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The Asteroid Orbital Elements Database

Introduction astorb.dat is an ASCII file of high-precision osculating orbital elements, ephemeris uncertainties, and some additional data for all the numbered asteroids and the vast majority of unnumbered asteroids (multi-apparition and single-apparition) for which it is possible to make reasonably determinate computations. It is currently about 17 Mb in size in its compressed form (astorb.dat.gz), 62 Mb in size when decompressed (astorb.dat), and contains 230532 orbits computed by me (Edward Bowell). Each orbit, based on astrometric observations downloaded from the Minor Planet Center, occupies one 266-column record.

Special Features of astorb.dat There are three primary differences between our database and conventional asteroid orbit files.

First, we update the database daily. Thus, observations in each new batch of Minor Planet Circulars will be used in new orbits on a monthly basis, and those in the Minor Planet Electronic Circulars shortly after they are published. Other changes, such as the addition of orbits resulting from our own astrometric observations and the computation of current ephemeris uncertainties, are being made on a quasi-daily basis. Automatic daily updates commence at 8 hr UT. The updating process is generally completed by 10:00 UT. On the UT date of full Moon, the updating process is not completed until 14 hr UT or later.

Second, all the orbits in a given version of the file have an epoch of osculation near the present. Consequently, the ephemerides of most non-Earth-approaching asteroids can be computed to arcsec accuracy or better within ± 50 days of the epoch using a 2-body ephemeris program.

Third, current and future ephemeris uncertainties are given. Observers will readily be able to estimate whether asteroids are likely to be within their telescopes' fields of view, and they will better be able to prioritize astrometric targets.

Landmarks For a reverse chronological listing of significant changes to the database, click here.

Downloading astorb.dat The file may be obtained by the following means:

- Get a decompressed version (astorb.dat) via ftp by clicking on here. The source (astorb.dat.gz) is compressed but your browser should automatically decompress it. If this fails, try getting the original, uncompressed version by clicking here. And if this fails, try ftp'ing astorb.dat to yourself using the recipe below (except type "get astorb.dat" rather than "get astorb.dat.gz"). To name the file on a Netscape browser, click on "File", then on "Save as", then on "OK" (the file will automatically be named astorb.dat unless you choose another name at this point).
- If the above doesn't work or if you know someone who would like astorb.dat and has ftp but not WWW access, note that the compressed version is available via anonymous ftp at ftp.lowell.edu/pub/elgb/astorb.dat.gz, as are text versions (astorb.txt and astorb_landmarks.txt) of astorb.html and astorb_landmarks.html. Type the following commands:
  ftp ftp.lowell.edu
  Name: anonymous
  Password: `your email address`
  ftp>cd pub/elgb
  ftp>get astorb.txt
  ftp>get landmarks.txt
  ftp>get astorb.dat.gz
  ftp>quit
  astorb.dat.gz has been compressed using a public-domain utility called `gzip`. To decompress the file (which will result in file astorb.dat), type
  gunzip astorb.dat.gz
  - `gzip` code is available at prep.ai.mit.edu/pub/gnu/gzip-1.2.4.tar (UNIX version) and prep.ai.mit.edu/pub/gnu/gzip-1.2.4.msdos.exe (DOS version). The `gzip` software accommodates both the `gzip` and the `gunzip` commands.
    Type the following commands:
    ftp prep.ai.mit.edu
    Name: anonymous
    Password: `your email address`
    ftp>cd pub/gnu
    ftp>get gzip-1.2.3.tar (or get gzip-1.2.4.msdos.exe)
    ftp>quit
- Tell your colleagues lacking both web and ftp access that we can supply them with a compressed copy of the file along with the decompression software, preferably on 3.5-in (9-cm) diskettes, in either UNIX or DOS format. To arrange delivery, email us at koehn@lowell.edu or call Bruce Koehn at +1-520-774-3358 (fax +1-520-774-6296), specifying the medium and format you prefer.

Incremental update files In response to users who have difficulty downloading the complete astorb.dat (see above for instructions), we have instituted (9 October 1996) a method of logging daily changes in the orbital elements therein. Users will find files such as yymmdd.add and yymmdd.del in our public ftp area accessible from the WWW. These cover update activities for the past 30 days or more. Thus, 961007.add comprises records for asteroids whose orbital elements were either added to or replaced in astorb.dat on 7 October 1996; and 960930.del contains records for asteroids whose orbits were deleted from astorb.dat on 30 September 1996. Note the following: (1) The *.add files are refreshed every day. Thus, an orbit that was replaced on, say, 961001 and then again on 961002 will be found only in the 961002.add file on or after the latter date. (2) The *.add files reflect changes in orbital elements only. Changes to other parameters (such as H, G, and integer codes), as well as daily updates of ephemeris uncertainties, are not reported in the *.add files. Users who are interested in the latter should download the entire astorb.dat. To download the *.add and *.del files, add the commands
ftp>mget *.add
ftp>mget *.del
to the ftp instructions above.

File Structure Here are two sample records (with one line of parameter numbers above and three lines of column counts below):

    (1)   (2)                (3)             (4)    (5)  (6)  (7)   (8)
        1 Ceres              E. Bowell        3.34  0.12 0.72 913.0 G?
     1693 Hertzsprung        E. Bowell       10.97  0.15 0.74  39.5 C
             0         0         0         0         0         0         0
             1         2         3         4         5         6         7
    1234567890123456789012345678901234567890123456789012345678901234567890

      (9)                   (10) (11)  (12)     (13)       (14)       (15)
      0   0   0   0   0   0 56959 4750 19960427  80.477333  71.802404  80.
      0   0   0   0   0   0 20972   25 19960427 322.276332 234.698906  70.
             0         0         1         1         1         1         1
             8         9         0         1         2         3         4
    1234567890123456789012345678901234567890123456789012345678901234567890

           (16)      (17)       (18)        (19)     (20)     (21)    (22)
    659857 10.600303 0.07604100   2.76788714 19960414 2.3E-02  1.4E-04 199
    393559 11.942428 0.27460300   2.79629204 19950513 9.0E-01  7.9E-03 199
             1         1         1         1         1         2         2
             5         6         7         8         9         0         1
    1234567890123456789012345678901234567890123456789012345678901234567890

         (23)             (24)             (25)
    60416 2.7E-02 19960530 3.1E-02 20040111 3.1E-02 20040111
    60416 1.2E+00 19960610 1.3E+00 20010812 9.0E-01 20010813
             2         2         2         2         2
             2         3         4         5         6
    12345678901234567890123456789012345678901234567890123456

A FORTRAN format statement for reading a record in astorb.dat is:
A5,1X,A18,1X,A15,1X,A5,1X,F5.2,1X,A4,1X,A5,1X,A4, 1X,6I4,1X,
2I5,1X,I4,2I2.2,1X,3(F10.6,1X),F9.6,1X,F10.8, 1X,F12.8,1X,I4,2I2.2,1X,F7.2,1X,F8.2,1X,I4,2I2,3(1X,F7.2,1X,I4,2I2)

Note that some numerical data (e.g., asteroid number) are encoded as character variables. You may need to decode them.

Parameters are:

Parameter | Description
--- | ---
(1) | Asteroid number (blank if unnumbered).
(2) | Name or preliminary designation.
(3) | Orbit computer.
(4) | Absolute magnitude H, mag [see E. Bowell et al., pp. 549-554, in "Asteroids II", R. P. Binzel et al. (eds.), The University of Arizona Press, Tucson, 1989 and more recent Minor Planet Circulars]. Note that H may be given to 2 decimal places (e.g., 13.41), 1 decimal place (13.4) or as an integer (13), depending on its estimated accuracy. H is given to two decimal places for all unnumbered asteroids, even though it may be very poorly known.
(5) | Slope parameter G ( ibid.).
(6) | Color index B-V, mag (blank if unknown; see E. F. Tedesco, pp. 1090-1138, op. cit. ).
(7) | IRAS diameter, km (blank if unknown; see E. F. Tedesco et al., pp. 1151-1161, op.cit.).
(8) | IRAS Taxonomic classification (blank if unknown; ibid.).
(9) | Six integer codes (see table of explanation below). Note that not all codes have been correctly computed.
(10) | Orbital arc, days, spanned by observations used in orbit computation.
(11) | Number of observations used in orbit computation.
(12) | Epoch of osculation, yyyymmdd (TDT). The epoch is the Julian date ending in 00.5 nearest the date the file was created. Thus, as the file is updated, epochs will succeed each other at 100-day intervals on or after Julian dates ending in 50.5 (19980328, 19980706, 19981014, 19990122,...)
(13) | Mean anomaly, deg.
(14) | Argument of perihelion, deg (J2000.0).
(15) | Longitude of ascending node, deg (J2000.0).
(16) | Inclination, deg (J2000.0).
(17) | Eccentricity.
(18) | Semimajor axis, AU.
(19) | Date of orbit computation, yymmdd (MST, = UTC - 7 hr).
(20) | Absolute value of the current 1- ephemeris uncertainty (CEU), arcsec.
(21) | Rate of change of CEU, arcsec/day.
(22) | Date of CEU, yyyymmdd (0 hr UT).
(23) | Next peak ephemeris uncertainty (PEU), arcsec, from date of CEU, and date of its occurrence, yyyymmdd.
(24) | Greatest PEU, arcsec, in 10 years from date of CEU, and date of its occurrence, yyyymmdd.
(25) | Greatest PEU, arcsec, in 10 years from date of next PEU, and date of its occurrence, yyyymmdd, if two observations (of accuracy equal to that of the observations currently included in the orbit--typically ± 1 arcsec) were to be made on the date of the next PEU [parameter (23)].

The meanings of the six integer codes [parameter (9)] are as follows (reference to "type 6:7", for example, means code 6, value 7):

Code | Value | Explanation
--- | --- | ---
1 |  | Planet-crossing asteroids. Note: Because some orbits are very poor (or erroneously linked), there may be errors in assignment of these parameter values.
| 1 | Aten asteroids (a < 1.0 AU).
2 | Apollo asteroids (a > 1.0 AU; 0 < q < 1.0
4 | Amor asteroids (a > 1.0167 AU; 1.0167 < q <&nb
8 | Mars crossers (1.3 < q < 1.6660 AU).
16 | Outer-planet crossers (excluding Jupiter and Mars Trojans). Asteroids that cross or pass into the heliocentric distance zones between the perihelion and aphelion distances of Jupiter (4.950 to 5.455 AU), Saturn (9.009 to 10.069 AU), Uranus (18.274 to 20 089 AU), and/or Neptune (29.800 to 30.317 AU).
n | Asteroids (excluding Mars and Jupiter Trojans) that cross both inner- and outer-planet orbits. For example, an asteroid having n = 24 crosse the orbits of both Mars (q < 1.6660 AU) and Jupiter (Q > 4.950 AU).
2 |  | Orbit computation.
| 1 | Orbits derived from uncertainly, perhaps erroneously linked observations.
2 | Eccentricity assumed.
4 | Eccentricity and semimajor axis assumed.
8 | Mainly for numbered asteroids, omitted observations have resulted in degradation of a so-called orbit-quality parameter (OQP, see K. Muinonen and E. Bowell, Icarus 104, 255-279, 1993), generally by more than 0.1. The corresponding ephemeris uncertainty has increased by about 25% or more.
16 | OQP degrades by more than 0.1 if unsubstantiated observations (e.g., one-night apparitions) are omitted.
32 | Orbit derived from data containing observations not in Minor Planet Center files.
| 64 | H is unknown. H = 14 mag assumed.
| 128 | Asteroid sought, but not found.
| n | Sum of preceding entries. For example, n = 3 pertains to an uncertainly linked orbit for which the eccentricity was assumed.
3 |  | Asteroids observed during the course of major surveys. Our definition includes asteroids that were observed but not discovered during the course of a survey.
| 1 | Palomar-Leiden survey (PLS) asteroids.
2 | Palomar-Leiden T-2 survey asteroids.
4 | Palomar-Leiden T-3 survey asteroids.
8 | U.K. Schmidt Telescope-Caltech asteroid survey (UCAS) asteroids.
16 | Palomar-Leiden T-1 survey asteroids.
n | Asteroids observed in more than one survey. For example, n = 3 denotes an asteroid observed in both the PLS and T-2 surveys.
4 |  | Minor Planet Center (MPC) critical-list numbered asteroids.
| 1 | Lost asteroid.
2 | Asteroids observed at only two apparitions.
3 | Asteroids observed at only three apparitions.
4 | Asteroids observed at four or more apparitions, last more than ten years ago.
5 | Asteroids observed at four or more apparitions, only one night in last ten years.
6 | Other poorly observed asteroids observed at four or more apparitions.
7 | Absolute magnitude poorly known (not on MPC critical-list).
5 |  | Lowell Observatory and related discoveries
| 1 | Asteroids discovered by E. Bowell.
2 | Non-Bowell discoveries from Lowell search programs.
| 3 | Sum of preceding entries. n = 3 pertains to an asteroid discovered jointly by E. Bowell and another person connected with Lowell search programs.
6 |  | Rank, in decreasing importance, for our collaborative program of astrometry using the transit circle of the U.S. Naval Observatory Flagstaff Station.
| 10 | Exceptionally important, to be observed frequently. Principally space mission targets and occultation candidates.
9 | Asteroids useful for mass determination.
8 | Asteroids for which one or two additional nights' observation are required to satisfy orbit-update requirements. Asteroids of type 6:7 whose ephemeris uncertainties are between 2 and 5 arcsec within the next ten years or so.
7 | Bowell unnumbered discoveries whose ephemeris uncertainties are less than 2 arcsec within the next ten years or so. MPC critical-list asteroids.
6 | Planet-crossers of type 6:5.
5 | Numbered asteroids whose ephemeris uncertainties are between 2 and 5 arcsec within the next ten years or so. Unnumbered asteroids that should be numberable after one or two more nights' observation.

Note that the codes have not been carefully checked. There are doubtless many errors.

Notes on File Content

- Osculating elements [parameters (13) through (18)] are heliocentric.

- It may be assumed that ephemeris uncertainties are along the line of variation. Except for very accurately known orbits (ephemeris uncertainty < 1 arcsec) and very poorly known orbits (arc < 10 days), positional uncertainty perpendicular to the line of variation is usually very small compared to that along the line of variation.

- The current ephemeris uncertainty [CEU, parameter (20)] and its rate of change [parameter (21)] indicate whether an asteroid ought to be located in an observer's field of view. A CEU greater than all three of the peak ephemeris uncertainties [PEUs, parameters (23) through (25)] implies that the asteroid's ephemeris uncertainty is currently greater than at any time in the next ten years. Such asteroids are prime targets for observation because their orbits are subject to the greatest improvement for years to come. Note that, because ephemeris uncertainties have been computed using 2-body rather than n-body error propagation (see K. Muinonen and E. Bowell, Icarus 104, 255-279, 1993), uncertainties for Earth-approaching asteroids may have been misestimated by a factor of several.

- Most single-apparition asteroids are hopelessly lost. They have large CEUs--typically ± 105 to ± 106 arcsec. CEUs may have been imperfectly computed for such asteroids (though it should hardly matter) because of poorly known or unknown observational accuracy and/or because orbital eccentricities have been assumed (integer code 2 equals 2 or 4; see the integer-code table above). Users who wish to estimate ephemeris uncertainties for lost asteroids at times close to when they were observed may make use of the approximate formulae (formulae require Netscape Version 2.0 or higher for proper rendering):

  (t) = ±4500(q - 1) (tf - t) / [tarc2 (N - 3)1/2 ] arcsec
  (t) = ±4500(q - 1) (t - tl) / [tarc2 (N - 3)1/2 ] arcsec,

  derived from K. Muinonen, E. Bowell, and L. H. Wasserman (Planet. Space Sci. 42, 307-313, 1994). Here, (t) is the 1- sky-plane uncertainty, along the line of variation, at time t; q is the perihelion distance in AU; tf and tl are the times of the first and last observations, respectively (tf - t and t - tl are in days); tarc and N are parameters (10) and (11) above; and is the Earth-asteroid distance in AU. For long-unobserved asteroids, tf and tl may be approximated from the designation. Thus, for 1982 EE, which has a 9-day arc, tf may be taken as 1 March 1982 and tl as 15 March 1982. The formula should be accurate to within a factor of five.

- Peak ephemeris uncertaities [parameters (23) through (25)] generally occur near opposition or conjunction (the latter are more prevalent for Earth-crossing asteroids). The next PEU [parameter (23)] usually indicates the best time to make astrometric observations for orbit improvement, as will the PEU over the next 10 years [parameter (24)]. Special effort should be made to observe asteroids whose next PEUs are the greatest during the next 10 years [i.e., parameter (23) exceeds both parameters (24) and (25)]. Parameter (25) may be used to quantify the amount of orbital improvement that would result from observing at or near the date of next PEU. For example, if the next PEU is 1.2D+02 arcsec, and parameter (25) has value 6.0D+00 arcsec, a 20-fold ephemeris improvement (and approximately equal improvement in the unceratinties of the orbital elements) could be made. Note that numbered asteroids whose orbits are satisfactory have all three PEUs less than about ± 2 arcsec (absolute). Consequently, numbered asteroids whose ephemeris uncertainties, as indicated by the CEU and PEUs, at any time exceed about 2 arcsec should be targeted for observation. Unnumbered asteroids whose ephemeris uncertainties [as per parameter (25)] could be brought below about ± 2 arcsec, would probably then be candidates for numbering. A parameter (25) PEU greater than a parameter (24) PEU implies that observing at or near the date of the next PEU [parameter (23)] may actually cause ephemeris and orbit degradation. Thus, there is no point in making such observations unless they are numerous and/or of high accuracy.

Computational Details To produce the database, our variable-timestep differential orbit correction program was run in an automatic mode. Perturbation due to all major planets (Mercury through Pluto, Earth and Moon separately), Ceres (assumed mass 5.0×10-10 M), Pallas (1.1×10-10 M), and Vesta (1.4×10-10 M) were included. Planetary positions were derived from JPL's DE403 planetary ephemeris. Positions of the three perturbing asteroids were derived, by iteration, from our own orbits. Relativistic effects have not been included. The orbit of one numbered asteroid (1566 Icarus) is known to be imperfect as it requires inclusion of relativistic effects. The orbits of other close-Sun-approaching asteroids are doubtless similarly affected, but their observational (O-C) residuals appear to be satisfactory.

For numbered asteroids, we have adopted a uniform policy regarding the inclusion or exclusion of observations in the orbit determination: namely, to exclude observations whose great-circle sky-plane residuals exceed 2.3 arcsec. (We have found from experience that, for well-determined orbits, 2.3 arcsec is an appropriate residual threshold separating "good" and "bad" observations.) For numbered asteroids of type 2:8 in the integer-code table above, our policy has resulted in degradation of the orbit-quality parameter (OQP), which is a reliable (logarithmic) measure of an asteroid orbit's quality, and which (for non-Earth approachers) correlates well with ephemeris uncertainty. Such asteroids need orbit improvement to the point where the exclusion of "poor" observations no longer degrades the OQP. For unnumbered asteroids, we have retained obviously inferior observations where doing so improved the OQP and ephemeris uncertainty, thus making it easier to reobserve them; these asteroids are identified by integer code 2:16.

Upcoming Changes in astorb.dat Eventually, we intend to produce a version of the database in a format resembling that espoused in our ACM93 paper [E. Bowell, K. Muinonen, and L. H. Wasserman (1994). A public-domain asteroid orbit database. In "Asteroids, Comets, Meteors 1993" (A. Milani et al., eds.), pp. 477-481. Kluwer, Dordrecht]. We will not be making this expanded file publicly accessible until we have checked it fairly thoroughly, incorporated it into our suite of asteroid-orbit software, and extracted data for a paper entitled something like "Orbit and ephemeris accuracy of multi-apparition asteroids".

In addition, we are near to making a second run on orbits for numbered asteroids in which close asteroid-asteroid encounters will be noted and a new perturbation scheme that includes two or three dozen asteroid perturbers is implemented.

We are also looking into the possibility of allowing approved WWW users to run selected programs on our system (ephemerides; which asteroids are in a given region of sky at a given time; selecting subsets of asteroids by orbital elements, predicted magnitude, location in the sky, etc.).

Acknowledgment and Attribution The research and computing needed to generate astorb.dat were funded principally by NASA grant NAG5-4741, and in part by the Lowell Observatory endowment. astorb.dat may be freely used, copied, and transmitted provided attribution to Dr. Edward Bowell and the aforementioned funding sources is made. Hypertext links to this WWW site are welcome.

Ted Bowell

##### Last updated 31 Oct 2003 at 11:06:08 U.T.

##### Contact: Bruce Koehn (koehn@lowell.edu)
Web Curators: Ted Bowell and Bruce Koehn

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