Sky and Telescope, May, 1954, pp. 216-217

Mars Clock and Calendar

by I. M. Levitt

Fels Planetarium
The Franklin Institute

Time, calendar date, and year are shown for Earth and Mars in the Levitt-Mentzer clock. The numbers around the face indicate Mars time, and the three smaller dials (here arbitrarily set) register Martian date, terrestrial time, and terrestrial date. The clock, which is 16 by 16 by 14 inches in size, can also be run at over 2,000 times its normal rate to serve as a computing device for time-conversion problems.


BASIC DATA FOR A MARS CLOCK

Sidereal period of Mars = 686.9797 solar days.
The Martian sidereal day = 24h 37m 22.6679s in mean solar units,
= 1.02595680 solar days.
686.9797 ¸ 1.02595680 = 669.599031 Martian sidereal days,
= 668.599051 Martian solar days.
One Martian solar day = 1 + 1/668.599051 Martian sidereal days.
The excess of the Martian solar day over its sidereal day is
1.02595680 - 668.599051 = 2 - 122.5791 in mean solar units.
The Martian solar day = 24h 39m 35.2470s mean solar units.


MARTIAN CALENDAR DATA

January 1, 1954, is 2,434,743.5 solar days after January 1, 4713 B.C., Greenwich noon. Since 2,434,743.5 / 668.599051 is 3641.5, January 1, 1954, falls in the Martian year 3641.

We adopt 668.6 for the number of Martian solar days in the Mars calendar year. Let two years out of every five be ordinary years of 668 days; the others will have 669 days. The calendar year is too long by 0.6 - 0.599051, which is 0.000949 day per year. This means that the calendar year will be out one day in about 1,000 years. Therefore, drop one day every 10th century.

Then the calendar year is 0.001 - 0.000949, or 0.000051 day too long, but the error amounts to only one day in 20,000 years.


One of the first pieces of scientific apparatus that the world's future pioneers into outer space will require is a timepiece that accurately records the 24 hours of the earth's day, and which may be instantly compared with time established for a planet, such as Mars, that may be the object of exploration. Even the return to Earth will probably have to be started at a precise hour, minute, and second of earth time, in order to rendezvous with an earth satellite station.

The construction of a chronometer that ties together the time on the earth and on Mars is necessarily complicated, because of the difference in rotation periods for these two planets. The earth turns once in 23 hours, 56 minutes, and four seconds, which we call the sidereal day. However, the day we normally use is the mean solar day of 24 hours by our clocks. Mars rotates more slowly than the earth - its sidereal day is 24 hours, 37 minutes, and 23 seconds. Its solar day is about 2.7 per cent longer than the solar day on earth.

The Hamilton space clock illustrated here was constructed from the writer's design by Ralph B. Mentzer, assistant director of the process development laboratory of the Hamilton Watch Company. To correlate the Martian day, month, and year with our own, computations were based on Lowell's rotation period of 24 hours, 37 minutes, 22.58 seconds, for Mars. Since this work was done, Joseph Ashbrook his presented evidence that Lowell's period is 0.088 second too short. The figures in this article have been amended from those originally announced to correspond with the new value for Mars' rotation.

The large dial on the clock indicates Martian time, and is connected by gears to the small, lower dial indicating Greenwich civil or Universal time on earth. The earth pointer makes one full revolution in 2 hours, but the Martian pointer requires 39.6 minutes longer.

Since Mars is about 1 1/2 times as from the sun as the earth, its year is nearly twice as long. Mars requires 686.9797 earth days or 668.5991 Mars days to swing around the sun once. Our two simultaneous calendars have been set to begin with the Julian Day epoch January 1, 4713 B. C. This date is selected as the start of Martian year. Using the 668.6-day year for Mars brings January 1, 1954, into the year 3641 M.Y. ( Mars Year) on this Martian calendar.

On the clock, two similar dials show the year, month, and day, one for each planet. The Martian year has been arbitrarily divided into 12 months, eight of 56 days and four of 55 days, bearing the same names as those on the earth but distinguished by a subscript letter "m." These months have days numbered up to 56, instead of to a maximum of 31. The four quarters are equal; the first and second months of each quarter have 56 days and the third has 55.

As the week is also arbitrary (both on the earth and Mars), with no relation to astronomical events, we may use seven-day week for Mars, where it fits a convenient eight times into the 56-day months. But it is troubloesome there, too, for some months are only 55 days long, thus, just as in the case of our own present calendar, the week does fit into the year exactly. In our proposed calendar, however, the last Saturday of each 55-day month is omitted, thereby keeping the weeks in step with the months throughout the year.

Mars has seasons very much like the earth’s because its axis is tipped away from the pole of its orbit about 25 degrees, corresponding closely to the 23 1/2-degree angle for the earth's axis. Therefore, the sun appears to move north and south in the Martian sky during the planet's revolution around the sun. Each season is, of course, nearly twice as long as are ours.

It is with the seasons that a calendar must keep step. To produce on Mars what corresponds to the earth's tropical year, it is necessary to include 0.6 day the end of the year. This interval corresponds to the extra quarter day of our years, which we take care of at four-year intervals by inserting a leap day. On Mars, we propose adding a day every three out of five years--the first and fourth years to contain 668 days, the other three years 669 days, and in these longer years December is given the extra day.

Just as the simple leap year rule is not enough for the earth, and the Gregorian calendar correction has to be added, so on Mars there is still 0.00095 day per year to account for. Therefore, each tenth century year, for instance, 4000, 5000, M.Y., will not be a leap year, in order to lose a day. After these adjustments, the Martian calendar will be in error by only one day in 20,000 years. This accuracy far surpasses our own Gregorian calendar, which is out one day every 3,000 years.

Built by Mr. Mentzer in his home workshop, the clock has almost 400 working parts. The basic motive power is a laboratory-type heavy-duty synchronous motor, 60 cycle, which provides sufficient power for a "time flyer." The device permits accelerating the clock by any amount to more than 2,000 times the clock's normal rate. This is achieved through an overhead-running clutch to bring into operation a high-speed aircraft-type geared-head series motor which is manually controlled by a variable transformer.

The experimental clock is really a computing mechanism, and can be used for demonstration purposes. A full 24-hour earth day can be observed in 45 seconds. The month and year indicators are 35-mm. film bands. We have projected the clock into the future, and its film strips indicate the course of time for a 20-year interval, January 1, 1970, to December 31, 1989, earth dates.