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Provided by: astronomical-almanac_5.6-2_i386

 

NAME

        aa - astronomical almanac - calculate planet and star positions
 

SYNOPSIS

        aa
 

DESCRIPTION

        The  aa  program computes the orbital positions of planetary bodies and
        performs rigorous coordinate  reductions  to  apparent  geocentric  and
        topocentric  place  (local altitude and azimuth).  It also reduces star
        catalogue positions given in either the FK4 or FK5  system.   Data  for
        the 57 navigational stars is included.  Most of the algorithms employed
        are from The Astronomical Almanac (AA) published by the U.S. Government
        Printing Office.
 
        The  aa program follows the rigorous algorithms for reduction of celes‐
        tial coordinates exactly as laid out in current editions of the  Astro‐
        nomical  Almanac.   The reduction to apparent geocentric place has been
        checked by a special version of the program (aa200) that  takes  plane‐
        tary positions directly from the Jet Propulsion Laboratory DE200 numer‐
        ical integration of the solar system. The results  agree  exactly  with
        the Astronomical Almanac tables from 1987 onward (earlier Almanacs used
        slightly different reduction methods).
 

Initialization

        The following items will be read in automatically  from  the  first  of
        these  files  to  be found: ./aa.ini, ~/.aa.ini, /etc/aa.ini.  The file
        contains one ASCII string number per line so is easily edited.  A  sam‐
        ple initialization file is supplied.  The entries are:
 
        lon    Terrestrial longitude of observer, degrees East of Greenwich
 
        lat    Geodetic  latitude  of  observer  (program calculates geocentric
               latitude)
 
        height Height above sea level, meters
 
        temp   Atmospheric temperature, degrees Centigrade
 
        pressure
               Atmospheric pressure, millibars
 
        tflag  Input time type: 1 = TDT, 2 = UT, 0 = TDT set equal to UT
 
        deltaT Value to use for deltaT, seconds; if 0  then  the  program  will
               compute it.
           Several  methods  of  calculating  the positions of the planets have
        been provided for in the program source code.  These range in  accuracy
        from  a  built-in computation using perturbation formulae to a solution
        from precise orbital elements that you supply from an almanac.
           The program uses as a default a set of trigonometric expansions  for
        the  position  of  the  Earth and planets.  These have been adjusted to
        match the Jet Propulsion Laboratory’s DE404 Long Ephemeris (1995)  with
        a  precision ranging from about 0.1" for the Earth to 1" for Pluto. The
        adjustment was carried out on the interval from 3000 B.C. to 3000  A.D.
        for  the  outer  planets.   The  adjustment  for  the  inner planets is
        strictly valid only from 1350 B.C. to 3000 A.D., but  may  be  used  to
        3000     B.C.     with     some     loss     of     precision.      See
        /usr/share/doc/aa/readme.404  for  additional  information.   The  true
        accuracy  of positions calculated for prehistoric or future dates is of
        course unknown.
           The Moon’s position is calculated by a modified version of the lunar
        theory  of  Chapront-Touze’  and Chapront.  This has a precision of 0.5
        arc second relative to DE404 for all dates between 1369 B.C.  and  3000
        A.D.   The  real  position of the Moon in ancient times is not actually
        known this accurately, due to uncertainty in the tidal acceleration  of
        the Moon’s orbit.
 
           In  the  absence of an interpolated polynomial ephemeris such as the
        DE200, the highest accuracy for current planetary positions is achieved
        by  using  the  heliocentric orbital elements that are published in the
        Astronomical Almanac. If precise orbital elements are provided for  the
        desired  epoch  then  the  apparent place should be found to agree very
        closely with Almanac tabulations.
           Entering 99 for the planet number generates a prompt for the name of
        a  file containing human-readable ASCII strings specifying the elements
        of orbits. The items in the specification are  (see  also  the  example
        file orbit.cat):
 
                  First line of entry:
               epoch of orbital elements (Julian date)
               inclination
               longitude of the ascending node
               argument of the perihelion
               mean distance (semimajor axis) in au
               daily motion
 
                  Second line of entry:
               eccentricity
               mean anomaly
               epoch of equinox and ecliptic, Julian date
               visual magnitude B(1,0) at 1au from earth and sun
               equatorial semidiameter at 1au, arc seconds
               name of the object, up to 15 characters
 
        Angles  in  the  above  are in degrees except as noted.  Several sample
        orbits are supplied in the file orbit.cat.  If you  read  in  an  orbit
        named  "Earth" the program will install the Earth orbit, then loop back
        and ask for an orbit number again.
          The entry for daily motion is optional.  It will be calculated by the
        program if it is set equal to 0.0 in your catalogue.  Almanac values of
        daily motion recognize the nonzero mass of  the  orbiting  planet;  the
        program’s calculation will assume the mass is zero.
          Mean  distance,  for  an elliptical orbit, is the length of the semi-
        major axis of the ellipse. If the eccentricity is given to be 1.0,  the
        orbit is parabolic and the "mean distance" item is taken to be the per‐
        ihelion distance.  Similarly a hyperbolic orbit has eccentricity >  1.0
        and  "mean  distance" is again interpreted to mean perihelion distance.
        In both these cases, the "epoch" is the perihelion date, and  the  mean
        anomaly is set to 0.0 in your catalogue.
          Elliptical cometary orbits are usually catalogued in terms of perihe‐
        lion distance also, but you must convert this to mean  distance  to  be
        understood by the program. Use the formula
 
          mean distance = perihelion distance / (1 - eccentricity)
 
        to  calculate the value to be entered in your catalogue for an ellipti‐
        cal orbit.
          The epoch of the orbital elements refers particularly to the date  to
        which  the given mean anomaly applies.  Published data for comets often
        give the time of perihelion passage as a calendar date and fraction  of
        a day in Ephemeris Time.  To translate this into a Julian date for your
        catalogue entry, run aa, type in the published date and  decimal  frac‐
        tion  of a day, and note the displayed Julian date. This is the correct
        Julian Ephemeris Date of the epoch for your catalogue  entry.   Example
        (Sky & Telescope, March 1991, page 297): Comet Levy 1990c had a perihe‐
        lion date given as 1990 Oct 24.68664 ET.  As  you  are  prompted  sepa‐
        rately  for the year, month, and day, enter 1990, 10, 24.68664 into the
        program. This date and fraction translates to JED  2448189.18664.   For
        comparison purposes, note that published ephemerides for comets usually
        give astrometric positions, not apparent positions.
           Exercise care about time scales when comparing  results  against  an
        almanac.  The orbit program assumes input date is Ephemeris Time (ET or
        TDT).  Topocentric altitude and azimuth are calculated  from  Universal
        Time  (UT).   The program converts between the two as required, but you
        must indicate whether your input entry is TDT or UT.  This is  done  by
        the  entry  for  input time type in aa.ini.  If you are comparing posi‐
        tions against almanac values, you probably want TDT.  If you are  look‐
        ing  up  at the sky, you probably want UT.  Ephemeris transit times can
        be obtained by declaring TDT = UT.  The  adjustment  for  deltaT  =  ET
        minus  UT  is accurate for the years 1620 through 2011, as the complete
        tabulation from the Astronomical Almanac is included  in  the  program.
        Outside  this range of years, approximate formulas are used to estimate
        deltaT.  These formulas are based on analyses of eclipse records  going
        back  to  ancient times (Stephenson and Houlden, 1986; Borkowski, 1988)
        but they do not predict future values  very  accurately.   For  precise
        calculations,  you should update the table in deltat.c from the current
        year’s Almanac. Note the civil time of day is UTC, which is adjusted by
        integral leap seconds to be within 0.9 second of UT.
 
           Updated deltaT values and predictions can be obtained from this net‐
http://maia.usno.navy.mil .  See the  file  deltat.c  for
        additional information.  In addition, the IAU has adopted several other
        definitions of time, but this program does not distinguish among  them.
        The  International  Earth  Rotation Service is in charge of UT. Precise
        data on Earth rotation and orientation are published in the  IERS  bul‐
        letins,  available at the IERS computer site www.iers.org as well as at
        the usno site.
           Each calculation of the time of local rising, meridian transit,  and
        setting  includes  a  first  order  correction  for the motion in right
        ascension and declination of the object between the entered input  time
        and  the  time  of the event.  Even so, the calculation has to be iter‐
        ated, or repeated with successively closer estimates of the event time.
        In  view of the first order correction the iteration has a second-order
        convergence characteristic and arrives at a precise result in just  two
        or  three steps.  On the other hand, the technique used is unstable for
        nearly-circumpolar objects, such as the Moon  observed  at  high  lati‐
        tudes.   Thus a failure to report rise and set times does not necessar‐
        ily mean that there was no rise or set event.
 
           The program reports the transit that is nearest to the  input  time.
        Rise  and  set  times ordinarily precede and follow the transit.  Check
        the date displayed next to the rise, set, or transit time  to  be  sure
        the  results  are for the desired date and not for the previous or next
        calendar day.  For the Sun and Moon, rise and set  times  are  for  the
        upper  limb  of the disc; but the indicated topocentric altitude always
        refers to the center of the disc.  The computed event times include the
        effects of diurnal aberration and parallax.
 
           Age  of  the Moon, in days from the nearest Quarter, also has a cor‐
        rection for orbital motion, but does not get the benefit  of  iterative
        improvement  and  may  be  off by 0.1 day (the stated Quarter is always
        correct, however). The estimated time can be made much more precise  by
        entering  the  input  date  and  time of day to be near the time of the
        event.  In other words, the rigorous calculation requires iterating  on
        the  time; in this case the program does not do so automatically, hence
        if you want maximum accuracy you must do the iteration by hand.
 

Stars

           Positions and proper motions of the 57 navigational stars were taken
        from  the  Fifth  Fundamental  Catalogue  (FK5).  They  are in the file
        /usr/share/aa/star.cat.  For all of  these,  the  program’s  output  of
        astrometric position agreed with the 1986 AA to the precision of the AA
        tabulation (an arc second).  The same is true for  1950  FK4  positions
        taken  from the SAO catalogue.  The program agrees to 0.01" with worked
        examples presented in the AA. Spot checks against  Apparent  Places  of
        Fundamental  Stars confirm the mean place agreement to <0.1".  The APFS
        uses an older nutation series, so direct comparison of  apparent  place
        is  difficult.   The  program  incorporates  the complete IAU Theory of
        Nutation    (1980).     Items    for     the     Messier     catalogue,
        /usr/share/aa/messier.cat,  are  from  either  the  AA or Sky Catalogue
        2000.
           To compute a star’s apparent position, its motion  since  the  cata‐
        logue epoch is taken into account as well as the changes due to preces‐
        sion of the equatorial coordinate system.  Star  catalogue  files  have
        the  following  data  structure.   Each star entry occupies one line of
        ASCII characters.  Numbers can be in any usual decimal computer  format
        and  are  separated  from  each  other  by one or more spaces. From the
        beginning of the line, the parameters are
 
               Epoch of catalogue coordinates and equinox
               Right ascension, hours
               Right ascension, minutes
               Right ascension, seconds
               Declination, degrees
               Declination, minutes
               Declination, seconds
               Proper motion in R.A., s/century
               Proper motion in Dec., "/century
               Radial velocity, km/s
               Distance, parsecs
               Visual magnitude
               Object name
        For example, the line
 
        2000 02  31  48.704   89  15  50.72  19.877  -1.52  -17.0  0.0070  2.02
        alUMi(Polaris)
 
        has the following interpretation:
 
               J2000.0      ;Epoch of coordinates, equator, and equinox
               2h 31m 48.704s    ;Right Ascension
               89deg 15’ 50.72"   ;Declination
               19.877       ;proper motion in R.A., s/century
               -1.52        ;proper motion in Dec., "/century
               -17.0        ;radial velocity, km/s
               0.007        ;parallax, "
               2.02         ;magnitude
               alUMi(Polaris)    ;abbreviated name for alpha Ursae Minoris (Polaris)
 
           Standard  abbreviations for 88 constellation names are expanded into
        spelled-out form (see constel.c). The program accepts two types of cat‐
        alogue coordinates.  If the epoch is given as 1950, the entire entry is
        interpreted as an FK4 item.  The program  then  automatically  converts
        the  data to the FK5 system.  All other epochs are interpreted as being
        in the FK5 system.
           Note that catalogue (and AA) star coordinates are  referred  to  the
        center  of  the  solar system, whereas the program displays the correct
        geocentric direction of the object.  The maximum difference is 0.8"  in
        the case of alpha Centauri.
 

OPTIONS

        aa does not accept any options.
 

FILES

        ./aa.ini, ~/.aa.ini, /etc/aa.ini Initialization data.
 
        /usr/share/doc/aa/readme.404
               Documentation of plan404 ephemerides.
 
        /usr/share/aa/star.cat
               Catalogue data on the 57 navigational stars.
 
        /usr/share/aa/messier.cat
               Items for the Messier catalogue
conjunct(1)
 

AUTHOR

        aa was written by Stephen L. Moshier <steve@moshier.net>.
 
        This  manual  page  was written by James R. Van Zandt <jrv@debian.org>,
        for the Debian project (but may be used by others).
 
AA(1)
 

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