Provided by: astronomical-almanac_5.6-8_amd64 
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 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).
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
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
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.
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 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
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 formula
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 UT.
Updated deltaT values and predictions can be obtained from this network archive:
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 bulletins, available at the IERS computer site www.iers.org 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 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 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.
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
SEE ALSO
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).
September 4, 2006 AA(1)