Timekeeping on Mars
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Various schemes have been used or proposed to keep track of time and date 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.
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[edit] Keeping track of time of day
The length of a Martian sidereal day is 24h 37m 22.663s in terms of Earth hours, and the length of its solar day is 24h 39m 35.244s (the latter is known as a sol, more precisely 88,775.24409 seconds). The corresponding values for Earth are 23h 56m 04.2s and 24h 00m 00.002s, respectively. Thus Mars's solar day is only about 2.7% longer than Earth's.
Because this is considered "close enough," a convention used by all the spacecraft lander projects to date has been to keep track of local solar time using a "24:60:60" clock, but on which the hours, minutes and seconds are "stretched" to 2.7% longer than their standard durations.
(Alternative clocks for Mars have been proposed, but no mission has chosen to use such. These include a metric time schema, with "millidays" and "centidays", and an extended which uses standard units but which counts to 24hr 39m 35s before ticking over to the next day.)
Kim Stanley Robinson's influential Mars Trilogy includes a system whereby the clocks work at a similar rate as those on Earth, but freeze at midnight for 39.5 minutes. As the 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 important to be aware of local solar time for purposes of planning the daily activities of Mars landers. Daylight is needed for the solar panels. Also, temperatures will rise and fall in very rapid synchronicity with the Sun because the thin atmosphere and lack of water do very little to buffer temperature fluctuations, unlike Earth.
As on Earth, on Mars there is also an equation of time that represents the difference between sundial time and clock time as displayed by a Martian timepiece (such timepieces have been made for NASA employees [1]). The equation of time is illustrated by an analemma. Because of Mars' greater orbital eccentricity, its equation of time is much larger 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. In the future, perhaps Mars could have time zones defined, as on Earth; however, for the time being, there is no need to co-ordinate the activities of the various landers, so each lander simply keeps track of its own local solar time, as cities did on Earth before the introduction of standard time in the 19th century.
Mars will also need an international date line for the same reason that Earth needs one. However, unlike Earth, Mars has no oceans, so the date line will be entirely on land. It will be possible for future Martian colonists to take a step across a line and be in a different day.
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. [2]
[edit] Coordinated Mars Time (MTC)
MTC is a 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 [3] 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.
Use of MTC has not yet been employed in official mission timekeeping. Of the five successful Mars landers to date, four employed variants of local mean solar time (LMST) for the lander site while the fifth (Mars Pathfinder) used local true solar time (LTST). [4] [5] Even the two Mars Exploration Rovers, which landed just 20 sols apart, used separately derived local timekeeping systems based on landing site LMST (with an offset intended to roughly match mission time to local true solar time at the middle of the nominal mission period) rather than, for example, time zones based on the landers' positions relative to the prime meridian. As a result, the difference in mission times for the two Mars Exploration Rovers is not an integral number of Mars hours, but is 11 hours, 58 minutes, 50 seconds.
[edit] Keeping track of sols
When a spacecraft lander begins operations on Mars, it keeps track of the passing Martian days (sols) by a simple numerical count. The two Viking missions defined the sol on which each lander touched down as "Sol 0" for each mission, but subsequent missions (i.e., Mars Pathfinder and the two Mars Exploration Rovers) instead defined touch down as "Sol 1". However, it appears that the Mars Phoenix project has chosen to commence counting with "Sol 0"[6].
Although these 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 operated simultaneously on Mars, when Opportunity landed on Mars and started its count from Sol 1, the mission date for Spirit had already reached Sol 22.
On Earth, astronomers often prefer to use Julian dates for timekeeping purposes. This is simply a sequential count of days, bypassing the complications of calendars. One proposed counterpart on Mars is the Mars Sol Date, or MSD, which is a running count of sols since approximately December 29, 1873 (in principle any start date (known as the "epoch") could be used; however, it should be far enough in the past that all historically recorded events occur after the epoch).
The Mars Sol Date is defined mathematically as MSD = (Julian date using International Atomic Time - 51549.0 + k)/1.02749125 + 44796.0, where k is a small correction of approximately 0.00014d (or 12sec) due to uncertainty in the exact geographical position of the prime meridian at Airy-0 crater.
At some point in the future, Mars will need a Julian-date-like count of days, and the MSD is as good a candidate as any (although some prefer an epoch back around 1608). However, MSD is not really used yet, as there was no effort made to synchronize the count of successive sols between Spirit and Opportunity to make them use a common count. In any case, Spirit and Opportunity are on opposite hemispheres, so when it is daylight for one it is night for the other, and they carry out activities completely independently, so there would be no practical advantage in a common sol count.
The word "yestersol" was coined by NASA 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 such as "tosol" (for "today") and "nextersol" or "morrowsol" (for "tomorrow") have been less successful.
[edit] Keeping track of calendar dates
Of course, for most day-to-day activities on Earth, people don't use Julian dates. They use the Gregorian calendar, which despite its various complications is quite useful. By looking at a Gregorian calendar date you immediately know whether that date is an anniversary of any other date, and you know whether the date is in winter or spring, and you can easily calculate the number of years between two dates. It is much less practical to do this with Julian dates.
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 proposal put forth for such a thing 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 the Earth's Moon would generally be visible to the naked eye along with the Earth when both 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.
[edit] Length of Martian year
The length of a sidereal year on Mars is about 686.98 Earth solar days, or 668.5991 sols. This is the time it takes for Mars to complete one orbit around the Sun. However, as on Earth, this is not the quantity that is needed for calendar purposes. Rather, the tropical year would be used because the tropical year gives the best match to the progression of the seasons. The length of the tropical year is slightly shorter than the sidereal year due to the precession of Mars' rotational axis. The length of the precession cycle on Mars is 93,000 Martian years, or 175,000 Earth years, which is considerably longer than the precession cycle of Earth. The length of the precession cycle in tropical years can be computed by dividing the difference between the sidereal year and tropical year by the length of the tropical year.
The tropical year is not a single value, but can vary according to which point is used as the starting point to measure the length of the year. The tropical year 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 length variation is due to the effects of Kepler's second law of planetary motion. The length of the Gregorian calendar is measured using the March equinox year.
On Earth the variation in the lengths of the tropical years is usually glossed over because the effect is not that important; however, on Mars, the differences are significantly larger. On Mars, 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 out over an entire orbital period gives a Martian tropical year of 668.5921 sols. Note that it is not possible to refer to Martian equinoxes and solstices unambiguously by using seasonal references alone, because like Earth, Mars has two hemispheres with opposite seasons. Thus, the location of the Sun (for solstices) and direction of motion of the Sun (for equinoxes) is used to remove this ambiguity.
[edit] Intercalation
Any 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 designs exist that employ an intercalary week.
For the Gregorian 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. This is close enough to the March equinox year. On Mars, a similar intercalation scheme for leap years would be needed. However, the exact intercalation scheme would depend 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.
The Darian calendar uses the northward equinox year length of 668.5907 sols as the basis of its intercalation scheme.
[edit] Simple Mars Clock (UTC to MTC)
[edit] Excel/OpenOffice.org formula
=((NOW()-"6 Jan 2000 12:00:00 AM"+(B1*-1*3600/86400))*(86400/88775.244))+44796-(20/86400)
Cell B1=UTC Offset in Hours
