Enumeration Of Mars Years And Seasons Since The Beginning .
Icarus 251 (2015) 332–338Contents lists available at ScienceDirectIcarusjournal homepage: www.elsevier.com/locate/icarusEnumeration of Mars years and seasons since the beginning of telescopicexplorationSylvain Piqueux a, , Shane Byrne b, Hugh H. Kieffer c,d, Timothy N. Titus e, Candice J. Hansen faJet Propulsion Laboratory, California Institute of Technology, M/S 183-601, 4800 Oak Grove Drive, Pasadena, CA 91109, USAUniversity of Arizona, Lunar and Planetary Laboratory, Tucson, AZ 85721-0092, USAcCelestial Reasonings, 180 Snowshoe Ln., POB 1057, Genoa, NV 89411-1057, USAdSpace Science Institute, 4750 Walnut Street, Suite 205, Boulder, CO 80301, USAeAstrogeology Science Center, United States Geological Survey, 2255 N. Gemini Dr., Flagstaff, AZ 86001, USAfPlanetary Science Institute, 1700 E. Fort Lowell, Suite 106, Tucson, AZ 85719, USAba r t i c l ei n f oArticle history:Received 6 August 2014Revised 10 November 2014Accepted 9 December 2014Available online 10 January 2015a b s t r a c tA clarification for the enumeration of Mars years prior to 1955 is presented, along with a table providingthe Julian Dates associated with Ls 0 for Mars years 183 (beginning of the telescopic study of Mars) to100. A practical algorithm for computing Ls as a function of the Julian Date is provided. No new scienceresults are presented.Ó 2015 Elsevier Inc. All rights reserved.Keywords:MarsMars, polar capsMars, atmosphereMars, climateWell before the start of the martian robotic exploration in the1960s with the US Mariner (Leighton et al., 1965) and soviet Mapc(Mars) programs (Florenski et al., 1975), Earth-based telescopicobservations led several generations of scientists to the understanding that both the surface and the atmosphere of Mars aredynamic units changing over the scale of hours to seasons. Brightclouds and hazes were observed to appear and disappear at specificlocations and local times (Slipher, 1927; Wright and Kuiper, 1935;Martin and Baum, 1969); local, regional, and global dust stormswere monitored and recognized to be prevalent at specific seasonsand areas (Antoniadi, 1930; de Vaucouleurs, 1954; Golitsyn, 1973);variations of the surface albedo and color far from the poles wereobserved locally and regionally (Antoniadi, 1930; Slipher, 1962);the seasonality of both polar caps was tracked for indications ofinter-annual and global scale environmental changes (Jameset al., 1992). A fuller description of historic telescopic observationsis given by Martin et al. (1992).The characterization of these large-scale phenomena was limited by the low spatial resolution of available data, observationalbiases due to orbital constraints on Earth-based observations,and limitations in telescopic remote sensing techniques. Theadvent of robotic exploration has revolutionized our view of Mars Corresponding author. Fax: 1 818 354 2494.E-mail address: Sylvain.Piqueux@jpl.nasa.gov (S. 2.0140019-1035/Ó 2015 Elsevier Inc. All rights reserved.as a dynamic system: globally available high spatial and temporalresolution datasets relying on various remote sensing and in situtechniques have opened the door to systematic surveys, and tothe characterization of inter-seasonal and inter-annual variability(see a few examples in Smith, 2004; Geissler, 2005; Titus, 2005;Benson et al., 2006). Studies of modern dynamic processes havealso become possible e.g., Sullivan et al. (2001), Russell (2008),Byrne et al. (2009), Verba et al. (2010), Hansen (2011), McEwenet al. (2011) and Daubar et al. (2013). Concomitantly, the enormous amount of data available has fueled a large body of dynamical numerical models emulating geological processes occurring atthe scale of seconds (e.g., Rafkin et al., 2001; Michaels, 2006;Mangold et al., 2010) to centuries e.g., Byrne and Ingersoll (2003)and Thomas et al. (2009).While a consensus has unanimously emerged in the communityto define martian local hours as 1/24th fraction of a Mars day(‘‘sol’’), and seasons as the aerocentric longitude of the Sun, theMars community has only recently adopted an absolute enumeration of individual martian years (referred to as MY in thispaper, not to be confused with Mega years). Under this systemdesigned by Clancy et al. (2000) for their inter-annual data comparison needs, MY 1 started on April 11 1955 (Temps UniverselCoordonné, UTC at 00:00:00) at Ls 0 (the year of the great1956 dust storm, Ls being measured from the intersection of theplane of Mars equator and the plane of its orbit, corresponding to
S. Piqueux et al. / Icarus 251 (2015) 332–338333Fig. 1. Martian graphical calendar from MY 23 to MY 32, with periods of activity of robotic missions (top) and global scale phenomena (bottom). ODY: Mars Odyssey; MER:Mars Exploration Rovers (MER A: Spirit and MER B: Opportunity); MRO: Mars Reconnaissance Orbiter; MSL: Mars Science Laboratory/Curiosity; MEX: Mars Express; MGS:Mars Global Surveyor; PTH: Mars Pathfinder; PHX: Phoenix Lander. Additional information can be found in Soderblom and Bell (2008). The different data acquisition phasesof the Mars Orbiter Camera (MOC) onboard MGS are indicated, as their nomenclature is not directly related to MGS orbit numbers. Black line indicates MEX periapsis latitude.Orbit numbers are indicated for orbiters (based on data archived in NASA’s Navigation and Ancillary Information Facility – NAIF – website, at m/ORMM MERGED 01098.ORB for MEX, ftp://naif.jpl.nasa.gov/pub/naif/MRO/kernels/spk (information contained in .norb files) for MRO, ftp://naif.jpl.nasa.gov/pub/naif/M01/kernels/spk (information contained in .norb files) for ODY, ice-6-v1.0/mgsp 1000/extras/orbnumand ice-6-v1.0/mgsp 1000/extras/orbnum/mgs (information contained in .nrb files) for MGS pre-mapping and mappingorbits. MOC dates can be extracted from https://starbase.jpl.nasa.gov/archive/mgs-m-moc-na wa-2-dsdp-l0-v1.0/mgsc 0010/index/cumindx.tab and http://pds-imaging.jpl.nasa.gov/data/mgs-m-moc-na wa-2-sdp-l0-v1.0/mgsc 1578/index/cumindex.tab. For MOC, additional information is available at http://www.msss.com/moc gallery/mocsubphases.html. Duration of surface activities for rovers and landers are indicated in sols. Gray shading shows the extent of the polar night. Blue shading indicates the extentof the seasonal polar caps (light blue is the minimum extent, and dark blue is the maximum extent) (Titus, 2005). Atmospheric pressures at 0 m elevation is indicated inpurple, from Tillman et al. (1993). Global dust storms are indicated in salmon. Dates of aphelion and perihelion are fixed at Ls 252 and 72 and indicated in red (dashed andsolid lines, respectively) and dates of conjunction and opposition relative to the Earth are in green (dashed and solid lines respectively) and calculated using the NAIFSpacecraft Planet Instrument C-Matrix Events (SPICE) toolkit (http://naif.jpl.nasa.gov/naif/toolkit.html). All time conversions between terrestrial and martian time done usingthe algorithms of Allison and McEwen (2000).the vernal equinox, see Allison and McEwen (2000), their Fig. 1)and lasted until Mars completed a full revolution around the Sun,i.e. February 26 1957 UTC (beginning of MY 2). The Mars community quickly adopted this enumeration system at a time whenclimatological records were starting to be established and becauseit greatly clarifies and simplifies the comparison with Julian calendar dates. However, an ambiguity has remained regarding thecount of MY prior to 1955. Such dates in the recent martian pastare regularly used in the literature, primarily for cyclical processesspanning a few martian decades (see for example references inTitus et al., 2008).Here we extend Clancy et al.’s (2000) definition by defining MY0 (May 24 1953), and any previous MY with ‘‘–’’ as a prefix (i.e., MY 1 starts on July 7th 1951, 2 on August 19 1949, etc.). For numerical calculations, the inclusion of MY 0 is a significant simplification. In addition, most time keeping systems start at 0. Marscalendar alternatives with different origins have been informallyproposed (e.g., Wood and Paige, 1992; Tamppari et al., 2000;Smith et al., 2001), without being widely accepted and were asarbitrary as the one adopted here.Table 1 provides a correspondence between the beginning ofevery MY (Ls 0 ) since the first known telescopic observationsof Mars by Galileo (circa 1610 , MY 183) to MY 100, the civil calendar, and days from the origin of the modern astronomical timesystem, J2000.0 (Julian Date (JD) 2451545.0). A similar table, butwithout the MY assignments, is presented in Kieffer et al. (1992);
334S. Piqueux et al. / Icarus 251 (2015) 332–338Fig. 1 (continued)
335S. Piqueux et al. / Icarus 251 (2015) 332–338Table 1Starting date of Mars years, as days from J2000, JD 2451545.Mars yearEarthDays from J2000Mars yearEarthDays from J2000Mars yearEarthDays from J2000YearMonDayYearMonDayYearMon 184 183 182 181 180160716091611161216144311211251228152 143425.630 142738.650 142051.670 141364.720 140677.740 89 88 87 86 85178517871789179117931211108730174218 78163.396 77476.419 76789.479 76102.520 15 12901.180 12214.210 11527.270 10840.290 10153.300 179 178 177 176 1751616161816201622162498653197241229 139990.750 139303.790 138616.820 137929.850 137242.910 84 83 82 81 8017951797179918011802542112261228164 74728.550 74041.600 73354.610 72667.640 52310 9466.317 8779.349 8092.373 7405.432 6718.466 174 173 172 171 17016261628162916311633211110814219724 136555.930 135868.920 135181.960 134495.002 133808.020 79 78 77 76 7518041806180818101812109764218261330 71293.710 70606.720 69919.760 69232.790 64 6031.469 5344.497 4657.544 3970.550 3283.590 169 168 167 166 1651635163716391641164375431122916319 133121.080 132434.120 131747.120 131060.140 130373.170 74 73 72 71 7018141816181718191821321211918321825 67858.880 67171.880 66484.880 65797.930 61431 2596.642 1909.654 1222.672 535.714151.264 164 163 162 161 160164416461648165016521210976624102915 129686.190 128999.230 128312.290 127625.300 126938.310 69 68 67 66 651823182518271829183186542133018420 64423.980 63737.040 63050.080 62363.090 1926838.2291525.1762212.1732899.1663586.124 159 158 157 156 15516541656165816591661532121132052410 126251.360 125564.390 124877.400 124190.460 123503.480 64 63 62 61 60183318341836183818401111087725123017 60989.140 60302.160 59615.210 58928.250 5234273.0904960.0705647.0126333.9797020.971 154 153 152 151 150166316651667166916719875428142196 122816.490 122129.530 121442.560 120755.590 120068.650 59 58 57 56 551842184418461848184964311242192512 57554.280 56867.320 56180.340 55493.360 230177707.9568394.9189081.8969768.84310455.797 149 148 147 146 145167316751676167816802111108219261431 119381.670 118694.660 118007.690 117320.730 116633.750 54 53 52 51 501851185318551857185910986530164208 54119.440 53432.450 52745.490 52058.520 1211142.79311829.77412516.72713203.71613890.691 144 143 142 141 1401682168416861688169076431195231026 115946.800 115259.850 114572.860 113885.880 113198.900 49 48 47 46 451861186318641866186832121110251028152 50684.610 49997.630 49310.620 48623.660 422914577.63415264.61815951.60916638.56917325.539 139 138 137 136 135169116931695169716991210986143118523 112511.930 111824.960 111138.030 110451.050 109764.050 44 43 42 41 401870187218741876187887542207251127 47249.720 46562.760 45875.810 45188.820 2816218012.51118699.45119386.43820073.43520760.397 134 133 132 131 13017011703170517071708532111112913118 109077.093 108390.130 107703.136 107016.185 106329.219 39 38 37 36 3518801881188318851887112109715220625 43814.860 43127.880 42440.920 41753.980 23021447.35522134.33822821.28623508.24224195.234 129 128 127 126 12517101712171417161718108754623112815 105642.226 104955.256 104268.295 103581.313 102894.364 34 33 32 31 3018891891189318951896643212112916119 40380.010 39693.050 39006.090 38319.090 072524882.22825569.19326256.17326943.13127630.078 124 123 122 121 12017201722172317251727311210921862310 102207.404 101520.398 100833.418 100146.468 99459.495 29 28 27 26 2518981900190219041906119865624122917 36945.180 36258.190 35571.220 34884.260 41928317.06829004.05529691.00930377.98531064.971 119 11817291731762714 98772.531 98085.589 24 231908191042319 33510.330 tinued on next page)
336S. Piqueux et al. / Icarus 251 (2015) 332–338Table 1 (continued)Mars yearEarthDays from J2000YearMon 117 116 1151733173517375321193 97398.606 96711.617 96024.640 114 113 112 111 11017381740174217441746121198722826131 109 108 107 106 10517481750175217541755542111 104 103 102 101 10017571759176117631765 99 98 97 96 95 94 93 92 91 90Mars yearDayEarthDays from J2000YearMonDay 22 21 201912191319151111072412 32136.350 31449.370 30762.420 95337.666 94650.693 93963.755 93276.782 92589.784 19 18 17 16 1519171919192119231925876432917220718521826 91902.815 91215.857 90528.864 89841.907 89154.953 14 13 12 11 10192719281930193219341121098108764133118522 88467.964 87780.989 87094.033 86407.054 85720.096 9 8 7 6 25133017 85033.149 84346.147 83659.157 82972.202 82285.232 4 3 2 10177617781780178217848653242292712 81598.256 80911.313 80224.337 79537.345 78850.36512345Mars yearEarthDays from 812.83934499.801 30075.450 29388.490 28701.540 28014.560 31028142 26640.590 25953.620 25266.650 24579.710 21219724928 23205.740 22518.780 21831.820 21144.820 19451947194919511953111087514219724 19770.910 19083.920 18396.940 17709.980 5519571959196019624211210112614119 16336.050 15649.090 14962.090 14275.110 Fig. 1 therein shows the progression of seasons through a Martianyear. Allison and McEwen (2000) present the date (as JD2400000.5) of Ls 0 over 1874–2126 but start the count of Marsyears in 1874. Both of those prior results and Table 1 used the Marspole orientation known at the time; each slightly different. Toobtain accuracy and smoothness over long periods, precise definition of the orbit plane and the spin-axis direction are neededbecause perturbations by the other planets results in small irregularities in Mars heliocentric position both along and normal to the‘‘average’’ orbit plane. The heliocentric position of Mars is based onplanetary and lunar ephemerides DE430 (Folkner et al., 2014)which uses the International Celestial Reference System, IRCS,and includes the effect of all planets, all significant satellitesand the largest several hundred asteroids. All calculations are inephemeris time (Barycentric Dynamical Time, TDB) and results inTable 1 are shown in ephemeris days relative to 2451545, whichis epoch J2000.0 (2000 January 1, 12 hour). To generate Table 1,the normal to the orbit plane is computed based on a least-squaresfit quadratic in time to the instantaneous cross-product ofthe heliocentric position and velocity of Mars evaluated for manyseasons each year:RA ¼ 273 :373218337 0:02985932966T 4:829810557 10 5 T 2Dec ¼ 65 :322934512 0:00128897471T þ 4:460153556 10 5 T 2ð1Þwith RA the right ascension ( ), Dec the declination ( ), and T theJulian centuries from epoch J2000.0. Calculation of the vernal equinox also requires the direction along the spin axis of the planet;here the determination of Kuchynka et al. (2014) is used, also inthe ICRF, but omitting terms with a period of one Mars year or less,all 0.00024 . Including those short-period terms advances the dateDayof Ls 0 by 0.000377 3.22 10 6 days, but would yield a vernalequinox direction that oscillates through a MY.The nomenclature and time referencing of the various datasetsacquired throughout the robotic exploration of Mars are generallyinstrument-specific and often related to spacecraft internal clocks,orbit numbers or Julian Dates, with little reference to Mars time(seasons or years). Consequently, fast and straightforward identification of mission/instrument duration and overlap in the contextof long-term observational studies is not easy. To address thisgap, Fig. 1 provides an overview of major robotic explorationevents since the arrival of Mars Pathfinder, along with global scaleprocesses (e.g., latitudinal extent of the polar night, surface atmospheric pressure at 0 m elevation, climatological seasonal polar capedges, etc.) in a format centered on Mars time (Ls and MY) as proposed in Table 1. Fig. 1starts after a hiatus of two decades in spacecraft exploration following the Viking missions. Similarinformation for all Mars spacecraft not included in Fig. 1 are givenby Snyder and Moroz (1992).All analytic expressions for LS here are empirical derived by fitting 285 Mars Years from 1607 to 2143. They are based on fits tominimize the root-mean-square (RMS) residual at 36 times perMars year uniformly spaced over the entire interval and use a formsimilar to Allison [2000].The linear-rate angle based on the tropical year is a where t isthe ephemeris time from J2000.0 in days.a ¼ a0 þ a1 t þ a2 T2 270:389001822 þ 0:52403850205 t 0:000565452 T 2M ¼ m0 þ m1 t 19:38028331517 þ 0:52402076345 tð2Þð3Þwhere M is the mean anomaly. Using eccentricity e defined ase ¼ e0 þ e1 T 0:093402202 þ 0:000091406 Tð4Þ
337S. Piqueux et al. / Icarus 251 (2015) 332–338Table 2Planetary perturbation terms. 2E-3M is shorthand for 1/(E/2 M/3) where E is the length of a year for Earth, M for Mars, J for Jupiter and V for Venus. Years are based on the semimajor axes at epoch J2000 given by Standish and Williams (2006).PlanetsCommensurate yearsPeriod days siAmplitude milli-deg 1000AiPhase degree M-E) * 450.69255256.06036228.99145to evaluate the true anomaly m using the equation of center yields: 2 e3 5e55e11e4 17e6sinðMÞ þsinð2MÞDBm M ¼ 2e þ þ4 96424192 13e3 43e5103e4 451e6þsinð3MÞ þsinð4MÞ 1264964801097e51223e5þsinð5MÞ þsinð6MÞ þ Oðe7 Þð5Þ960960Major perturbations by other planets are treated as:PP S ¼NX tAi cos 2p þsii¼1p180 /ið6Þwhere s is the commensurate period in days and / is phase indegrees; coefficient values are given in Table 2.Ls ¼ a þ180pD þ PP sð7ÞUsing only the first seven terms in Table 2, this model is adequate to match the DE430 calculations with maximum error of0.0073 over the 536 years of MY 184
dar dates. However, an ambiguity has remained regarding the count of MY prior to 1955. Such dates in the recent martian past are regularly used in the literature, primarily for cyclical processes spanning a few martian decades (see for example references in Titus et al., 2008). Here we extend Clancy
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