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] Time of day
The average 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. This yields a conversion factor of 1.027346 sols/day. Thus Mars's 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 and Mars Exploration Rover 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.[1]
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, unlike on Earth, the thin atmosphere and lack of water do very little to buffer temperature fluctuations.
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.
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. In the future, perhaps Mars could have time zones defined at regular intervals from the prime meridian, as on Earth. However, for the time being, there is no need to co-ordinate the activities of the various landers, so each lander uses its own timezone (some approximation of local solar time), as cities did on Earth before the introduction of standard time in the 19th century.
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 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[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.
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.
[edit] Timezones
Each lander mission so far has used its own timezone, corresponding to average local solar time at the landing location. 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]
Mars Pathfinder used local apparent solar time at the landing location. Its timezone 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 travelled distances that make a few seconds difference to local solar time.) Spirit uses 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.
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 timezones. It remains to be seen whether this will in fact be done.
[edit] Sols
The term sol is used by planetary astronomers to refer to the duration of a solar day on Mars.[6] A mean Martian solar day, or "sol", is 24 hours, 39 minutes, and 35.244 seconds.[7]
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, Mars Phoenix project planners chose to commence counting with "Sol 0"[8].
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 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 may 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 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 such as "tosol" (for "today") and "nextersol" or "morrowsol" (for "tomorrow") were less successful.
[edit] Martian Time in fiction
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 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. Philip K. Dick's much earlier Martian Timeslip 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 (e.g. 1 January, 2 January, 1 February, 2 February, etc.).[9]
[edit] Calendar dates
Mars scientists typically keep track of the Martian year by use of the heliocentric longitude (or "seasonal longitude"), typically abbreviated Ls, the position of Mars in its orbit around the Sun.[10] Ls is defined as 0 degrees at the Martian Northern-hemisphere vernal equinox, and hence is 90 degrees at the first sol of Northern-hemisphere summer, 180 at the first sol of northern hemisphere autumn, and 270 degrees at the first sol of northern hemisphere winter.
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.
[edit] Martian year
This 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, with northern-hemisphere spring the longest season (Ls = 0 to 90), lasting 194 Martian sols, and northern hemisphere autumn (Ls = 180 to 270), the shortest, lasting only 142 Martian sols.[11]
As on Earth, the sidereal year is not the quantity that is needed for calendar purposes. Rather, the tropical year would 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.)
[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 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. Most years would be leap years since the fractional sol - the remainder of a sol left each year after a whole number of days has passed - is more than 0.5. One example intercalation, having a leap year 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, 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.
The proposed Darian calendar uses the northward equinox year length of 668.5907 sols as the basis of its intercalation scheme.
[edit] Formula to convert UTC to MTC
MTC = (seconds since 6 Jan 2000 12:00:00 AM UTC)×(86400/88775.244)) + 44795.9998
[edit] Relation between Earth/Mars Solar Cycles
Approximations to the ratio between a Mars year and an Earth year are 2:1, 15:8, 32:17, 47:25, 79:42, 679:361 . . . .[citation needed]
| 79 Years on Earth | 42 Years on Mars | |
|---|---|---|
| Number of Earth days | 28854.16 | 28853.16 |
| Number of Martian days | 28082.13 | 28081.16 |
[edit] See also
[edit] References
- ^ "Watchmaker With Time to Lose," January 8, 2004, article on the MER page
- ^ ESA - Mars Express - Where is zero degrees longitude on Mars?
- ^ NASA GISS: Mars24 Sunclock - Time on Mars
- ^ Allison, M., and M. McEwen, 2000: A post-Pathfinder evaluation of aerocentric solar coordinates with improved timing recipes for Mars seasonal/diurnal climate studies. Planet. Space Sci., 48, 215-235, doi:10.1016/S0032-0633(99)00092-6.
- ^ Technical Notes on Mars Solar Time
- ^ NASA - Opportunity's View, Sol 959 (Vertical)
- ^ Technical Notes on Mars Solar Time
- ^ Phoenix Mars Mission - Mission - Mission Phases - On Mars
- ^ Green Mars, Blue Mars
- ^ H. H. Kieffer, B. M. Jakowsky and C. W. Snyder, "Mars' Orbit and Seasons," Mars, H. H. Kieffer, B. M. Jakowsky, C. W. Snyder and M. S. Matthews, eds., U. Arizona Press 1992, pp. 24-28.
- ^ J. Appelbaum and G. A. Landis, Solar Radiation on Mars-- Update 1991, NASA Technical Memorandum TM-105216, September 1991 (also published in Solar Energy, Vol. 50 No. 1 (1993)).
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