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:
Conversion Between Earth and Mars Dates

Stephen Ashworth

April 2015 ~ Aries MA 26

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Back to description of month/week pattern

Definition of annum 0

The martian vernal equinox on 5 September 1964 defines the start of the annum in which Mariner IV made the first close-up observations of Mars. This is Mariner Anniversary annum 0, or MA 0.

The following annum began with the equinox on 24 July 1966, and contains the first anniversary of Mariner IV’s flight. It is therefore Mariner Anniversary annum 1, or MA 1.

Date conversion method

Calendar dates are converted, firstly, into the Modified Julian Date (MJD) on Earth, or the Mars Sol Date (MSD) on Mars. A simple formula converts between MJD and MSD. The result may then be turned back into a calendar date.

MJD = Modified Julian Date:

The Modified Julian Day (MJD) is an abbreviated version of the old Julian Day (JD) dating method which has been in use for centuries by astronomers, geophysicists, chronologers, and others who needed to have an unambiguous dating system based on continuing day counts.
[…]
     Start of the JD count is from 0 at 12 noon 1 JAN -4712 (4713 BC), Julian proleptic calendar. Note that this day count conforms with the astronomical convention starting the day at noon, in contrast with the civil practice where the day starts with midnight (in popular use the belief is widespread that the day ends with midnight, but this is not the proper scientific use).
[…]
     The Modified Julian Day, on the other hand, was introduced by space scientists in the late 1950’s. It is defined as
     MJD = JD – 2400000.5
     The half day is subtracted so that the day starts at midnight in conformance with civil time reckoning. This MJD has been sanctioned by various international commissions such as IAU, CCIR, and others who recommend it as a decimal day count which is independent of the civil calendar in use.
     (U.S. Naval Observatory)

MSD = Mars Sol Date:

This represents a sequential count of Mars solar days elapsed since 1873 December 29 at approximately Greenwich noon (Julian Date 2405522.0). This epoch was prior to the great 1877 perihelic opposition of Mars and precedes nearly all detailed observations of temporal changes on the planet. It corresponds to a Mars Ls of 277°, approximately the same planetocentric solar longitude as that for the Earth on the same date. MSD 44796.0 is approximately coincident with 2000 January 6.0, at a near-coincidence of prime meridian midnights on the two planets and a repetition of Mars Ls = 277°. The period 44796 sols also represents a near commensurability of 126 Julian years and 67 Mars tropical revolutions.
     (NASA Goddard)

A MSD which is a whole number corresponds to midnight on the martian prime meridian.

Thus 6 January 2000 at 00:00:00 corresponds to MJD 51549.00, MSD 44796.00.

The conversion formula is:

MSD – 44796 = (MJD – 51549) / 1.02749125

The NASA Goddard Mars24 software gives MSD 32235.62 at the moment of the vernal equinox which we have chosen to begin MA 0. Thus the starting-point for the MA calendar, 00:00:00 AMT on 1 Gemini MA 0, is MSD 32235.00. From this we can work forwards and backwards using the formula for long and short years described earlier to find the exact sols which begin subsequent annums.

The exact moment of the vernal equinox will not necessarily fall on 1 Gemini each annum, any more than the vernal equinox on Earth falls on 21 March each year. But since the equinox in this particular annum falls fairly close to the middle of the sol, and since long and short years are interspersed at frequent intervals, we may expect that most of the time the equinox will indeed fall on this date.

Similarly, the southward equinox of that annum occurs (so far as one can tell from Mars24) around 08:00 AMT on 22 Sept. 1965, sufficiently far into the sol that variation of a few hours each way will not usually prevent it from coinciding with 1 Sagittarius.

Conversion tables

The following three tables convert between the start of Mars annums and MSD numbers, between the start of Earth years and MJD numbers, and between calendar dates within the annum or the year and numbers of sols/days to obtain a precise MSD or MJD.

Table 1: the Mars Sol Date values for the start of Mariner Anniversary annums

MA annum Length of annum MSD of 1 Gemini
00:00:00 AMT
0 Long (669 sols) 32235.00
1 Long 32904.00
2 Short (66 sols) 33573.00
3 Long 34241.00
4 Short 34910.00
5 Long 35578.00
6 Short 36247.00
7 Long 36915.00
8 Short 37584.00
9 Long 38252.00
10 Long 38921.00
11 Long 39590.00
12 Short 40259.00
13 Long 40927.00
14 Short 41596.00
15 Long 42264.00
16 Short 42933.00
17 Long 43601.00
18 Short 44270.00
19 Long 44938.00
20 Long 45607.00
21 Long 46276.00
22 Short 46945.00
23 Long 47613.00
24 Short 48282.00
25 Long 48950.00
26 Short 49619.00
27 Long 50287.00
28 Short 50956.00
29 Long 51624.00
30 Long 52293.00

Table 2: the Modified Julian Date values for the start of Earth years

The number of days in a decade = 3650 + the number of leap years in that decade (counting year 0 to year 9), which is 3 if the decade begins year 20, 40, 60, 80, or 2 if it begins year 10, 30, 50, 70, 90, 00 (except for year 2000, which was a leap year).

Earth year MJD of 1 January
00:00:00 GMT
  Earth year MJD of 1 January
00:00:00 GMT
1900 15020.00   2000 51544.00
1910 18672.00   2010 55197.00
1920 22324.00   2020 58849.00
1930 25977.00   2030 62502.00
1940 29629.00   2040 66154.00
1950 33282.00   2050 69807.00
1960 36934.00   2060 73459.00
1970 40587.00   2070 77112.00
1980 44239.00   2080 80764.00
1990 47892.00   2090 84417.00
  2100 88069.00

Table 3: MSD/MJD values within an annum/year

In order to find the MSD or MJD for any sol/day other than 1 Gemini/1 January, the number of 24-hour sols/days elapsed since the start of the year must be added. This is the sol of the annum/day of the year, minus one. All whole number dates refer to the beginning of the day or sol at midnight.

MA calendar date Elapsed sols Earth calendar date Elapsed days
1 Gemini 0 1 January 0
1 Cancer 63 1 February 31
1 Leo 126 1 March 59/60
1 Virgo 189 1 April 90/91
1 Libra 252 1 May 120/121
1 Scorpio 315 1 June 151/152
1 Sagittarius 371 1 July 181/182
1 Capricornus 420 1 August 212/213
1 Aquarius 469 1 September 243/244
1 Pisces 514/515 1 October 273/274
1 Aries 563/564 1 November 304/305
1 Taurus 612/613 1 December 334/335

Example of date conversion

I am writing this on 16 April 2015 at about 09:30 GMT. From Table 3, this gives day 90 + (16 – 1) + 0.40 = 105.4 of the year.

From Table 2, 1 January 2010 was MJD 55197.00, therefore 1 January 2015 was 55197 + (5 × 365) + 1 = 57023. Adding 105.4 makes today MJD 57128.4.

Using the conversion formula produces MSD 50226.12.

From Table 1, MA annum 26 (a short annum) began on MSD 49619, which subtracted from 50226 leaves 607 sols over. Returning to Table 3, the start of 1 Aries is sol 563, leaving 44 sols over.

The martian date and time are therefore 44 Aries MA 26, at about 02:53 AMT. An accuracy of +/–0.01 sol/day would convert to about +/– a quarter of an hour.

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