Timekeeping on Mars

From Freepedia

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.

Contents

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 00.0s, respectively. Thus Mars's solar day is only about 2.7% longer than Earth's.

Because this is close enough, a convention used by all the various spacecraft landers such as Viking and Pathfinder and the Mars Exploration Rovers Spirit and Opportunity is to keep track of local solar time in a way similar to timekeeping on Earth: a local solar time may be expressed as "10:23:56", for instance. Some have argued in favor of metric time for Mars, with "millidays" and "centidays"; however, in practice this has not been used by any of the lander missions.

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, since the thin atmosphere and lack of water do very little to buffer temperature fluctuations, unlike Earth.

Image:Mars analemma.GIF

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's 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 to take a step across a line and be in a different day. However, this is an issue for hypothetical future Mars colonists and of little practical importance for the time being.

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]

Keeping track of sols

When a spacecraft lander begins operations on Mars, it keeps track of the passing Martian days (sols) by simply labelling them "Sol 1", "Sol 2", "Sol 3", and so forth, counting forward from the moment of landing. Although Spirit and Opportunity operated simultaneously on Mars, no effort was made to synchronize the counts between the two. Thus, the transit of Deimos that took place on March 4 2004 at Opportunity's landing site was on Sol 39 by its count, but the transit of Deimos that took place on March 13 2004 at Spirit's landing site was on Sol 68 by its count, since Spirit landed first.

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.

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.

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.

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.

Simple Mars Clock (UTC to MTC)

Excel/OpenOffice.org

=((NOW()-"6 Jan 2000 12:00:00 AM"+(B1*-1*3600/86400))*(86400/88775.244))+44796-(20/86400)

Cell B1=UTC Offset in Hours

See also

External links

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