******************************************************************************* Revised: July 31, 2013 Moon / (Earth) 301 GEOPHYSICAL DATA (updated 2018-Aug-15): Vol. mean radius, km = 1737.53+-0.03 Mass, x10^22 kg = 7.349 Radius (gravity), km = 1738.0 Surface emissivity = 0.92 Radius (IAU), km = 1737.4 GM, km^3/s^2 = 4902.800066 Density, g/cm^3 = 3.3437 GM 1-sigma, km^3/s^2 = +-0.0001 V(1,0) = +0.21 Surface accel., m/s^2 = 1.62 Earth/Moon mass ratio = 81.3005690769 Farside crust. thick. = ~80 - 90 km Mean crustal density = 2.97+-.07 g/cm^3 Nearside crust. thick.= 58+-8 km Heat flow, Apollo 15 = 3.1+-.6 mW/m^2 Mean angular diameter = 31'05.2" Heat flow, Apollo 17 = 2.2+-.5 mW/m^2 Sid. rot. rate, rad/s = 0.0000026617 Geometric Albedo = 0.12 Mean solar day = 29.5306 d Obliquity to orbit = 6.67 deg Orbit period = 27.321582 d Semi-major axis, a = 384400 km Eccentricity = 0.05490 Mean motion, rad/s = 2.6616995x10^-6 Inclination = 5.145 deg Apsidal period = 3231.50 d Nodal period = 6798.38 d Perihelion Aphelion Mean Solar Constant (W/m^2) 1414+-7 1323+-7 1368+-7 Maximum Planetary IR (W/m^2) 1314 1226 1268 Minimum Planetary IR (W/m^2) 5.2 5.2 5.2 ******************************************************************************** ******************************************************************************* Ephemeris / API_USER Tue Oct 27 19:32:18 2026 Pasadena, USA / Horizons ******************************************************************************* Target body name: Moon (301) {source: DE441} Center body name: Earth (399) {source: DE441} Center-site name: (user defined site below) ******************************************************************************* Start time : A.D. 1053-Nov-13 04:00:00.0000 UT Stop time : A.D. 1053-Nov-13 08:00:00.0000 UT Step-size : 5 minutes ******************************************************************************* Target pole/equ : MOON_ME {East-longitude positive} Target radii : 1737.4, 1737.4, 1737.4 km {Equator_a, b, pole_c} Center geodetic : 113.191, 39.554, -1.05861E-12 {E-lon(deg),Lat(deg),Alt(km)} Center cylindric: 113.191, 4924.39018, 4039.9279 {E-lon(deg),Dxy(km),Dz(km)} Center pole/equ : ITRF93 {East-longitude positive} Center radii : 6378.137, 6378.137, 6356.752 km {Equator_a, b, pole_c} Target primary : Earth Vis. interferer : MOON (R_eq= 1737.400) km {source: DE441} Rel. light bend : Sun {source: DE441} Rel. lght bnd GM: 1.3271E+11 km^3/s^2 Atmos refraction: NO (AIRLESS) RA format : DEG Time format : CAL Calendar mode : Mixed Julian/Gregorian RTS-only print : NO EOP file : eop.261027.p270123 EOP coverage : DATA-BASED 1962-JAN-20 TO 2026-OCT-27. PREDICTS-> 2027-JAN-22 Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass (>38.000=NO), Daylight (NO ) Table cut-offs 2: Solar elongation ( 0.0,180.0=NO ),Local Hour Angle( 0.0=NO ) Table cut-offs 3: RA/DEC angular rate ( 0.0=NO ) Table format : Comma Separated Values (spreadsheet) ************************************************************************************************************************************* Date__(UT)__HR:MN, , ,R.A._(a-app), DEC_(a-app), Azi_(a-app), Elev_(a-app), Ang-diam, delta, deldot, TDB-UT, ************************************************************************************************************************************* $$SOE 1053-Nov-13 04:00,*,m, 234.01032, -19.48233, 176.778424, 30.900119, 1818.139, 0.00263514074085, 0.0217997, 1411.151871, 1053-Nov-13 04:05,*,m, 234.03723, -19.49650, 178.125831, 30.927999, 1818.104, 0.00263519145672, 0.0287810, 1411.151831, 1053-Nov-13 04:10,*,e, 234.06413, -19.51055, 179.473740, 30.933758, 1818.060, 0.00263525617567, 0.0357648, 1411.151791, 1053-Nov-13 04:15,*,t, 234.09103, -19.52448, 180.821337, 30.917390, 1818.005, 0.00263533489972, 0.0427480, 1411.151750, 1053-Nov-13 04:20,*,m, 234.11794, -19.53829, 182.167811, 30.878914, 1817.941, 0.00263542762439, 0.0497273, 1411.151710, 1053-Nov-13 04:25,*,m, 234.14486, -19.55199, 183.512355, 30.818373, 1817.868, 0.00263553433868, 0.0566996, 1411.151670, 1053-Nov-13 04:30,*,m, 234.17181, -19.56556, 184.854170, 30.735838, 1817.784, 0.00263565502516, 0.0636616, 1411.151630, 1053-Nov-13 04:35,*,m, 234.19879, -19.57902, 186.192470, 30.631404, 1817.692, 0.00263578965991, 0.0706100, 1411.151590, 1053-Nov-13 04:40,*,m, 234.22580, -19.59235, 187.526485, 30.505191, 1817.589, 0.00263593821258, 0.0775416, 1411.151550, 1053-Nov-13 04:45,*,m, 234.25286, -19.60557, 188.855462, 30.357343, 1817.477, 0.00263610064635, 0.0844533, 1411.151510, 1053-Nov-13 04:50,*,m, 234.27997, -19.61867, 190.178674, 30.188028, 1817.356, 0.00263627691800, 0.0913419, 1411.151470, 1053-Nov-13 04:55,*,m, 234.30714, -19.63165, 191.495414, 29.997434, 1817.225, 0.00263646697791, 0.0982041, 1411.151429, 1053-Nov-13 05:00,*,m, 234.33438, -19.64451, 192.805009, 29.785772, 1817.084, 0.00263667077012, 0.1050369, 1411.151389, 1053-Nov-13 05:05,*,m, 234.36169, -19.65725, 194.106811, 29.553274, 1816.934, 0.00263688823230, 0.1118369, 1411.151349, 1053-Nov-13 05:10,*,m, 234.38908, -19.66988, 195.400208, 29.300190, 1816.775, 0.00263711929582, 0.1186012, 1411.151309, 1053-Nov-13 05:15,*,m, 234.41656, -19.68238, 196.684619, 29.026787, 1816.607, 0.00263736388582, 0.1253266, 1411.151269, 1053-Nov-13 05:20,*,m, 234.44414, -19.69477, 197.959502, 28.733351, 1816.429, 0.00263762192116, 0.1320100, 1411.151229, 1053-Nov-13 05:25,*,m, 234.47182, -19.70705, 199.224350, 28.420182, 1816.242, 0.00263789331453, 0.1386484, 1411.151189, 1053-Nov-13 05:30,*,m, 234.49961, -19.71920, 200.478694, 28.087593, 1816.046, 0.00263817797251, 0.1452386, 1411.151149, 1053-Nov-13 05:35,*,m, 234.52752, -19.73125, 201.722104, 27.735911, 1815.841, 0.00263847579555, 0.1517776, 1411.151108, 1053-Nov-13 05:40,*,m, 234.55555, -19.74317, 202.954187, 27.365476, 1815.627, 0.00263878667809, 0.1582625, 1411.151068, 1053-Nov-13 05:45,*,m, 234.58371, -19.75498, 204.174589, 26.976633, 1815.404, 0.00263911050855, 0.1646904, 1411.151028, 1053-Nov-13 05:50,*,m, 234.61201, -19.76668, 205.382998, 26.569741, 1815.173, 0.00263944716945, 0.1710581, 1411.150988, 1053-Nov-13 05:55,*,m, 234.64046, -19.77827, 206.579134, 26.145164, 1814.933, 0.00263979653742, 0.1773629, 1411.150948, 1053-Nov-13 06:00,*,m, 234.66905, -19.78974, 207.762759, 25.703271, 1814.684, 0.00264015848332, 0.1836018, 1411.150908, 1053-Nov-13 06:05,*,m, 234.69781, -19.80111, 208.933668, 25.244439, 1814.426, 0.00264053287224, 0.1897721, 1411.150868, 1053-Nov-13 06:10,*,m, 234.72672, -19.81236, 210.091695, 24.769046, 1814.161, 0.00264091956360, 0.1958708, 1411.150828, 1053-Nov-13 06:15,*,m, 234.75581, -19.82350, 211.236706, 24.277474, 1813.887, 0.00264131841125, 0.2018953, 1411.150787, 1053-Nov-13 06:20,*,m, 234.78508, -19.83454, 212.368599, 23.770106, 1813.605, 0.00264172926349, 0.2078428, 1411.150747, 1053-Nov-13 06:25,*,m, 234.81453, -19.84547, 213.487306, 23.247327, 1813.315, 0.00264215196319, 0.2137105, 1411.150707, 1053-Nov-13 06:30,*,m, 234.84417, -19.85629, 214.592787, 22.709521, 1813.016, 0.00264258634785, 0.2194959, 1411.150667, 1053-Nov-13 06:35,*,m, 234.87401, -19.86701, 215.685031, 22.157071, 1812.711, 0.00264303224969, 0.2251964, 1411.150627, 1053-Nov-13 06:40,*,m, 234.90405, -19.87763, 216.764057, 21.590357, 1812.397, 0.00264348949571, 0.2308093, 1411.150587, 1053-Nov-13 06:45,*,m, 234.93429, -19.88815, 217.829904, 21.009759, 1812.076, 0.00264395790783, 0.2363321, 1411.150547, 1053-Nov-13 06:50,*,m, 234.96475, -19.89856, 218.882640, 20.415651, 1811.747, 0.00264443730293, 0.2417624, 1411.150507, 1053-Nov-13 06:55,*,m, 234.99543, -19.90887, 219.922352, 19.808405, 1811.412, 0.00264492749295, 0.2470977, 1411.150466, 1053-Nov-13 07:00,*,m, 235.02634, -19.91909, 220.949149, 19.188388, 1811.069, 0.00264542828502, 0.2523356, 1411.150426, 1053-Nov-13 07:05,*,m, 235.05747, -19.92921, 221.963160, 18.555963, 1810.719, 0.00264593948149, 0.2574738, 1411.150386, 1053-Nov-13 07:10,*,m, 235.08885, -19.93924, 222.964531, 17.911487, 1810.362, 0.00264646088012, 0.2625100, 1411.150346, 1053-Nov-13 07:15,*,m, 235.12046, -19.94917, 223.953424, 17.255311, 1809.999, 0.00264699227409, 0.2674419, 1411.150306, 1053-Nov-13 07:20,*,m, 235.15232, -19.95901, 224.930016, 16.587780, 1809.629, 0.00264753345216, 0.2722675, 1411.150266, 1053-Nov-13 07:25,*,m, 235.18443, -19.96876, 225.894499, 15.909235, 1809.252, 0.00264808419874, 0.2769844, 1411.150226, 1053-Nov-13 07:30,*,m, 235.21680, -19.97842, 226.847076, 15.220007, 1808.870, 0.00264864429403, 0.2815907, 1411.150186, 1053-Nov-13 07:35,*,m, 235.24943, -19.98800, 227.787962, 14.520425, 1808.481, 0.00264921351410, 0.2860844, 1411.150145, 1053-Nov-13 07:40,*,m, 235.28232, -19.99749, 228.717382, 13.810806, 1808.086, 0.00264979163101, 0.2904634, 1411.150105, 1053-Nov-13 07:45,*,m, 235.31549, -20.00690, 229.635570, 13.091466, 1807.686, 0.00265037841294, 0.2947258, 1411.150065, 1053-Nov-13 07:50,*,m, 235.34893, -20.01622, 230.542768, 12.362708, 1807.280, 0.00265097362425, 0.2988698, 1411.150025, 1053-Nov-13 07:55,*,m, 235.38265, -20.02547, 231.439226, 11.624833, 1806.869, 0.00265157702568, 0.3028936, 1411.149985, 1053-Nov-13 08:00,*,m, 235.41665, -20.03464, 232.325200, 10.878133, 1806.453, 0.00265218837436, 0.3067955, 1411.149945, $$EOE ************************************************************************************************************************************* Column meaning: TIME Times PRIOR to 1962 are UT1, a mean-solar time closely related to the prior but now-deprecated GMT. Times AFTER 1962 are in UTC, the current civil or "wall-clock" time-scale. UTC is kept within 0.9 seconds of UT1 using integer leap-seconds for 1972 and later years. Conversion from the internal Barycentric Dynamical Time (TDB) of solar system dynamics to the non-uniform civil UT time-scale requested for output has not been determined for UTC times after the next July or January 1st. Therefore, the last known leap-second is used as a constant over future intervals. Time tags refer to the UT time-scale conversion from TDB on Earth regardless of observer location within the solar system, although clock rates may differ due to the local gravity field and no analog to "UT" may be defined for that location. Any 'b' symbol in the 1st-column denotes a B.C. date. First-column blank (" ") denotes an A.D. date. CALENDAR SYSTEM Mixed calendar mode was active such that calendar dates after AD 1582-Oct-15 (if any) are in the modern Gregorian system. Dates prior to 1582-Oct-5 (if any) are in the Julian calendar system, which is automatically extended for dates prior to its adoption on 45-Jan-1 BC. The Julian calendar is useful for matching historical dates. The Gregorian calendar more accurately corresponds to the Earth's orbital motion and seasons. A "Gregorian-only" calendar mode is available if such physical events are the primary interest. NOTE: "n.a." in output means quantity "not available" at the print-time. SOLAR PRESENCE (OBSERVING SITE) Time tag is followed by a blank, then a solar-presence condition code: '*' Daylight (refracted solar upper-limb on or above apparent horizon) 'C' Civil twilight/dawn 'N' Nautical twilight/dawn 'A' Astronomical twilight/dawn ' ' Night OR geocentric ephemeris LUNAR PRESENCE WITH TARGET RISE/TRANSIT/SET EVENT MARKER (OBSERVING SITE) The solar-presence code column is immediately followed by another marker: 'm' Refracted upper-limb of Moon on or above apparent horizon ' ' Refracted upper-limb of Moon below apparent horizon OR geocentric The lunar presence marker (an ongoing state) can be over-ridden by a target event marker if an event has occurred since the last output step: 'r' Rise (target body on or went above cut-off RTS elevation) 'e' Elevation max (target body maximum elevation angle has occurred) 't' Transit (target body at or passed through observer meridian) 's' Set (target body on or went below cut-off RTS elevation) RTS MARKERS (TVH) Rise and set are with respect to the reference ellipsoid true visual horizon defined by the elevation cut-off angle. Horizon dip and yellow-light refraction (Earth only) are considered. Accuracy is < or = to twice the requested search step-size. 'R.A._(a-app), DEC_(a-app),' = Airless apparent right ascension and declination of the target center with respect to an instantaneous reference frame defined by the Earth equator of-date (z-axis) and meridian containing the Earth equinox of-date (x-axis, EOP-corrected IAU76/80). Compensated for down-leg light-time delay, gravitational deflection of light, stellar aberration, precession & nutation. Note: equinox (RA origin) is offset -53 mas from the of-date frame defined by the IAU06/00a P & N system. Units: RA in decimal degrees, ddd.fffff{ffff} DEC in decimal degrees sdd.fffff{ffff} 'Azi_(a-app), Elev_(a-app),' = Airless apparent azimuth and elevation of target center. Compensated for light-time, the gravitational deflection of light, stellar aberration, precession and nutation. Azimuth is measured clockwise from north: North(0) -> East(90) -> South(180) -> West(270) -> North (360) Elevation angle is with respect to a plane perpendicular to the reference surface local zenith direction. TOPOCENTRIC ONLY. Units: DEGREES 'Ang-diam,' = The equatorial angular width of the target body full disk, if it were fully illuminated and visible to the observer. If the target body diameter is unknown "n.a." is output. Units: ARCSECONDS 'delta, deldot,' = Apparent range ("delta", light-time aberrated) and range-rate ("delta-dot") of the target center relative to the observer. A positive "deldot" means the target center is moving away from the observer, negative indicates movement toward the observer. Units: AU and KM/S 'TDB-UT,' = Difference between the uniform Barycentric Dynamical time-scale and the Earth-rotation dependent Universal Time. Prior to 1962, the difference is with respect to UT1 (TDB-UT1) and the 0.002 second maximum amplitude distinction between TT and TDB is not maintained. For 1962 and later, the difference is with respect to UTC (TDB-UTC) and periodic terms less than 1.e-6 second are ignored. Values beyond the next July or January 1st may change if a leap-second is later required by the IERS. Values from the present date forward through the next ~78 days are predictions. Beyond that prediction interval, the last prediction is taken as a constant for all future dates. Units: SECONDS Computations by ... Solar System Dynamics Group, Horizons On-Line Ephemeris System 4800 Oak Grove Drive, Jet Propulsion Laboratory Pasadena, CA 91109 USA General site: https://ssd.jpl.nasa.gov/ Mailing list: https://ssd.jpl.nasa.gov/email_list.html System news : https://ssd.jpl.nasa.gov/horizons/news.html User Guide : https://ssd.jpl.nasa.gov/horizons/manual.html Connect : browser https://ssd.jpl.nasa.gov/horizons/app.html#/x API https://ssd-api.jpl.nasa.gov/doc/horizons.html command-line telnet ssd.jpl.nasa.gov 6775 e-mail/batch https://ssd.jpl.nasa.gov/ftp/ssd/horizons_batch.txt scripts https://ssd.jpl.nasa.gov/ftp/ssd/SCRIPTS Inquiries : Jon.D.Giorgini@jpl.nasa.gov *************************************************************************************************************************************