*(Updated July 30, 2004)*

These notes provide a technical brief on the definitions of numeric readouts in Mars24. Further details can be found in the appended references. A less technical account of solar time on Mars is provided in the 1998 article "Telling Time on Mars" on the NASA GISS website. Information about the specific controls and displays in Mars24 is provided in the accompanying User's Guide.

Following the long-standing practice originally adopted in 1976 by the Viking
Lander missions, the daily variation of Mars solar time is reckoned in terms of
a "24-hour" clock, representing a 24-part division of the planet's solar day,
along with the traditional sexagesimal subdivisions of 60 minutes and 60 seconds.
A **Mars solar day** has a mean period of **24 hours 39 minutes 35.244 seconds**,
and is customarily referred to as a **"sol"** in order to distinguish this from
the roughly 3% shorter solar day on Earth. The Mars sidereal day, as measured with
respect to the fixed stars, is 24h 37m 22.663s, as compared with 23h 56m 04.0905s
for Earth.

The apparent seasonal advance of the Sun at Mars is commonly measured in terms
of the **areocentric longitude L_{s}**, as referred to the planet's vernal
equinox (the ascending node of the apparent seasonal motion of the Sun on the planet's
equator). As defined,

In terms of `L _{s}`, the seasonally variable,
planet-centered

As a result of the planet's orbital eccentricity, `L _{s}` advances somewhat
unevenly with time, but can be efficiently evaluated as a trigonometric power series
for the orbital eccentricity and the orbital mean anomaly measured with respect to
the perihelion. The areocentric longitude at perihelion,

The period for the repetition of the planet-centered measure of mean Solar
longitude is referred to as the tropical year. (This period is linked to the rate
of advance of the "Fictitious Mean Sun," as discussed below.) The **Mars tropical
year** is **686.9726 day or 668.5921 sol**. For comparison,
the Mars sidereal year, as measured with respect to the fixed stars, is
668.5991 sol. The difference between these values results from the
precession of the planet's spin axis.

The mean interval between the repetition of the planet's perihelion passage, or
anomalistic year, is 668.6146 sol, and corresponds to the rate of advance
of the planet's orbital mean anomaly. The mean repetition period for a particular
solar season varies with the `L _{s}`. The mean repetition intervals for the
vernal equinox, summer solstice, autumnal equinox , and winter solstice on Mars are
668.5906 sol, 668.5880 sol, 668.5940 sol, and
668.5958 sol, respectively, and the average of these is just the tropical year.

Also as a result of a planet's orbital eccentricity, as well as its obliquity,
there is a seasonally variable discrepancy between the even advance of an artificially
defined Mean Solar Time and of the True Solar Time corresponding to the actual
planet-centered position of the Sun in its sky. Following the conventional usage
of terrestrial timekeeping, Mean Solar Time on Mars has been defined in reference
to the so-called Right Ascension of the **Fictitious Mean Sun (FMS)**. As defined,
the FMS is the angle between the planet's vernal equinox, measured along the plane of
its equator, and an artificially defined "dynamical mean Sun" advancing at a rate
corresponding to the planet's solar tropical year (i.e., the Mars FMS advances at
a rate of 360°/686.9726 day or 0.5240384°/day). Its numerical value
(to within an arbitrary multiple of 360°) is just the sum of the orbital mean
anomaly, M, and the areocentric longitude at perihelion, `L _{s,p}`.
The FMS
at Mars was evaluated by Allison and McEwen (2000) (hereafter "AM2000") as a mean
fit to an accurate calculation of the areocentric longitude over 134 Mars orbits
(for the years 1874-2127), adjusted in its angular placement by the (~0°.0046)
solar aberration. This evaluation has been adopted by the Mars Exploration Rover
project for its definition of Mars Mean Solar Time (cf. Roncoli et al., 2002).

The difference between the True Solar Time (TST) and the Mean Solar Time (MST),
equivalent in the corresponding angular measure to the difference between the right
ascensions of the FMS and the true Sun, is referred to as the **Equation of Time
(EOT)**. For Earth, the EOT varies between -14.2min and +16.3min. Mars, with its
more than five times larger orbital eccentricity, has an EOT varying between -51.1min
and +39.9min. The parametric plot of the EOT vs. the solar declination is called
the solar analemma. For Earth, this takes the form of the
figure-8 pattern marked
on some sundials and globes (for the latter typically in the empty space of the South
Pacific). For Mars, the
analemma assumes the shape of a
raindrop,
as shown for example by Allison (1997).

In the mid-1800s the use of locally measured and defined time on Earth was gradually supplanted by the use of time zones in order to facilitate standardization of railroad schedules and, to a lesser extent, of recording scientific observations. This process culminated in 1884 in an international conference which created the global system of time zones and specified the longitude of Greenwich as the prime meridian. Each zone is approximately 15° wide, the exact width and shape being subject to political boundaries and significant geographic features, and within each clocks are referenced to the same hour.

Mars24 includes the option to display the local time at the selected location in terms of similarly constructed "Mars time zones". We have defined these Mars time zones to be exactly 15° wide and centered on successive 15° multiples of longitude, at 0°, 15°, 30°, etc. We have not attempted to name these time zones, as for example "Olympus Standard Time", but do identify their read-out with a suffix indicating the timezone offset. Thus, again using the case of Olympus Mons, the timezone identifier is "MTC-9", or nine hours behind MTC.

The prime meridian of Mars is defined by the location of the crater
Airy-0
(De Vaucoulers et al., 1973), named in honor of the British astronomer who built
the telescope at Greenwich whose location defines the prime meridian on Earth.
Although it might be tempting to refer to "standard" time on the Mars prime
meridian as "Airy Mean Time" (AMT) in analogy to Earth's "Greenwich Mean Time"
(GMT), the latter term has been supplanted by
Coordinated Universal Time
(UTC) in international timekeeping services. Mars24 therefore refers to the Mean Solar
Time on the Mars prime meridian as **Mars Coordinated Time, or MTC**, by analogy
to the terrestrial UTC.

Each landed mission on Mars has adopted a different reference for its solar time keeping.

The Viking Lander "Sol Numbers" were reckoned from a zero starting point at each of the local true solar midnights immediately prior to their touchdowns. Time tags for the Mars Pathfinder Lander were referenced with respect to the local true solar time, with elapsed sols reckoned from the local true solar midnight preceding its landing, but designated with a starting number "1" rather than zero. Conversion formulae are provided by AM2000.

The derivation of mission time adopted by the Mars Exploration Rover Project at the Jet Propulsion Laboratory is an offset modification of an evenly advancing mean solar time, based on its definition by Roncoli et al. (2002). For MER-A spirit, the difference between lander mission time and local mean solar time is more than 41 minutes; for MER-B Spirit the difference is more than 37 minutes. At approximately the middle of each of the MER A and B nominal missions, lander mission time should align with local true solar time to within 30 seconds. As with Pathfinder, "Sol 1" denotes the solar day on which landing occurred.

Although numerous month-year calendars have been proposed for Mars, we
have not attempted to support any of these as a feature of Mars24. We have,
however, included as a Mars24 read-out the **"Mars Sol Date" (MSD)**
defined by AM2000. This represents a sequential count of Mars solar days
elapsed since 1873 December 29 at approximately Greenwich noon
(Julian Day 2405522.0).
This epoch was prior to the great 1877 perihelic opposition of Mars and
precedes nearly all detailed observations of temporal changes on the planet.
It corresponds to a Mars `L _{s}` of 277°, approximately the same
planetocentric solar longitude as that for the Earth on the same date.
MSD 44796.0 is approximately coincident with 2000 January 6.0, at a
near-coincidence of prime meridian midnights on the two planets and a
repetition of Mars

Mars24 uses the short-series representation of the seven-largest
short-period planetary perturbations of the Mars orbital longitude specified
by AM2000, as adapted from Simon et al. (1994). Detailed comparisons with an
accurate ephemeris suggest that the maximum error in the calculated
`L _{s}` by the adopted algorithm is 0°.008 over ±100 years
of J2000. According to the implicit dependence of the calculated EOT on the

Of course, the calculation of Local (True or Mean) solar time cannot be any more accurate than the longitudinal placement of the local point of interest! Predicted solar times for a given lander location may therefore need to be revised post-touchdown as improved navigation for their coordinates becomes available.

Mars24's estimate of times of local sunrise and sunset, as well as times of Earthrise and Earthset, requires correct input of planetographic latitude. Even so, the results may be in error due to local topography and atmospheric refraction. Comparison to known times for a limited number of solar and Earth rise and set events at Mars lander sites suggest that absent topographic and atmospheric effects, the error in calculating these times is less than 30 seconds.

The current version of Mars24 is posted in the Software Tools section of the NASA GISS website. Interested users may want to revisit this site for occasional updates. Alternatively, you may e-mail the author and request to be added to the update announcements mailing list.

A brief history of significant timekeeping modifications to the code is summarized as follows:

- April 1998: Version 1.0 applet released, using timing formulae published in Allison (1997). An outgrowth of an earlier Mars Pathfinder clock applet, Version 1.0 allowed lookup of the time anywhere on the planet and displayed a equirectangular sunclock.
- January 2000: Version 2.0 released, using formulae subsequently published in AM2000.
- September 2000: Version 3.0 released.
- January 2002: Version 4.0 released, using a revised specification of the inertial location of the Mars prime meridian, replacing that given in Table 4 of AM2000, consistent with the recommendations of Seidelmann et al. (2000, 2002).
- July 2003: Version 5.0 released. First stand-alone application version.
- August 2003: The conversion between the terrestrial time TT and Universal Coordinated Time UTC as given by Equation 27 of AM2000 was modified for greater accuracy with a fourth-order polynomial representation, accurate to within 3 s for 1975-2005.
- October 2003: Calculation of Mars' heliocentric longitude and latitude refined, which in turn allowed for calculation of the light-distance between Earth and Mars to within one second.
- December 2003: Calculation of local sunrise and sunset times added.
- January 2004: Calculation of sub-Earth point added.
- February 2004: Calculation of local earthrise and earthset times added.

The NASA GISS Mars24 application was written by Dr. Robert B. Schmunk. If you wish to be notified when new versions of Mars24 are released or if you would like to report a bug, please contact:

Robert B. Schmunk

NASA Goddard Institute for Space Studies

2880 Broadway

New York, NY 10025 USA

rschmunk@giss.nasa.gov

Technical questions related to the definition of Mars Solar Time and the mathematical algorithms adopted for its calculation by Mars24 may be directed to:

Michael D. Allison

NASA Goddard Institute for Space Studies

2880 Broadway

New York, NY 10025 USA

mallison@giss.nasa.gov

We thank members of the Mars Climate Orbiter and Mars Exploration Rover Projects at NASA's Jet Propulsion Laboratory for their encouragement over many years on behalf of the development of our solar timing algorithms and Mars24 sunclock.

The base map image used by Mars24 in its sunclock is derived from an image created by the Mars Global Surveyor MOLA and MOC teams for the National Geographic Society. See the MOLA science webpage at NASA Goddard Space Flight Center.

Mars24 includes software developed by the JDOM Project and which is copyright 2000-2003 Jason Hunter and Brett McLaughlin. For more information about JDOM, including source code and conditions of use, please see the JDOM homepage.

Mars24 includes software developed as part of the GNU JAXP project, including the AElfred2 parser. For more information about GNU JAXP, including source code and conditions of use, please see the GNU JAXP homepage.

Mars24 uses PngEncoder by J. David Eisenberg. For more information, including source code and conditions of use, please see catcode.com.

Mars24 uses QuantizeFilter by Jerry Huxtable. For more information, including source code, please see the JH Labs website.

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