Provided by: astronomical-almanac_5.6-4_amd64 bug


       aa - astronomical almanac - calculate planet and star positions




       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 celestial coordinates
       exactly as laid out in current editions 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 Astronomical 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 Greenwich

       lat    Geodetic latitude of observer (program calculates geocentric 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 UT

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

Orbit Computations

          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
          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

                 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 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 perihelion 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 perihelion distance also,
       but you must convert this to mean distance to  be  understood  by  the  program.  Use  the

         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 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 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 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

          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 bulletins,
       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

          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 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.


          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 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/, 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 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 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 displays 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 others).

                                        September 4, 2006                                   AA(1)