Timekeeping on Mars

Martian season lengths and time as compared to seasons on the Earth.

Various schemes have been used or proposed for timekeeping on the planet Mars independently of Earth time and calendars.

Mars has an axial tilt and a rotation period similar to those of Earth. Thus it experiences seasons of spring, summer, autumn and winter much like Earth, and its day is about the same length. Its year, however, is almost twice as long as Earth's, and its orbital eccentricity is considerably larger, which means among other things that the lengths of various Martian seasons differ considerably, and sundial time can diverge from clock time much more than on Earth.

Time of day

The average length of a Martian sidereal day is 24h 37m 22.663s (based on SI units), and the length of its solar day (often called a sol) is 88,775.24409 seconds or 24h 39m 35.24409s. The corresponding values for Earth are 23h 56m 4.0916s and 24h 00m 00.002s, respectively. This yields a conversion factor of 1.0274912510 days/sol. Thus Mars' solar day is only about 2.7% longer than Earth's.

A convention used by spacecraft lander projects to date has been to keep track of local solar time using a 24 hour "Mars clock" on which the hours, minutes and seconds are 2.7% longer than their standard (Earth) durations. For the Mars Pathfinder, Mars Exploration Rover, Phoenix, and Mars Science Laboratory missions, the operations team has worked on "Mars time", with a work schedule synchronized to the local time at the landing site on Mars, rather than the Earth day. This results in the crew's schedule sliding approximately 40 minutes later in Earth time each day. Wristwatches calibrated in Martian time, rather than Earth time, were used by many of the MER team members.

Local solar time has a significant impact on planning the daily activities of Mars landers. Daylight is needed for the solar panels of landed spacecraft. Its temperature rises and falls rapidly at sunrise and sunset because Mars does not have the Earth's thick atmosphere and oceans that buffer such fluctuations.

Alternative clocks for Mars have been proposed, but no mission has chosen to use such. These include a "metric" schema, with "millidays" and "centidays", and an extended day which uses standard units but which counts to 24:39:34 or 24:39:35 before ticking over to 00:00:00 of the next day. Some formula would be devised to determine which days have that extra second. (One such formula for the Darian calendar is that if the day of the month is divisible by four, the day is "long". This is accurate to within a second per century; "leap second" adjustments made on leap days could correct the remaining inaccuracy.)

The analemma for Mars.

As on Earth, on Mars there is also an equation of time that represents the difference between sundial time and uniform (clock) time. The equation of time is illustrated by an analemma. Because of orbital eccentricity, the length of the solar day is not quite constant. Because its orbital eccentricity is greater than that of Earth, the length of day varies from the average by a greater amount than that of Earth, and hence its equation of time shows greater variation than that of Earth: on Mars, the Sun can run 50 minutes slower or 40 minutes faster than a Martian clock (on Earth, the corresponding figures are 14min 22sec slower and 16min 23sec faster).

Mars has a prime meridian, defined as passing through the small crater Airy-0. However, Mars does not have time zones defined at regular intervals from the prime meridian, as on Earth. Each lander so far has used an approximation of local solar time as its frame of reference, as cities did on Earth before the introduction of standard time in the 19th century. (The two Mars Exploration Rovers happen to be approximately 12 hours and one minute apart.)

Note that the modern standard for measuring longitude on Mars is "planetocentric longitude", which is measured from 0°–360° East and measures angles from the center of Mars. The older "planetographic longitude" was measured from 0°–360° West and used coordinates mapped onto the surface.

Coordinated Mars Time (MTC)

MTC is a proposed Mars analog to Universal Time (UT) on Earth. It is defined as the mean solar time at Mars's prime meridian (i.e., at the centre of the crater Airy-0). The name "MTC" is intended to parallel the Terran Coordinated Universal Time (UTC), but this is somewhat misleading: what distinguishes UTC from other forms of UT is its leap seconds, but MTC does not use any such scheme. MTC is more closely analogous to UT1.

Use of the term "MTC" as the name of a planetary standard time for Mars first appeared in the Mars24 sunclock coded by the NASA Goddard Institute for Space Studies. It replaced Mars24's previous use of the term "Airy Mean Time" (AMT), which was a direct parallel of Greenwich Mean Time (GMT). In an astronomical context, "GMT" is a deprecated name for Universal Time, or sometimes more specifically for UT1.

AMT has not yet been employed in official mission timekeeping. This is partially attributable to uncertainty regarding the position of Airy-0 (relative to other longitudes), which meant that AMT couldn't be realized as accurately as local time at points being studied. At the start of the Mars Exploration Rover missions, the positional uncertainty of Airy-0 corresponded to roughly a 20 second uncertainty in realizing AMT.

Time zones

Each lander mission so far has used its own time zone, corresponding to average local solar time at the landing location. Of the six successful Mars landers to date, five employed offsets from local mean solar time (LMST) for the lander site while the sixth (Mars Pathfinder) used local true solar time (LTST).

Mars Pathfinder used the local apparent solar time at its location of landing. Its time zone was AAT-02:13:01, where "AAT" is Airy Apparent Time, meaning apparent solar time at Airy-0.

The two Mars Exploration Rovers don't use precisely the LMST of the landing points. For mission operations purposes, they defined a time scale that would match the clock used for the mission to the apparent solar time about halfway through the nominal 90-sol prime mission. This is referred to in mission planning as "Hybrid Local Solar Time". The time scales are uniform in the sense of mean solar time (they are actually mean time of some longitude), and are not adjusted as the rovers travel. (The rovers have traveled distances that make a few seconds difference to local solar time.) Spirit used AMT+11:00:04. Mean solar time at its landing site is AMT+11:41:55. Opportunity uses AMT-01:01:06. Mean solar time at its landing site is AMT-00:22:06. Neither rover is likely to ever reach the longitude at which its mission time scale matches local mean time. For science purposes, Local True Solar Time is used.

The Curiosity Rover local time is AMT+09:09:46.

With the location of Airy-0 now known much more precisely than when these missions landed, it is technically feasible for future missions to use a convenient offset from Airy Mean Time, rather than completely non-standard time zones.

Sols

The term sol is used by planetary astronomers to refer to the duration of a solar day on Mars. A mean Martian solar day, or "sol", is 24 hours, 39 minutes, and 35.244 seconds.

When a spacecraft lander begins operations on Mars, the passing Martian days (sols) are tracked using a simple numerical count. The two Viking missions, Mars Phoenix and the Mars Science Laboratory rover Curiosity count the sol on which each lander touched down as "Sol 0"; Mars Pathfinder and the two Mars Exploration Rovers instead defined touchdown as "Sol 1".

Although lander missions have twice occurred in pairs, no effort was made to synchronize the sol counts of the two landers within each pair. Thus, for example, although Spirit and Opportunity were sent to operate simultaneously on Mars, each counted its landing date as "Sol 1", putting their calendars approximately 21 sols out of synch. Spirit and Opportunity differ in longitude by 179 degrees, so when it is daylight for one it is night for the other, and they carried out activities independently while both were operational.

On Earth, astronomers often use Julian Dates – a simple sequential count of days – for timekeeping purposes. A proposed counterpart on Mars is the Mars Sol Date (MSD), which is a running count of sols since December 29, 1873 (coincidentally the birth date of astronomer Carl Otto Lampland). Another proposal suggests a start date (or epoch) in the year 1608 (invention of the telescope). Either choice is intended to ensure that all historically recorded events related to Mars occur after it. The Mars Sol Date is defined mathematically as MSD = (Julian Date using International Atomic Time - 2451549.5 + k)/1.02749125 + 44796.0, where k is a small correction of approximately 0.00014 d (or 12 s) due to uncertainty in the exact geographical position of the prime meridian at Airy-0 crater.

The word "yestersol" was coined by the NASA Mars operations team early during the MER mission to refer to the previous sol (the Mars version of "yesterday") and came into fairly wide use within that organization during the Mars Exploration Rover Mission of 2003. It was even picked up and used by the press. Other neologisms include "tosol" (for "today") and "nextersol", "morrowsol", or "solmorrow" (for "tomorrow").

Martian year

The length of time for Mars to complete one orbit around the Sun is its sidereal year, and is about 686.98 Earth solar days, or 668.5991 sols. Because of the eccentricity of Mars' orbit, the seasons are not of equal length. Assuming that seasons run from equinox to solstice or vice versa, the season L_s 0 to L_s 90 (northern-hemisphere spring / southern-hemisphere autumn) is the longest season lasting 194 Martian sols, and L_s 180 to L_s 270 (northern hemisphere autumn / southern-hemisphere spring) is the shortest season, lasting only 142 Martian sols. One commonly used system in the scientific literature denotes year number relative to Mars Year 1 (MY1) beginning with the northern Spring equinox of April 11, 1955.

As on Earth, the sidereal year is not the quantity that is needed for calendar purposes. Rather, the tropical year would be likely to be used because it gives the best match to the progression of the seasons. It is slightly shorter than the sidereal year due to the precession of Mars' rotational axis. The precession cycle is 93,000 Martian years (175,000 Earth years), much longer than on Earth. Its length in tropical years can be computed by dividing the difference between the sidereal year and tropical year by the length of the tropical year.

Tropical year length depends on the starting point of measurement, due to the effects of Kepler's second law of planetary motion. It can be measured in relation to an equinox or solstice, or can be the mean of various possible years including the March (northward) equinox year, June (northern) solstice year, the September (southward) equinox year, the December (southern) solstice year, and other such years. The Gregorian calendar uses the March equinox year.

On Earth, the variation in the lengths of the tropical years is small, but on Mars it is much larger. The northward equinox year is 668.5907 sols, the northern solstice year is 668.5880 sols, the southward equinox year is 668.5940 sols, and the southern solstice year is 668.5958 sols. Averaging over an entire orbital period gives a tropical year of 668.5921 sols. (Since, like Earth, the northern and southern hemispheres of Mars have opposite seasons, equinoxes and solstices must be labelled by hemisphere to remove ambiguity.)

Calendar dates

Mars scientists typically keep track of the Martian seasons by use of the heliocentric longitude (or "seasonal longitude", or "solar longitude"), typically abbreviated L_s, the position of Mars in its orbit around the Sun. L_s is defined as the angle described by the line connecting the Sun to the position of Mars in its orbit, relative to the planet position at northern hemisphere spring equinox. L_s is therefore 0 degrees at the Martian northward equinox, 90 degrees at the Martian northern solstice, 180 at the Martian southward equinox, and 270 degrees at the Martian southern solstice.

For most day-to-day activities on Earth, people don't use Julian days, but the Gregorian calendar, which despite its various complications is quite useful. It allows for easy determination of whether one date is an anniversary of another, whether a date is in winter or spring, and what is the number of years between two dates. This is much less practical with Julian days count.

For similar reasons, if it is ever necessary to schedule and co-ordinate activities on a large scale across the surface of Mars it would be necessary to agree on a calendar. One proposed calendar is the Darian calendar. It has 24 "months", to accommodate the longer Martian year while keeping the notion of a "month" that is reasonably similar to the length of an Earth month. On Mars, a "month" would have no relation to the orbital period of any moon of Mars, since Phobos and Deimos orbit in about 7 hours and 30 hours respectively. However, Earth and Moon would generally be visible to the naked eye when they were above the horizon at night, and the time it takes for the Moon to move from maximum separation in one direction to the other and back as seen from Mars is close to a Lunar month. Neither the Darian calendar nor any other Martian calendar is currently in use.

Intercalation (Leap Years)

Any solar calendar must use intercalation (leap years) to make up for the fact that a year is not equivalent to an integer number of days. Without intercalation, the year will accumulate errors over time. Most designs for Martian calendars intercalate single days, but a few use an intercalary week. The time system currently used by Mars scientists, basing the seasonal date on Mars based on the heliocentric longitude, obviates the need for intercalation by not marking time in terms of days, but instead in terms of Mars' position in orbit.

For the Gregorian (Earth) calendar, the leap-year formula is every 4th year except for every 100th year except for every 400th year, which produces an average calendar year length of 365.2425 solar days, close to the Earth equinox year. On Mars, a similar intercalation scheme for leap years would be needed. If the calendar intercalates single days, the majority of years would be leap years because the fractional sol – the remainder of a sol left each year after a whole number of days has passed – is more than 0.5. This also happens to be true if the calendar is a leap-week calendar with weeks of seven days. One example intercalation, having a leap day every odd year or year ending in 0 except every 100th year, except every 500th year, would produce an average year of 668.592 sols: $1-{\frac {1}{2}}+{\frac {1}{10}}-{\frac {1}{100}}+{\frac {1}{500}}=0.592$, which would be nearly perfect for the mean tropical year (average of all seasons). The scheme, however, would depend slightly on exactly which year was adopted for calendar purposes: calendars based on the southern solstice year or on the northward equinox year would differ by one sol in as little as two hundred or so Martian years.

Other intercalation schemes are possible. For example, the Hebrew Calendar (a lunisolar calendar) uses a simple mathematical formula to intercalate seven extra months in a 19-year cycle: a month is inserted if the remainder of (Hebrew Year Number × 7 + 1) / 19 is less than 7. (The leap year rule is specified differently but is mathematically equivalent.) Such an intercalation scheme would insert the leap years in a more evenly-spaced pattern than Gregorian-based rules, and unlike Gregorian-based rules would have no exceptions. To create a similar intercalation scheme for a Martian calendar, one must find a fractional equivalent for the year length, often using continued fractions to reduce the size of the fractions. For example, an intercalation scheme that intercalates single days and is based on the mean Martian tropical year of 668.5921 days can be approximated closely with a cycle of 45 leap years in 76 years because 66845⁄76 ≈ 668.592105 and 0.5921 × 76 = 44.9996.

A simpler rule, which would closely align the calendar with the northward vernal equinox year of 668.5907 sols and would produce a short calendrical cycle of only 22 years, specifies 13 leap years per 22. The fraction 13⁄22 = 0.5909... Leap years can then be easily determined from a single rule based on the modulo operator:

    A year is a leap year if year mod 22 mod 5 ∈ {0, 2, 3}

In other words, to determine if a particular year is a leap year:

1. Modulo the year number by 22 to get an integer from 0..21.
2. Modulo the result by 5 to get an integer from 0..4.
3. If the result equals 0, 2 or 3, then it's a leap year.

Martian time in fiction

In Kim Stanley Robinson's Mars Trilogy, clocks retain Earth-standard seconds, minutes, and hours, but freeze at midnight for 39.5 minutes. As the fictional colonization of Mars progresses, this "timeslip" becomes a sort of witching hour, a time when inhibitions can be shed, and the emerging identity of Mars as a separate entity from Earth is celebrated. (It is not said explicitly whether this occurs simultaneously all over Mars, or at local midnight in each longitude.) Philip K. Dick's much earlier Martian Time-Slip deals with the vagaries as well.

Also in the Mars Trilogy, the calendar year is divided into twenty-four months. The names of the months are the same as the Gregorian calendar, except for a "1" or "2" in front to indicate the first or second occurrence of that month (for example, 1 January, 2 January, 1 February, 2 February). In the manga and anime series Aria by Kozue Amano, set on a terraformed Mars, the calendar year is also divided into twenty-four months. Following the modern Japanese calendar, the months are not named but numbered sequentially, running from 1st Month to 24th Month.

In Robert A. Heinlein's novel Red Planet, humans living on Mars use a 24-month calendar, alternating between familiar Earth months and newly created months such as Ceres and Zeus. For example, Ceres comes after March and before April, while Zeus comes after October and before November.

Formula to convert MJD/UTC to MSD/MTC

• Modified Julian Date
  • MJD = JD − 2,400,000.5

• Coordinated Universal Time
  • UTC = (MJD mod 86400) * 24

• Mars Solar Date
  • MSD = (seconds since January 6, 2000 00:00:00 UTC)/88775.244 + 44795.9998

• Mars Time Coordinated
  • MTC = (MSD mod 86400) * 24

See also

• Astronomy on Mars
• Universal Time
• Universal Time Coordinated
• Darian calendar

External links

• MARS24 Application
• NASA Algorithms
• NASA Mars Clock (Curiosity Rover)
• mclock - Command Line Mars Clock