Astronomical Society of the Pacific Leaflets

LEAFLET 95--December, 1936

Time Measures on Mars

By Robert G. Aitken
Director Emeritus of Lick Observatory

A few days ago, while I was reading with special interest the announcement that the American Philosophical Society, like the American Academy of Arts and Sciences, had definitely endorsed the twelve-month World Calendar, my friend, the Man from Mars, entered my office and, seeing the "Journal of Calendar Reform" and other papers on my desk, was moved to comment.

He expressed his surprise that the human race, which prided itself upon its progressiveness, had so long been content to puf up with the present hodgepodge calendar and that it should be so slow and hesitant about adopting the revision proposed by The World Calendar Association, a revision that would so obviously improve and simplify particularly since the adoption of the new system could be effected with so little inconvenience to anyone. He readily agreed that any plan of revision, to succeed, must commend itself to the Church as well as to the worlds of business and science. "But," said he, "now that the highest authorities in your great ritual churches, as well as so large a number of great business organizations and scientific societies have expressed their approval of the twelve-month World Calendar, I find it difficult to understand the reasons for further delay."

I tried to explain to him the power of tradition and the reluctance of the conservative element to give up an old custom or tradition in favor of a new one, even though the new one offered definite advantages. But this, he contended, was unreasonable. "It is all right," he said, "to heed the injunction of your great apostle Paul to 'hold fast that which is good,' but the apostle certainly did not and would not advise holding something that is not so good and that can so easily be made better." He wrinkled his oddly shaped brow and paused a moment to consider the matter.

"Of course," he continued, "it would be most convenient if your year contained an exact number of days, and if that number were exactly divisible by both seven and twelve. But Dame Nature, if she be the responsible party, has been culpably indifferent to commensurability in the rotation periods and revolution periods of the Earth and of all of the other planets. Happily, this is of no consequence except for Mars and the Earth, for, as we know, the other planets are uninhabitable, or at any rate uninhabited.

"Think of the tribulations of calendar makers on the planet Jupiter, if there were any! Not only are there about 10,500 Jovian days in the Jovian year, but if the equatorial acceleration in the rotation period, which we observe in the outer layers of its atmosphere, extends down to the layer on which the imaginary Jovians might be supposed to live, the number of days in the year varies with the latitude and at the equator may be fully go greater than in high north and south latitudes." He smiled at the odd picture he had conjured up, and I smiled with him.

"Even with us Martians," he added, "it is bad enough, as you know, for your astronomers have measured the length of our day and of our year accurately in your units of time, just as we have measured the lengths of the Earth's day and year."

It is true that we know the lengths of the Martian day and year in mean solar days very precisely. Mars makes one sidereal rotation in 24 hours 37 minutes and 22-58 seconds of mean solar (terrestrial) time, and one complete revolution about the Sun in 686.98 mean solar days. Expressed in units of Martian mean solar days, this means that the Martian sidereal year has 669.599 days, and since on Mars, as on the Earth, sidereal time gains one full day on mean solar time in one revolution, that is, in one year, the Martian calendar year will have 668.60 days.

As compared with our 365.2564-day calendar year, this fractional number apparently has disadvantages but also advantages. I questioned my visitor on the subject. "Yes," said he, "the incommensurability raises a problem, and at a very early stage in our history this was fully realized and alternative possible solutions were vigorously debated. We wish, of course, to keep our year dates in step with our seasons; and these, as you know, closely parallel your own, since the inclination of our equator to the plane of our orbit (25 degrees to minutes) is but little greater than the inclination of the terrestrial equator (23 degrees 26 minutes 59 seconds) to the plane of the ecliptic.

"Three schemes were considered. We might have four years of 669 days each, followed by one of but 667 days, or four years of 668 days each, followed by one with 671 days. By either plan we should have 3,343 days in five years -- what the actual rotation and revolution periods require.

"It was agreed, however, after full debate, that these plans were far inferior to the plan of having our years run alternately 668 and 669 days, and then inserting an extra leap-day every ten years to care for the odd one-tenth of a day. We adopted this arrangement, which will keep our year dates in step with the seasons for more than 10,000 years.

"We divide our year into quarters, as you do, but make it begin with the date of the Vernal Equinox, and we insert the intercalary day required in the decennial years at midyear, between the second and third quarters, calling it Mid-year Day and celebrating it as a holiday.

"Our years, then, run as follows:

Days in --Spring SummerAutumn Winter
Odd years167 167167 167equals 668
Even years167 167167 168equals 669
Decennial years167 167 (1)167 168equals 670

"Even before we adopted this calendar we had found it desirable to set aside one day in seven as a rest day, such as your Sunday was designed to be. We have nothing on Mars that corresponds exactly to your lunar month, for, as you are aware, we have two satellites or Moons, the outer one of which makes one complete revolution in its orbit in about 1.25 of our days, while the inner one revolves nearly four times as fast, so that it actually rises in the west. It was, however, convenient to divide the seasons, or quarter years, into periods of a few weeks each, just as you divide yours into months, and it seemed to our calendar makers local to continue the quarter system. Our year, therefore, has sixteen periods of 42 or 41 days (six weeks) each all odd-numbered years begin on a Sunday, in your nomenclature, and all even-numbered years on a Wednesday. All four quarter periods of Spring in the odd-numbered years also begin on Sunday, those of Summer on Saturday, of Autumn on Friday, and of Winter on Thursday. In the even-numbered years, the quarter periods of Spring, Summer, Autumn and Winter begin, in order, on Wednesday, Tuesday, Monday and Sunday. Since the last quarter of the even-numbered years always has 42 days, the odd-numbered years again begin on a Sunday, and since the intercalary Mid-year Dayhas no weekday name, this setup is cyclical, so our calendar is perpetual on a two-year basis.

"Moreover, you will note that the first three quarter-periods of each season in both odd-and even-numbered years all have 36 working days per month (except for specially decreed holidays), and the last quarter-period in each season, 35 with, however, 36 in the last period of Winter in even-numbered years.

"Here, then, is our Perpetual Calendar:

Odd-numbered Years

Spring
Summer
Autumn
Winter
Quarters First Day No. of Days First Day No. of Days First Day No. of Days First Day No. of Days
1 Sun. 42 Sat. 42 Fri. 42 Thurs. 42
2 Sun. 42 Sat. 42 Fri. 42 Thurs. 42
3 Sun. 42 Sat. 42 Fri. 42 Thurs. 42
4 Sun. 41 Sat. 41 Fri. 41 Thurs. 41

Even-numbered Years

Spring
Summer
Autumn
Winter
Quarters First Day No. of Days First Day No. of Days First Day No. of Days First Day No. of Days
1 Wed. 42 Tues. 42 Mon. 42 Sun. 42
2 Wed. 42 Tues. 42 Mon. 42 Sun. 42
3 Wed. 42 Tues. 42 Mon. 42 Sun. 42
4 Wed. 41 Tues. 41* Mon. 41 Sun. 42

*Mid-year Day, a holiday. Insert in all years whose number is divisible by ten.

"I have used your weekday names instead of our own for your convenience. You can readily see that this calendar, in this form or given in detail for all (lays in the year so that holidays may be noted, is not at all difficult to master and that it divides the quarters of the four seasons, and the number of working days in each quarter as evenly as is possible. Any set holiday, like your Christmas for example, will always fall upon the same weekday in odd-numbered years, and likewise in even-numbered years, though the weekday in the odd- and even-numbered years will differ by a fixed number of days."

Just then my visitor glanced at his watch and found that he had barely time to catch the next "Interplanetary Express" (which, incidentally, has as real an existence as my Martian friend himself) and hurried away, leaving me to ponder over the simple Martian calendar and to regret that on our Earth we have not yet been able to secure the adoption of the even simpler and better calendar proposed by The World Calendar Association.

(Reprinted by courtesy of "Journal of Calendar Reform," 630 Fifth Avenue. New York City)