All Astronautical Evolution posts in 2015:

Britain Takes the Wrong Approach to Manned Spaceflight (Dec.) (Comments)

“Drowning in Process” (Nov.)

Does Intergalactic SETI Make Any Sense? (Oct.)

SETI and Sanity (Oct.)

SpaceX, SpaceY, SpaceZ (Sept.)

A Letter to Britain’s New Space Minister (June)

Mars: 25 Years After Mars Direct – Discussion (May)

The Astronist Mars Strategy (May)

Mars: Still So Distant, 25 Years After Mars Direct (May)

The Mariner Anniversary Calendar for Mars (April)

Mars: An Awful or an Awesome Place? (April)

Should We Phone ET? (March)

More Pluto Controversy (Feb.)

The Pluto Controversy (Jan.)

New in 2015:

Short story The Marchioness


AE posts:

2017: Mars…

2016: Stragegic goal for manned spaceflight…

2015: The Pluto Controversy, Mars, SETI…

2014: Skylon, the Great Space Debate, exponential growth, the Fermi “paradox”…

2013: Manned spaceflight, sustainability, the Singularity, Voyager 1, philosophy, ET…

2012: Bulgakov vs. Clarke, starships, the Doomsday Argument…

2011: Manned spaceflight, evolution, worldships, battle for the future…

2010: Views on progress, the Great Sociology Dust-Up…

Chronological index

Subject index


General essays:

Index to essaysincluding:

Talk presented to students at the International Space University, May 2016

Basic concepts of Astronautical Evolution

Options for Growth and Sustainability

Mars on the Interstellar Roadmap (2015)

The Great Sociology Debate (2011)

Building Selenopolis (2008)


The Mariner Anniversary Calendar for Mars:
Basic Month/Week Pattern

Stephen Ashworth

April 2015 ~ Aries MA 26

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Months and weeks on Mars

The martian year and seasons are similar to those on Earth but with two major differences: they last almost twice as long, and the seasons vary in length more than on Earth because of the greater ellipticity of Mars’s orbit.

When managing a Mars lander mission, planetary scientists currently use a calendar based on two numbers. They count the sols (martian days), beginning with sol 0 or sol 1 when the landing takes place. And they use the areocentric longitude Ls to indicate the point in the martian orbital/seasonal cycle, where Ls = 0° at the vernal equinox.

The longitude was used as a calender by the colonists in Kim Stanley Robinson’s novel Red Mars. But Ls is actually not much good for organising surface activities because it does not match the day/night cycle of the sols. One degree of longitude corresponds to an average of 1.857 sols, increasing to 2.229 sols at aphelion and decreasing to 1.533 sols at perihelion. If Ls = 150° represents the sol when Mars is at aphelion, Ls = 151° may be two or it may be three sols later, depending on whether 150° is reached at an early or late clock time of sol.

The subject of a more detailed civil calendar for Mars is at present a speculative one. But it implies that people can live there permanently. It anticipates the humanisation of the planet. Whether our descendants will live there in reality is not yet known, but the calendar is a statement of belief that they will.

Because of the broad similarity of martian and terrestrial seasons, a martian civil calendar should carry forward the terrestrial system of 12 months to the year. These break the annual cycle up into easily understood portions which are whole numbers of sols. Proposals for a 24-month martian year have been made, e.g. the Darian calendar, but I don’t find this helpful: it adds complexity and reduces clarity.

Probably the best-known 12-month martian calendar is by Robert Zubrin from his book The Case for Mars, and we adopt this here. The month names are the constellations of the zodiac in which Mars appears as seen from the Sun. As Zubrin says, in order to predict the seasons, a calendar must divide the planet’s orbit not into equal numbers of days – or on Mars, sols – but into equal angles of travel around the Sun. This, however, results in a chaotic pattern in which nearly every month has a different number of sols.

Furthermore, Zubrin does not say anything about weeks. The 7-day week is a useful and familiar way of organising one’s working time. Can it be integrated into the Zubrin calendar?

It turns out that it can. Firstly, month lengths are made to vary according to the following pattern:

That produces a total of 672 sols. The martian year is in fact 668.6 sols long, so 3 or 4 sols must be dropped, giving an odd half week in the middle short month. The annual cycle begins, according to astronomical practice, with the vernal equinox:

Month Length (sols) Begins on sol number
Gemini 63 1
Cancer 63 64
Leo 63 127
Virgo 63 190
Libra 63 253
Scorpio 56 316
Sagittarius 49 372
Capricornus 49 421
Aquarius 45/46 470
Pisces 49 515/516
Aries 49 564/565
Taurus 56 613/614

How well does this scheme reflect astronomical reality? Zubrin’s calendar was designed to match that reality, so a comparison will reveal any problems:

Astronomical marker Sol number Ls Zubrin date Modified date
Vernal equinox 1 1 Gemini 1 Gemini
Aphelion 150 71° 24 Leo 24 Leo
Northern solstice 193 90° 1 Virgo 4 Virgo
Southbound equinox 372 180° 1 Sagittarius 1 Sagittarius
Perihelion 484 251° 16 Aquarius 15 Aquarius
Southern solstice 515 270° 1 Pisces 46 Aquarius/1 Pisces

By starting both versions with the vernal equinox on 1 Gemini, two or three of the other markers are identical, one or two are just one sol out, and the northern solstice is just 3 sols out. (All our modified months begin within 3 sols of Zubrin’s original monthly starting points, except for the modified Libra, which is 5 sols behind, still less than 1% of the martian year.)

However, even Zubrin’s original calendar could not have produced perfect astronomical accuracy, since the times between the astronomical markers are not whole numbers of sols. In return for tolerating up to 3 sols discrepancy in one of these key dates, every month except Aquarius is now a whole number of 7-sol weeks.

Naming the sols of the week

The names of the sols of the week will presumably be derived from the English names used on Earth. It would be logical to remove Tues- (which is a reference to Mars itself) and substitute a reference to Earth, which is now an astronomical body. Terrasol, Gaiasol or Geosol would all be possible names; here we use the latter of these. Making it the first sol of the week, because of its obvious importance, the Moon now becomes the second sol, and is renamed Lunasol to avoid confusion with Monday.

The half week following perihelion in Aquarius needs special treatment. We propose here to use four extra sol names, outside the normal cyclic sequence, in order to preserve the alignment between sols of the week and months of the martian year: if 1 Gemini is a Geosol one year, then it is a Geosol every year, and every month matches an exact number of weeks, always beginning at the start of a new week (Geosol) and ending at the end of a week (Sunsol).

Sol names for the four intercalary days at perihelion can be formed logically enough by going beyond Saturn. They will presumably be used to mark some sort of perihelion festival. In summary:

Geosol
Lunasol
Wensol
Thursol
Frisol
Satursol
Sunsol

Uranisol
Neptunisol
Plutonisol
Eridisol

A similar pattern could of course be used to replace the Gregorian calendar on Earth: 4 months of 5 weeks each, 8 months of 4 weeks each, plus one or (in leap years) two intercalary feast days.

Long years and short years

Next, the calendar will need to alternate between long years of 669 sols and short years of 668 sols. Long years will have an Eridisol the 46th of Aquarius, short years will end Aquarius on Plutonisol the 45th. The length of the martian year from one vernal equinox to the next (thus taking precession into account) is given by NASA Goddard as 668.5906 sols. This implies the following pattern:

Period Number of long years (669 sols) Number of short years (668 sols) Average sols/year
10 years 6 4 668.6
100 years 59 41 668.59
1000 years 591 409 668.591
10,000 years 5906 4092 668.5907

Thus the following practical formula for determining long and short years may be followed:

When to begin Mars year 1

Finally, a start point for year 1 is necessary. Some recent vernal equinox dates are given by the Planetary Society (shown here in the table below). They report the convention chosen in a paper by Bruce Cantor, Philip James and Wendy Calvin, published in 2010, to begin year 1 at the equinox on 11 April 1955.

Zubrin chooses the equinox three martian years later, which he says coincides with the Earth date 1 January 1961. But according to the Planetary Society’s table he is a month out; that equinox in fact came on 1 December 1960. Zubrin’s logic is to choose a martian year which begins close to the beginning of an Earth calendar year, and specifically the year which precedes all the space probes sent to Mars.

It is indeed logical to begin the martian calendar at the start of the space age, because all observations of Mars made prior to then are in a sense very much the prehistory of martian observation. Only with close-up spacecraft observation has it been possible for humanity to really get to grips with Mars – a watershed moment in any martian calendar. But trying to align the start of Mars year 1 with the start of an Earth year, either on 1 January or with the equinox on or around 21 March, is not helpful: the two annual cycles are independent of each other, and the dates 1 January or 21 March on Earth overlap extremely rarely with the sol containing the vernal equinox on Mars.

The logical choice would therefore be the martian equinox on 5 September 1964. This defines the start of the martian year in which Mariner IV is launched and returns the first ever close-up pictures of the planet (Earth dates: launch on 28 Nov. 1964; flyby on 15 July 1965). This martian year would be number 6 in the Cantor/James/Calvin system, and number 3 in Zubrin’s system.

Mariner Anniversary annum dates

In my novelette Halfway There! I used the term annum for a martian year, and shall now continue to do so here. From here on, “year” is always an Earth year.

Since the martian vernal equinox in September 1964 defines the annum of Mariner IV, the following annum contains the first anniversary of that event, and is therefore Mariner Anniversary annum 1, or MA 1.

The following table reproduces the dates given by the Planetary Society, but counting by Mariner Anniversary annums. The Cantor/James/Calvin numbering = MA+6. The Zubrin numbering = MA+3.

Some precise times of equinox have been added using NASA Goddard’s Mars24 Sunclock app. Finding the moment when Ls changes from 360.0° to 0.0° in the app identifies the Mars vernal equinox.

AMT = Airy Mean Time, thus the martian equivalent to GMT/UT, referenced to the crater Airy which anchors zero longitude. Note that all martian sols, hours, minutes and seconds are longer than their terrestrial equivalents by a factor of 1.02749125.

MA annum Begins on Earth date MJD/MSD of
vernal equinox
–5 11 April 1955
–4 26 Feb. 1957
–3 14 Jan. 1959
–2 1 Dec. 1960
–1 19 Oct. 1962
0 5 Sept. 1964
Earth time 07:44:05 UT
Mars time 14:56:02 AMT
MJD 38643.32
MSD 32235.62
1 24 July 1966
2 10 June 1968
3 28 April 1970
4 15 March 1972
5 31 Jan. 1974
6 19 Dec. 1975
7 5 Nov. 1977
8 23 Sept. 1979
9 10 Aug. 1981
10 28 June 1983
11 15 May 1985
12 1 April 1987
13 16 Feb. 1989
14 4 Jan. 1991
15 21 Nov. 1992
16 9 Oct. 1994
17 26 Aug. 1996
18 14 July 1998
19 31 May 2000
20 18 April 2002
21 5 March 2004
22 21 Jan. 2006
23 9 Dec. 2007
24 26 Oct. 2009
25 13 Sept. 2011
26 31 July 2013
Earth time 13:49:06 UT
Mars time 23:39:19 AMT
MJD 56504.58
MSD 49618.99
27 18 June 2015
Earth time 12:28:49 UT
Mars time 13:12:18 AMT
MJD 57191.52
MSD 50287.55
28 5 May 2017
29 23 March 2019
30 7 Feb. 2021
31 26 Dec. 2022
32 12 Nov. 2024
33 30 Sept. 2026
34 17 Aug. 2028

MJD/MSD: see next page:

Forward to conversion between Earth and Mars dates

References

Robert Zubrin with Richard Wagner, The Case for Mars (1996; Touchstone, 1997), p.166-70.

Stephen Ashworth, Halfway There!, in Visionary (British Interplanetary Society, 2014), p.169-233.

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