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AA(1)                                                          AA(1)

       aa  -  astronomical almanac - calculate planet and star posi‐


       The aa program computes the orbital  positions  of  planetary
       bodies  and performs rigorous coordinate reductions to appar‐
       ent 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.  Govern‐
       ment Printing Office.

       The  aa program follows the rigorous algorithms for reduction
       of celestial coordinates exactly as laid out in current  edi‐
       tions of the Astronomical Almanac.  The reduction to apparent
       geocentric place has been checked by a special version of the
       program  (aa200) that takes planetary positions directly from
       the Jet Propulsion Laboratory DE200 numerical integration  of
       the  solar  system. The results agree exactly with the Astro‐
       nomical Almanac tables from  1987  onward  (earlier  Almanacs
       used slightly different reduction methods).

       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 sample  initialization  file  is
       supplied.  The entries are:

       lon    Terrestrial  longitude  of  observer,  degrees East of

       lat    Geodetic latitude of observer (program calculates geo‐
              centric latitude)

       height Height above sea level, meters

       temp   Atmospheric temperature, degrees Centigrade

              Atmospheric pressure, millibars

       tflag  Input time type: 1 = TDT, 2 = UT, 0 = TDT set equal to

       deltaT Value to use for deltaT, seconds; if 0 then  the  pro‐
              gram will compute it.

Orbit Computations
          Several  methods of calculating the positions of the plan‐
       ets have been provided for in the program source code.  These
       range in accuracy from a built-in computation using perturba‐
       tion 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

          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  ele‐
       ments that are published in the Astronomical Almanac. If pre‐
       cise 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  specifi‐
       cation are (see also the example file

                 First line of entry:
              epoch of orbital elements (Julian date)
              longitude of the ascending node
              argument of the perihelion
              mean distance (semimajor axis) in au
              daily motion

                 Second line of entry:
              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   If  you
       read  in  an orbit named "Earth" the program will install the
       Earth orbit, then loop back  and  ask  for  an  orbit  number
         The  entry for daily motion is optional.  It will be calcu‐
       lated by the program if it is set equal to 0.0 in your  cata‐
       logue.   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 dis‐
       tance" item is taken to be the  perihelion  distance.   Simi‐
       larly  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  perihelion  distance  also,  but you must convert this to
       mean distance to be understood by the program. Use  the  for‐

         mean distance = perihelion distance / (1 - eccentricity)

       to calculate the value to be entered in your catalogue for an
       elliptical 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 fraction 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  perihelion date given as 1990 Oct 24.68664 ET.
       As you are prompted separately 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.

Ephemeris Time and Other Time Scales
          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 con‐
       verts 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
       positions  against almanac values, you probably want TDT.  If
       you are  looking  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 esti‐
       mate 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  network  archive: .  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 as
       well as at the usno site.

Rise and Set Times
          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 iterated, 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 latitudes.  Thus a  failure  to  report
       rise  and  set times does not necessarily 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  correction  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 esti‐
       mated 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 automat‐
       ically, hence if you want maximum accuracy you  must  do  the
       iteration by hand.

          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/  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 sec‐
       ond).  The same is true for 1950 FK4 positions taken from the
       SAO catalogue.  The program agrees to 0.01" with worked exam‐
       ples 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/,
       are from either the AA or Sky Catalogue 2000.
          To compute a star's apparent position,  its  motion  since
       the  catalogue  epoch  is  taken  into account as well as the
       changes due to precession of the equatorial  coordinate  sys‐
       tem.  Star catalogue files have the following data structure.
       Each star entry occupies one line of ASCII characters.   Num‐
       bers can be in any usual decimal computer format and are sep‐
       arated from each other by one or more spaces. From the begin‐
       ning 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

       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 catalogue 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 dis‐
       plays the correct geocentric direction of  the  object.   The
       maximum difference is 0.8" in the case of alpha Centauri.

       aa does not accept any options.

       ./aa.ini, ~/.aa.ini, /etc/aa.ini Initialization data.

              Documentation of plan404 ephemerides.

              Catalogue data on the 57 navigational stars.

              Items for the Messier catalogue


       aa was written by Stephen L. Moshier <>.

       This   manual   page  was  written  by  James  R.  Van  Zandt
       <>, for the Debian project (but may be used  by

                          September 4, 2006                    AA(1)
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