Timekeeping on Mars
Encyclopedia
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.
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 04.2s and 24h 00m 00.002s, respectively. This yields a conversion factor of 1.027491 days/sol. 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
, Mars Exploration Rover
, and Phoenix
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. Temperatures rise and fall rapidly at sunrise and sunset, because Mars lacks Earth's thick atmosphere and oceans which buffer such 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 day which uses standard units but which counts to 24hr 39m 35s before ticking over to the next day. Kim Stanley Robinson
's science fiction Mars Trilogy
describes digital clocks that use standard minutes and hours but freeze for a "timeslip" of roughly 39 minutes at midnight.
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 zone
s 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.
(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 second
s, 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.
) used local true solar time (LTST).
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 Rover
s 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.
. A mean Martian solar day, or "sol", is 24 hours, 39 minutes, and 35.244 seconds.
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 and Mars Phoenix 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 carry out activities independently.
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, or MSD, which is a running count of sols since approximately December 29, 1873. Some prefer a start date (or epoch
) around the year 1608; 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
- 51549.0 + 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 such as "tosol" (for "today") and "nextersol" or "morrowsol" (for "tomorrow") were less successful.
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.
, 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 Ls 0 to Ls 90 (northern-hemisphere spring / southern-hemisphere autumn) is the longest season lasting 194 Martian sols, and Ls 180 to Ls 270 (northern hemisphere autumn / southern-hemisphere spring) is the shortest season, lasting only 142 Martian sols.
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.)
(leap year
s) 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:
, 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.
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 fraction
s 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 668 ≈ 668.592105 and 0.5921 × 76 = 44.9996.
'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 (e.g. 1 January, 2 January, 1 February, 2 February, etc.) 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 modern Japanese practice, the months are not named but numbered sequentially, running from 1st Month to 24th Month.
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...
independently of Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
time and calendars.
Mars has an axial tilt
Axial tilt
In astronomy, axial tilt is the angle between an object's rotational axis, and a line perpendicular to its orbital plane...
and a rotation period similar to those of Earth. Thus it experiences seasons of spring
Spring (season)
Spring is one of the four temperate seasons, the transition period between winter and summer. Spring and "springtime" refer to the season, and broadly to ideas of rebirth, renewal and regrowth. The specific definition of the exact timing of "spring" varies according to local climate, cultures and...
, summer
Summer
Summer is the warmest of the four temperate seasons, between spring and autumn. At the summer solstice, the days are longest and the nights are shortest, with day-length decreasing as the season progresses after the solstice...
, autumn
Autumn
Autumn is one of the four temperate seasons. Autumn marks the transition from summer into winter usually in September or March when the arrival of night becomes noticeably earlier....
and winter
Winter
Winter is the coldest season of the year in temperate climates, between autumn and spring. At the winter solstice, the days are shortest and the nights are longest, with days lengthening as the season progresses after the solstice.-Meteorology:...
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
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...
is considerably larger, which means among other things that the lengths of various Martian seasons differ considerably, and sundial
Sundial
A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style onto a surface marked with lines indicating the hours of the day. The style is the time-telling edge of the gnomon, often a thin rod or a...
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 SISi
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
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 04.2s and 24h 00m 00.002s, respectively. This yields a conversion factor of 1.027491 days/sol. 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
Mars Pathfinder
Mars Pathfinder was an American spacecraft that landed a base station with roving probe on Mars in 1997. It consisted of a lander, renamed the Carl Sagan Memorial Station, and a lightweight wheeled robotic rover named Sojourner.Launched on December 4, 1996 by NASA aboard a Delta II booster a...
, Mars Exploration Rover
Mars Exploration Rover
NASA's Mars Exploration Rover Mission is an ongoing robotic space mission involving two rovers, Spirit and Opportunity, exploring the planet Mars...
, and Phoenix
Phoenix (spacecraft)
Phoenix was a robotic spacecraft on a space exploration mission on Mars under the Mars Scout Program. The Phoenix lander descended on Mars on May 25, 2008...
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. Temperatures rise and fall rapidly at sunrise and sunset, because Mars lacks Earth's thick atmosphere and oceans which buffer such fluctuations.
Alternative clocks for Mars have been proposed, but no mission has chosen to use such. These include a metric time
Metric time
Metric time is the measure of time interval using the metric system, which defines the second as the base unit of time, and multiple and submultiple units formed with metric prefixes, such as kiloseconds and milliseconds. It does not define the time of day, as this is defined by various time...
schema, with "millidays" and "centidays", and an extended day which uses standard units but which counts to 24hr 39m 35s before ticking over to the next day. Kim Stanley Robinson
Kim Stanley Robinson
Kim Stanley Robinson is an American science fiction writer known for his award-winning Mars trilogy. His work delves into ecological and sociological themes regularly, and many of his novels appear to be the direct result of his own scientific fascinations, such as the fifteen years of research...
's science fiction Mars Trilogy
Mars trilogy
The Mars trilogy is a series of award-winning science fiction novels by Kim Stanley Robinson that chronicles the settlement and terraforming of the planet Mars through the intensely personal and detailed viewpoints of a wide variety of characters spanning almost two centuries...
describes digital clocks that use standard minutes and hours but freeze for a "timeslip" of roughly 39 minutes at midnight.
Equation of time
The equation of time is the difference between apparent solar time and mean solar time. At any given instant, this difference will be the same for every observer...
that represents the difference between sundial time and uniform (clock) time. The equation of time is illustrated by an analemma
Analemma
In astronomy, an analemma is a curve representing the angular offset of a celestial body from its mean position on the celestial sphere as viewed from another celestial body relative to the viewing body's celestial equator...
. Because of orbital eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...
, 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
Prime Meridian
The Prime Meridian is the meridian at which the longitude is defined to be 0°.The Prime Meridian and its opposite the 180th meridian , which the International Date Line generally follows, form a great circle that divides the Earth into the Eastern and Western Hemispheres.An international...
, defined as passing through the small crater Airy-0
Airy-0
Airy-0 is a crater on Mars whose location defines the position of the prime meridian of that planet. It is about across and lies within the larger crater Airy in the region Sinus Meridiani....
. However, Mars does not have time zone
Time zone
A time zone is a region on Earth that has a uniform standard time for legal, commercial, and social purposes. In order for the same clock time to always correspond to the same portion of the day as the Earth rotates , different places on the Earth need to have different clock times...
s 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
Standard time
Standard time is the result of synchronizing clocks in different geographical locations within a time zone to the same time rather than using the local meridian as in local mean time or solar time. Historically, this helped in the process of weather forecasting and train travel. The concept...
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 TimeUniversal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...
(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
Airy-0
Airy-0 is a crater on Mars whose location defines the position of the prime meridian of that planet. It is about across and lies within the larger crater Airy in the region Sinus Meridiani....
). The name "MTC" is intended to parallel the Terran Coordinated Universal Time
Coordinated Universal Time
Coordinated Universal Time is the primary time standard by which the world regulates clocks and time. It is one of several closely related successors to Greenwich Mean Time. Computer servers, online services and other entities that rely on having a universally accepted time use UTC for that purpose...
(UTC), but this is somewhat misleading: what distinguishes UTC from other forms of UT is its leap second
Leap second
A leap second is a positive or negative one-second adjustment to the Coordinated Universal Time time scale that keeps it close to mean solar time. UTC, which is used as the basis for official time-of-day radio broadcasts for civil time, is maintained using extremely precise atomic clocks...
s, 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
Goddard Institute for Space Studies
The NASA Goddard Institute for Space Studies , at Columbia University in New York City, is a component laboratory of NASA's Goddard Space Flight Center Earth-Sun Exploration Division and a unit of The Earth Institute at Columbia University...
. It replaced Mars24's previous use of the term "Airy Mean Time" (AMT), which was a direct parallel of Greenwich Mean Time
Greenwich Mean Time
Greenwich Mean Time is a term originally referring to mean solar time at the Royal Observatory in Greenwich, London. It is arguably the same as Coordinated Universal Time and when this is viewed as a time zone the name Greenwich Mean Time is especially used by bodies connected with the United...
(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
Mars Exploration Rover
NASA's Mars Exploration Rover Mission is an ongoing robotic space mission involving two rovers, Spirit and Opportunity, exploring the planet Mars...
missions, the positional uncertainty of Airy-0 corresponded to roughly a 20 second uncertainty in realizing AMT.
Timezones
Each lander mission so far has used its own timezone, 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 PathfinderMars Pathfinder
Mars Pathfinder was an American spacecraft that landed a base station with roving probe on Mars in 1997. It consisted of a lander, renamed the Carl Sagan Memorial Station, and a lightweight wheeled robotic rover named Sojourner.Launched on December 4, 1996 by NASA aboard a Delta II booster a...
) used local true solar time (LTST).
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 Rover
Mars Exploration Rover
NASA's Mars Exploration Rover Mission is an ongoing robotic space mission involving two rovers, Spirit and Opportunity, exploring the planet Mars...
s 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.
Sols
The term sol is used by planetary astronomers to refer to the duration of a solar day on MarsMars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...
. A mean Martian solar day, or "sol", is 24 hours, 39 minutes, and 35.244 seconds.
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 and Mars Phoenix 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
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
by 179 degrees, so when it is daylight for one it is night for the other, and they carry out activities independently.
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, or MSD, which is a running count of sols since approximately December 29, 1873. Some prefer a start date (or epoch
Epoch (astronomy)
In astronomy, an epoch is a moment in time used as a reference point for some time-varying astronomical quantity, such as celestial coordinates, or elliptical orbital elements of a celestial body, where these are subject to perturbations and vary with time...
) around the year 1608; 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
International Atomic Time
International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...
- 51549.0 + 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
Mars Exploration Rover
NASA's Mars Exploration Rover Mission is an ongoing robotic space mission involving two rovers, Spirit and Opportunity, exploring the planet Mars...
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.
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. Ls is defined as 0 degrees at the Martian northward equinox, and hence is 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
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
, 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
Darian calendar
The Darian Calendar better known as the "Calendar of Adam" is a proposed system of time-keeping designed to serve the needs of any possible future human settlers on the planet Mars...
. 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
Phobos (moon)
Phobos is the larger and closer of the two natural satellites of Mars. Both moons were discovered in 1877. With a mean radius of , Phobos is 7.24 times as massive as Deimos...
and Deimos
Deimos (moon)
Deimos is the smaller and outer of Mars's two moons . It is named after Deimos, a figure representing dread in Greek Mythology. Its systematic designation is '.-Discovery:Deimos was discovered by Asaph Hall, Sr...
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
Lunar month
In lunar calendars, a lunar month is the time between two identical syzygies . There are many variations. In Middle-Eastern and European traditions, the month starts when the young crescent moon becomes first visible at evening after conjunction with the Sun one or two days before that evening...
. Neither the Darian calendar nor any other Martian calendar is currently in use.
Martian year
This length of time for Mars to complete one orbit around the Sun is its sidereal yearSidereal year
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It was equal to at noon 1 January...
, 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 Ls 0 to Ls 90 (northern-hemisphere spring / southern-hemisphere autumn) is the longest season lasting 194 Martian sols, and Ls 180 to Ls 270 (northern hemisphere autumn / southern-hemisphere spring) is the shortest season, lasting only 142 Martian sols.
As on Earth, the sidereal year is not the quantity that is needed for calendar purposes. Rather, the tropical year
Tropical year
A tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...
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
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
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
Equinox
An equinox occurs twice a year, when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the center of the Sun being in the same plane as the Earth's equator...
or solstice
Solstice
A solstice is an astronomical event that happens twice each year when the Sun's apparent position in the sky, as viewed from Earth, reaches its northernmost or southernmost extremes...
, 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.)
Intercalation
Any calendar must use intercalationIntercalation
Intercalation is the insertion of a leap day, week or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.- Solar calendars :...
(leap year
Leap year
A leap year is a year containing one extra day in order to keep the calendar year synchronized with the astronomical or seasonal year...
s) 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:
, 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.
Other intercalation schemes are possible. For example, the Hebrew Calendar
Hebrew calendar
The Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
(a lunisolar calendar
Lunisolar calendar
A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year then the calendar will...
) 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 fraction
Continued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...
s 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 668 ≈ 668.592105 and 0.5921 × 76 = 44.9996.
Martian time in fiction
In Kim Stanley RobinsonKim Stanley Robinson
Kim Stanley Robinson is an American science fiction writer known for his award-winning Mars trilogy. His work delves into ecological and sociological themes regularly, and many of his novels appear to be the direct result of his own scientific fascinations, such as the fifteen years of research...
's Mars Trilogy
Mars trilogy
The Mars trilogy is a series of award-winning science fiction novels by Kim Stanley Robinson that chronicles the settlement and terraforming of the planet Mars through the intensely personal and detailed viewpoints of a wide variety of characters spanning almost two centuries...
, clocks retain Earth-standard seconds, minutes and hours, but freeze at midnight for 39.5 minutes. As the fictional colonization of Mars
Colonization of Mars
The colonization of Mars by humans is the focus of speculation and serious study because the surface conditions and availability of water on Mars make it arguably the most hospitable planet in the solar system other than Earth...
progresses, this "timeslip" becomes a sort of witching hour
Witching hour
The witching hour is a the time of day when supernatural creatures such as witches, demons and ghosts are thought to appear and be at their most powerful, and black magic at its most effective...
, 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
Philip K. Dick
Philip Kindred Dick was an American novelist, short story writer and essayist whose published work is almost entirely in the science fiction genre. Dick explored sociological, political and metaphysical themes in novels dominated by monopolistic corporations, authoritarian governments and altered...
's much earlier Martian Time-Slip
Martian Time-Slip
Martian Time-Slip is a 1964 science fiction novel by Philip K. Dick. The novel uses the common science fiction concept of a human colony on Mars...
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
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
, 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.) In the manga
Manga
Manga is the Japanese word for "comics" and consists of comics and print cartoons . In the West, the term "manga" has been appropriated to refer specifically to comics created in Japan, or by Japanese authors, in the Japanese language and conforming to the style developed in Japan in the late 19th...
and anime
Anime
is the Japanese abbreviated pronunciation of "animation". The definition sometimes changes depending on the context. In English-speaking countries, the term most commonly refers to Japanese animated cartoons....
series Aria
ARIA (manga)
is a utopian science fantasy manga by Kozue Amano. The series was originally titled when it was published by Enix in the magazine Monthly Stencil, being retitled when it moved to Mag Garden's magazine Comic Blade. Aqua was serialized in Stencil from 2001 to 2002 and collected in two tankōbon volumes...
by Kozue Amano
Kozue Amano
is a female Japanese manga artist. She is widely known as the creator of Aria, which proved to be a best-selling hit, and was adapted into an anime television series consisting of 3 seasons and an OVA....
, set on a terraformed Mars, the calendar year is also divided into twenty-four months. Following modern Japanese practice, the months are not named but numbered sequentially, running from 1st Month to 24th Month.
Formula to convert MJD/UTC to MSD/MTC
- Modified Julian Date
- MJDJulian dayJulian day is used in the Julian date system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon...
= JDJulian dayJulian day is used in the Julian date system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon...
− 2,400,000.5
- MJD
- Coordinated Universal Time
- UTC = (MJDJulian dayJulian day is used in the Julian date system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon...
modModulo operationIn computing, the modulo operation finds the remainder of division of one number by another.Given two positive numbers, and , a modulo n can be thought of as the remainder, on division of a by n...
86400) * 24
- UTC = (MJD
- Mars Time Coordinated
- MTC = (MSD modModulo operationIn computing, the modulo operation finds the remainder of division of one number by another.Given two positive numbers, and , a modulo n can be thought of as the remainder, on division of a by n...
86400) * 24
- MTC = (MSD mod
- Mars Solar Date
- MSD = (seconds since January 6, 2000 00:00:00 UTC)/88775.244 + 44795.9998