [April 7, 1970, Eastern standard time]) [. . .]

Measuring the difference in lunar time and in Earth time between the two, and dividing one by the other, we come to the conclusion that the era of the system is on Julian day 2423430.71104534 (January 11, 1923, at 05:03:54 UT) and that each lunation lasts 29.4908439117438 Earth days. However, as pointed out above, the actual lunation is slightly longer than that, and the era doesn’t correspond to any notable event.

Playing a little with numbers, and sticking to the actual duration of a lunation, I found that using Julian day 2423407.013853 (December 18, 1922, at 12:19:56 UT), which corresponds to an actual new moon, and the proper duration for the lunation gives results very close to those mentioned by the New York Times article: 585‑1‑18‑88 and 585‑10‑9‑3, respectively. Now, removing 0.01469 to each unrounded lunation number gives precisely 585‑9‑22‑45 for the Apollo 13 lunar landing (if not for their accident…), just like in the article… and 585‑1‑8‑31 for the moment the press conference ended. Could there have been a typo in the original article? That is my belief—after all, they did write “centilunes” instead of “centilunours” in that paragraph—but it raises another question: Why subtract 0.01469?

Another thing to consider is that maybe it was impossible to construct a watch which precisely follows the mathematical system devised by Franklin, so maybe some corrections had to be made. The subtraction of 0.01469 may then apply only to 1970 or even part of it. Either way, when extending the system to 2021, I get an error of about 4 hours in the date of February’s new moon, which is very acceptable and normal, since each lunation is not exactly 29.530587981 days—this is an average value; known extremes are the “lunar month ended July 17, 1708 [which] lasted 29.271819 days (29 days, 6 hours, 31 minutes, and 25 seconds), [and] the one that ended on January 14, 1611 and lasted 29.832568 days (29 days, 19 hours, 58 minutes, and 54 seconds).”

Nevertheless, I decided to try and create an interactive simulation of the Helbros Moon watch or “Luna-Lectric,” as it seems to have been named (see image here). The mathematical algorithm used here is the following:

$$ \begin{array}{rcl} A & = & \displaystyle \frac {Julian\ Day - 2423407.013853} {29.530587981} - 0.01469 \\ \\ Lunation & = & \lfloor A \rfloor \\ \\ B & = & 30\ (A - Lunation) \\ \\ Lune & = & \lfloor B \rfloor \\ \\ C & = & 24\ (B - Lune) \\ \\ Lunour & = & \lfloor C \rfloor \\ \\ D & = & 100\ (C - Lunour) \\ \\ Centilunour & = & \lfloor D \rfloor \\ \\ Millilunour & = & \lfloor 100\ (D - Centilunour) \rfloor \\ \end{array}$$