Time and date and astronomy on Mars

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.

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.

The analemma for Mars

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.

Mars Exploration Rover image timestamps

Although this is unrelated to the rest of this article, it is interesting to note that it is possible to tell the time an image was taken by the Mars Exploration Rovers from the image's filename.

The images taken by Spirit and Opportunity have filenames with a built-in timestamp: characters 3–11 represent the number of (Earth) seconds since the J2000.0 epoch (January 1 2000 11:58:55.816 UTC) [3]. Thus an image with a name like "1P132176262ESF05A6P2670R8M1.JPG" has a timestamp of 132176262 seconds, which corresponds to March 10 2004 07:36:37.816 UTC.

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. Of course, on Mars, a "month" would have no relation to the orbital period of any moon as it does on Earth, since Phobos and Deimos orbit in about 7 hours and 30 hours respectively.

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; this is different from the sidereal year due to the effects of precession.

Actually, on Earth it is more accurate to say that the "vernal equinox year" is used for calendar purposes, and the tropical year is simply the average of various other possible years including the "summer solstice year", the "autumnal equinox year", the "winter solstice year" and other such years. All of these differ slightly; on Earth this is usually glossed over because the effect is not that important; however, on Mars, the differences are significantly larger. On Mars, the vernal equinox year is 668.5907 sols; the summer solstice year is 668.5880 sols; the "autumnal equinox year" is 668.5940 sols; and the "winter solstice year" is 668.5958 sols. Averaging out over an entire orbital period gives a Martian tropical year of 668.5921 sols. Note that 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.

Any calendar must use intercalation of days (leap years) to make up for the fact that a year is not equivalent to an integer number of days. On Earth, the leap-year formula (every 4th year except for every 100th year except for every 400th year) produces an average calendar year length of 365.2425 solar days, which is close enough to the vernal equinox year. On Mars, a similar intercalation scheme of 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 winter solstice year or on the vernal equinox year would differ by one sol in as little as two hundred or so Martian years. The Darian calendar uses the vernal equinox year length of 668.5907 sols as the basis of its intercalation scheme.

Seasons

Mars has an axial tilt of 25.2°, quite close to the value of 23.45° for Earth, and thus Mars has seasons of spring, summer, autumn, winter as Earth does (if the axial tilt was 0° there would be no seasons). As on Earth, the southern and northern hemispheres have summer and winter at opposing times.

However, the orbit of Mars has significantly greater eccentricity than that of Earth. Therefore the seasons are of unequal length, much more so than on Earth:

In practical terms, this means that summers and winters have different lengths and intensities in the northern and southern hemispheres. Winters in the north are warm and short (because Mars is moving fast near its perihelion), while winters in the south are long and cold (Mars is moving slowly near aphelion). Similarly, summers in the north are long and cool, while summers in the south are short and hot. Therefore extremes of temperature are considerably wider in the southern hemisphere than in the north.

The seasonal lag on Mars is no more than a couple of days [4], due to its lack of large bodies of water and similar factors that would provide a buffering effect. Thus, for temperatures on Mars, spring is approximately the mirror image of summer and autumn is approximately the mirror image of winter, and if Mars had a circular orbit the maximum and minimum temperatures would occur a couple of days after the summer and winter solstices rather than about one month after as on Earth. The only difference between spring temperatures and summer temperatures is due to the relatively high eccentricity of Mars's orbit: in northern spring Mars is farther from the Sun than during northern summer, and therefore by coincidence spring is slightly cooler than summer and autumn is slightly warmer than winter. However, in the southern hemisphere the opposite is true.

Of course, the temperature variations between spring and summer are much less than the very sharp variations that occur within a single Martian sol. On a daily basis, temperature peak at local solar noon and reach a minimum at local midnight. This is similar to the effect in Earth's deserts, only much more pronounced.

It is interesting to note that the axial tilt and eccentricity of Earth (or Mars) are by no means fixed, but rather vary due to gravitational perturbations from other planets in the solar system on a timescale of tens of thousands or hundreds of thousands of years. Thus, for example Earth's eccentricity of about 1% regularly fluctuates and can increase up to 6%, and at some point in the distant future the Earth will also have to deal with the calendrical implications of seasons of widely differing length (not to mention the major climate disruptions that go along with it).

Aside from the eccentricity, the Earth's axial tilt can also vary from 21.5° to 24.5°, and the length of this "obliquity cycle " is 41,000 years. These and other similar cyclical changes are thought to be responsible for ice ages (see Milankovitch cycles). By contrast, the obliquity cycle for Mars is much more extreme: from 15° to 35° over a 124,000-year cycle. Some recent studies even suggest that over tens of millions of years, the swing may be as much as 0° to 60°. [5] Earth's large Moon apparently plays an important role in keeping Earth's axial tilt within reasonable bounds; Mars has no such stabilizing influence and its axial tilt can vary more chaotically.

The color of the sky

Around sunset and sunrise the Martian sky is pinkish-red in color, but in the vicinity of the setting sun it is blue. This is the exact opposite of the situation on Earth. However, during the day the sky is a yellow-brown "butterscotch" color.[6]

On Mars Rayleigh scattering is usually a very small effect. It is believed that the color of the sky is caused by the presence of 1% by volume of magnetite in the dust particles.

Twilight lasts a long time after the Sun has set and before it rises, because of all the dust in Mars's atmosphere.

At times, the Martian sky takes on a violet color, due to scattering of light by very small water ice particles in clouds.[7]

Generating accurate true-color images of Mars's surface is surprisingly complicated. [8] There is much variation in the color of the sky as reproduced in published images; many of those images however are using filters to maximize the science value and are not trying to show true color. Nevertheless, for many years, the sky on Mars was thought to be more pinkish than it now is believed to be.

Astronomical phenomena

Earth and Moon from Mars, imaged by Mars Global Surveyor on May 8 2003 13:00 UTC. South America is visible.

Earth and Moon

As seen from Mars, the Earth is an inner planet like Venus (a "morning star" or "evening star"). The Earth and Moon appear starlike to the naked eye, but observers with telescopes would see them as crescents, with some detail visible.

Unusually, the Moon's orbital plane is much closer to the Earth's ecliptic than to Earth's equator. This is not the case for most other satellites of other planets in the solar system.

The maximum separation of the Earth and Moon is about 17′ when Earth is closest to Mars (near inferior conjunction) but only about 3.5′ when the Earth is farthest from Mars (near superior conjunction).

Mars Global Surveyor imaged the Earth and Moon on May 8 2003 13:00 UTC, very close to maximum elongation and at a distance of 0.930 AU from Mars. The apparent magnitudes were given as -2.5 and +0.9 [9]. At different times the actual magnitudes will vary considerably depending on distance and the phases of the Earth and Moon.

From one day to the next, the view of the Moon would change very differently for an observer on Mars than for an observer on Earth. The phase of the Moon as seen from Mars would not change much from day to day; it would match the phase of the Earth, and would only gradually change as both Earth and Moon move in their orbits around the Sun. On the other hand, an observer on Mars would see the Moon rotate, with the same period as its orbital period, and would see far side features that can never be seen from Earth.

Since Earth is an inner planet, observers on Mars can occasionally view transits of Earth across the Sun. The next one will take place in 2084. Of course, they can also view transits of Mercury and transits of Venus as well.

Phobos and Deimos

The moon Phobos appears about one third the angular diameter that the full Moon appears from Earth; on the other hand, Deimos appears more or less starlike with a disk barely discernible if at all. Phobos orbits so fast that it rises in the west and sets in the east; Deimos on the other hand rises in the east and sets in the west, but orbits only a few hours slower than a Martian sol, so it takes about two and a half days between rising and setting.

The maximum brightness of Phobos at "full moon" is about magnitude -9 or -10, while for Deimos it is about -5. [10] By comparison, the full Moon as seen from Earth is considerably brighter at magnitude -12.7. Phobos is still bright enough to cast shadows; Deimos is only slightly brighter than Venus is from Earth. Of course, just like Earth's Moon, both Phobos and Deimos are considerably fainter at non-full phases. Unlike Earth's Moon, Phobos's phases and angular diameter visibly change from hour to hour; Deimos is too small for its phases to be visible with the naked eye.

Both Phobos and Deimos have low-inclination equatorial orbits and orbit fairly close to Mars. As a result, Phobos is not visible from latitudes north of 70.4°N or south of 70.4°S; Deimos is not visible from latitudes north of 82.7°N or south of 82.7°S. Observers at high latitudes (less than 70.4°) would see a noticeably smaller angular diameter for Phobos because they are farther away from it.

Observers on Mars can view transits of Phobos and transits of Deimos across the Sun. The transits of Phobos could also be called partial eclipses of the Sun by Phobos, since the angular diameter of Phobos is up to half the angular diameter of the Sun. However, in the case of Deimos the term "transit" is appropriate, since it appears as a small dot on the Sun's disk.

Since Phobos orbits in a low-inclination equatorial orbit, there is a seasonal variation in the latitude of the position of Phobos's shadow projected onto the Martian surface, cycling from far north to far south and back again. At any given fixed geographical location on Mars, there are two intervals per Martian year when the shadow is passing through its latitude and about half a dozen transits of Phobos can be observed at that geographical location over a couple of weeks during each such interval. The situation is similar for Deimos, except only zero or one transits occur during such an interval.

It is easy to see that the shadow always falls on the "winter hemisphere", except when it crosses the equator during the vernal equinox and the autumnal equinox. Thus transits of Phobos and Deimos happen during Martian autumn and winter in the northern hemisphere and the southern hemisphere. Close to the equator they tend to happen around the autumnal equinox and the vernal equinox; farther from the equator they tend to happen closer to the winter solstice. In either case, the two intervals when transits can take place occur more or less symmetrically before and after the winter solstice (however, the large eccentricity of Mars's orbit prevents true symmetry).

The rapid motion of Mars's moons creates the possibility of using them for celestial navigation. In particular, their position among the stars could be used as a basis for telling global time accurately, and combined with knowledge of local time from observing the Sun this could be used to determine the longitude of the observer's position. On Earth, this was historically known as the "lunar distances" method of determining longitude, but was less practical because of the Moon's much slower motion and was superseded by John Harrison's invention of a sufficiently accurate chronometer. An additional complication of the lunar distances method on Earth was the fact that the Moon's considerable mass and its greater distance from Earth makes determining its orbit a three-body problem beyond the capabilities of accurate computation by early astronomers.

Observers on Mars can also view lunar eclipses of Phobos and Deimos. Phobos spends about an hour in Mars's shadow; for Deimos it is about two hours. Surprisingly, despite its orbit being nearly in the plane of Mars's equator and despite its very close distance to Mars, there are some occasions when Phobos escapes being eclipsed.

Phobos and Deimos both have synchronous rotation, which means that they have a "far side" that observers on the surface of Mars can't see. The phenomenon of libration occurs for Phobos as it does for Earth's Moon, despite the low inclination and eccentricity of Phobos's orbit. [11][12] Due to the effect of librations and the parallax due to the close distance of Phobos, by observing at high and low latitudes and observing as Phobos is rising and setting, the overall total coverage of Phobos's surface that is visible at one time or another from one location or another on Mars's surface is considerably higher than 50%.

The large Stickney crater is visible along the middle of the left-hand edge of the face of Phobos. It is easily visible with the naked eye from the surface of Mars.

Celestial poles and ecliptic

The orientation of Mars's axis is such that its north celestial pole is in Cygnus at R.A. 21h 10m 42s Decl. 52° 53.0' (or more precisely, 317.67669 +52.88378), near the 6th-magnitude star BD +52 2880 (also known as HR 8106, HD 201834, or SAO 33185), which in turn is at R.A. 21h 10min 15.6sec Decl. +53° 33' 48".

This position is about halfway between Deneb and Alpha Cephei, less than 10° from the former. This means that in nearly all of the northern hemisphere except areas close to the equator, Deneb never sets, but permanently circles the north pole. The orientation of Deneb would make a useful clock hand for telling sidereal time.

Mars's north celestial pole is also only a few degrees away from the galactic plane. Thus the Milky Way, especially rich in the area of Cygnus, is always visible.

The south celestial pole is correspondingly found at 9h 10m 42s and -52° 53.0', which is a couple of degrees from the 2.5 magnitude star Kappa Velorum (which is at 9h 22m 06.85s -55° 00.6'), which could therefore be considered the southern polar star. The star Canopus, second brightest in the sky, is a circumpolar star for most southern latitudes, except close to the equator.

The zodiac constellations of Mars's ecliptic are almost the same as those of Earth — after all, the two ecliptic planes only have a mutual inclination of 1.85° — but on Mars, the Sun spends 6 days in the constellation Cetus, leaving and re-entering Pisces as it does so. The equinoxes and solstices are different as well: for the northern hemisphere, vernal equinox is in Ophiuchus, summer solstice is at the border of Aquarius and Pisces, autumnal equinox is in Taurus, and winter solstice is in Virgo.

As on Earth, precession will cause the solstices and equinoxes to cycle through the zodiac constellations over thousands and tens of thousands of years.

Other

As on Earth, the effect of precession causes the north and south celestial poles to move in a very large circle, but on Mars the cycle is 175,000 Earth years rather than 26,000 years as on Earth.

As on Earth, there is a second form of precession: the point of perihelion in Mars's orbit changes slowly, causing the anomalistic year to differ from the sidereal year. However, on Mars, this cycle is 51,000 years rather than 21,000 years as on Earth.

As on Earth, the period of rotation of Mars (the length of its day) is slowing down. However, this effect is three orders of magnitude smaller than on Earth because the gravitational effect of Phobos is negligible and the effect is mainly due to the Sun.[13] On Earth, the gravitational influence of the Moon has a much greater effect. Eventually, in the far future, the length of a day on Earth will equal and then exceed the length of a day on Mars.

As on Earth, Mars experiences Milankovitch cycles that cause its axial tilt (obliquity) and orbital eccentricity to vary over long periods of time, which has long term effects on its climate. The variation of Mars's axial tilt is much larger than for Earth because it lacks the stabilizing influence of a large moon like Earth's moon. Mars has a 124,000-year obliquity cycle compared to 41,000 years for Earth.

See also

• Darian calendar
• Skies of other planets

• Transit of Phobos from Mars
• Transit of Deimos from Mars

• Transit of Mercury from Mars
• Transit of Venus from Mars
• Transit of Earth from Mars

External links

• Martian Time
• Mars fact sheet
• Mars24 - Time on Mars
• Technical Notes on keeping track of time on Mars
• Analemma on Mars
• What is a "Year" (on Earth or Mars?)

• Darian calendar
• Custom-made Martian timepieces were made for NASA staff