The Mariner Anniversary Calendar for Mars:
Conversion Between Earth and Mars Dates

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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 L_s 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 L_s = 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.