The Asteroid Orbital Elements Database

High-precision osculating orbital elements

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Introduction

astorb.dat is an ASCII file of high-precision osculating orbital elements, ephemeris uncertainties, and some additional data for all numbered asteroids and the majority of unnumbered asteroids (multi- and single-apparition). It is currently about 104 MB in size in its compressed form (astorb.dat.gz) and 382 MB in size when decompressed (astorb.dat). Each orbit, based on astrometric observations downloaded from the Minor Planet Center, occupies one 266-column record.

Reference

For details on astorb.dat, astorbDB, and website tools and for reference when appropriate, see: The astorb database at Lowell Observatory

Special Features of astorb.dat

  1. We update the database daily. Observations in each new batch of Minor Planet Circulars are used to compute new orbits on a monthly basis, and those in the Minor Planet Electronic Circulars shortly after they are published. Other updates, such as the computation of current ephemeris uncertainties, are being made on a quasi-daily basis.

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

  3. 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.

Downloading astorb.dat

The file may be obtained by the following means:

  • Get a compressed version (astorb.dat) via http by clicking here. If this fails, try getting the original, uncompressed version by clicking here.

  • 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 http://www.gzip.org. The gzip software accommodates both the gzip and the gunzip commands.

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 19
.393559 11.942428 0.27460300   2.79629204 19950513 9.0E-01  7.9E-03 19
         1         1         1         1         1         2         2
         5         6         7         8         9         0         1
1234567890123456789012345678901234567890123456789012345678901234567890

      (23)             (24)             (25)
960416 2.7E-02 19960530 3.1E-02 20040111 3.1E-02 20040111
960416 1.2E+00 19960610 1.3E+00 20010812 9.0E-01 20010813
         2         2         2         2         2
         2         3         4         5         6
123456789012345678901234567890123456789012345678901234567

A FORTRAN format statement for reading a record in astorb.dat is (revised 2018/01/02 to allow for an inclination over 99.99999 deg):

A6,1X,A18,1X,A15,1X,A5,1X,F5.2,1X,A4,1X,A5,1X,A4,1X,6I4,1X,
2I5,1X,I4,2I2.2,1X,2(F10.6,1X),F10.6,F10.6,1X,F10.8,F13.8,1X,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. Also, to allow for semi-major axes greater than 1000 AU, a change was made (in 2018) to the output for semi-major axis. If the semi-major axis is less than 1000, the value is written as F13.8; if equal to or larger than 1000, the value is written as F13.7. In either case, the value can be read as F13.8. Note that with these two changes, there may or may not be a space preceeding the inclination and/or the semi-major axis.

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-σ 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 < 1.0AU).
2 Apollo asteroids (a > 1.0AU 0 < q < 1.0).
4 Amor asteroids (a > 1.0167AU; 1.0167 < q <
8 Mars crossers (1.3 < q < 1.6660AU).
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:

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

    derived from K. Muinonen, E. Bowell, and L. H. Wasserman (Planet. Space Sci. 42, 307-313, 1994). Here, σ(t) is the 1-σ 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 𝚫 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), 1 Ceres (assumed mass 4.74×10-10 M☉), 2 Pallas (1.02×10-10 M☉), 3 Juno (1.35×10-11 M☉), 4 Vesta (1.31×10-10 M☉), 10 Hygiea (5.29×10-11 M☉), 15 Eunomia (1.31×10-11 M☉), 31 Euphrosyne (1.1×10-11 M☉), 52 Europa (1.67×10-11 M☉), 511 Davida (1.48×10-11 M☉), and 704 Interamnia (1.82×10-11 M☉) were included. Planetary positions were derived from JPL's DE430 planetary ephemeris. Positions of the perturbing asteroids were derived, by iteration, from our own orbits. Relativistic effects have been included. For Near Earth Objects, perturbations due to the Earth's J2 have been included.

For the vast majority of asteroids the threshold for inclusion or exclusion of observations in orbit determination is where the great-circle sky-plane residuals exceed 2.3 arc seconds. In rare cases observations with higher residuals are manually accepted. In no cases are residuals greater than 10 arc seconds accepted. Generally higher residuals are accepted from older, pre-CCD data that offer significant arc extension.

Acknowledgment and Attribution

The resources to support astorb.dat were originally provided by NASA grant NAG5-4741 (PI E. Bowell) and the Lowell Observatory endowment, and more recently by NASA PDART grant NNX16AG52G (PI N. Moskovitz). astorb.dat may be freely used, copied, and transmitted provided attribution is made to the aforementioned funding sources.