Swiss ephemeris 4 Computer ephemeris for developers of astrological software 4

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2.3. Asteroids

  1. Asteroid ephemeris files

The standard distribution of SWISSEPH includes the main asteroids Ceres, Pallas, Juno, Vesta, as well as 2060 Chiron, and 5145 Pholus. To compute them, one must have the main-asteroid ephemeris files in the ephemeris directory.

The names of these files are of the following form:

seas_18.se1 main asteroids for 600 years from 1800 - 2400

The size of such a file is about 200 kb.

All other asteroids are available in separate files. The names of additional asteroid files look like:

se00433.se1 the file of asteroid No. 433 (= Eros)

These files cover the period 3000 BC - 3000 AD.

A short version for the years 1500 – 2100 AD has the file name with an 's' imbedded, se00433s.se1.

The numerical integration of the all numbered asteroids is an ongoing effort. In December 1998, 8000 asteroids were numbered, and their orbits computed by the devlopers of Swiss Ephemeris. In January 2001, the list of numbered asteroids reached 20957, in January 2014 more than 380’000, and it is still growing very fast.

Any asteroid can be called either with the JPL, the Swiss, or the Moshier ephemeris flag, and the results will be slightly different. The reason is that the solar position (which is needed for geocentric positions) will be taken from the ephemeris that has been specified.

Availability of asteroid files:

- all short files (over 200000) are available for free download at our ftp server

The purpose of providing this large number of files for download is that the user can pick those few asteroids he/she is interested in.

- for all named asteroids also a long (6000 years) file is available in the download area.

      1. How the asteroids were computed

To generate our asteroid ephemerides, we have modified the numerical integrator of Steve Moshier, which was capable to rebuild the DE200 JPL ephemeris.

Orbital elements, with a few exceptions, were taken from the asteroid database computed by E. Bowell, Lowell Observatory, Flagstaff, Arizona (astorb.dat). After the introduction of the JPL database mpcorb.dat, we still keep working with the Lowell data because Lowell elements are given with one more digit, which can be relevant for long-term integrations.

For a few close-Sun-approaching asteroids like 1566 Icarus, we use the elements of JPL’s DASTCOM database. Here, the Bowell elements are not good for long term integration because they do not account for relativity.

Our asteroid ephemerides take into account the gravitational perturbations of all planets, including the major asteroids Ceres, Pallas, and Vesta and also the Moon.

The mutual perturbations of Ceres, Pallas, and Vesta were included by iterative integration. The first run was done without mutual perturbations, the second one with the perturbing forces from the positions computed in the first run.

The precision of our integrator is very high. A test integration of the orbit of Mars with start date 2000 has shown a difference of only 0.0007 arc second from DE200 for the year 1600. We also compared our asteroid ephemerides with data from JPL’s on-line ephemeris system ”Horizons” which provides asteroid positions from 1600 on. Taking into account that Horizons does not consider the mutual perturbations of the major asteroids Ceres, Pallas and Vesta, the difference is never greater than a few 0.1 arcsec.

(However, the Swisseph asteroid ephemerides do consider those perturbations, which makes a difference of 10 arcsec for Ceres and 80 arcsec for Pallas. This means that our asteroid ephemerides are even better than the ones that JPL offers on the web.)

The accuracy limits are therefore not set by the algorithms of our program but by the inherent uncertainties in the orbital elements of the asteroids from which our integrator has to start.

Sources of errors are:

 Only some of the minor planets are known to better than an arc second for recent decades. (See also informations below on Ceres, Chiron, and Pholus.)

 Bowells elements do not consider relativistic effects, which leads to significant errors with long-term integrations of a few close-Sun-approaching orbits (except 1566, 2212, 3200, 5786, and 16960, for which we use JPL elements that do take into account relativity).

The orbits of some asteroids are extremely sensitive to perturbations by major planets. E.g. 1862 Apollo becomes chaotic before the year 1870 AD when he passes Venus within a distance which is only one and a half the distance from the Moon to the Earth. In this moment, the small uncertainty of the initial elements provided by the Bowell database grows, so to speak, ”into infinity”, so that it is impossible to determine the precise orbit prior to that date. Our integrator is able to detect such happenings and end the ephemeris generation to prevent our users working with meaningless data.

      1. Ceres, Pallas, Juno, Vesta

The orbital elements of the four main asteroids Ceres, Pallas, Juno, and Vesta are known very precisely, because these planets have been discovered almost 200 years ago and observed very often since. On the other hand, their orbits are not as well-determined as the ones of the main planets. We estimate that the precision of the main asteroid ephemerides is better than 1 arc second for the whole 20th century. The deviations from the Astronomical Almanac positions can reach 0.5” (AA 1985 – 1997). But the tables in AA are based on older computations, whereas we used recent orbital elements. (s. AA 1997, page L14)

MPC elements have a precision of five digits with mean anomaly, perihelion, node, and inclination and seven digits with eccentricity and semi-axis. For the four main asteroids, this implies an uncertainty of a few arc seconds in 1600 AD and a few arc minutes in 3000 BC.

      1. Chiron

Positions of Chiron can be well computed for the time between 700 AD and 4650 AD. As a result of close encounters with Saturn in Sept. 720 AD and in 4606 AD we cannot trace its orbit beyond this time range. Small uncertainties in today's orbital elements have chaotic effects before the year 700.

Do not rely on earlier Chiron ephemerides supplying a Chiron for Cesar's, Jesus', or Buddha's birth chart. They are completely meaningless.

      1. Pholus

Pholus is a minor planet with orbital characteristics that are similar to Chiron's. It was discovered in 1992. Pholus' orbital elements are not yet as well-established as Chiron's. Our ephemeris is reliable from 1500 AD through now. Outside the 20th century it will probably have to be corrected by several arc minutes during the coming years.
      1. ”Ceres” - an application program for asteroid astrology

Dieter Koch has written the application program Ceres which allows to compute all kinds of lists for asteroid astrology. E.g. you can generate a list of all your natal asteroids ordered by position in the zodiac. But the program does much more:

- natal positions, synastries/transits, composite charts, progressions, primary directions etc.

- geocentric, heliocentric, topocentric, house horoscopes

- lists sorted by position in zodiac, by asteroid name, by declination etc.

The program is on the asteroid short files CD-ROM and the standard Swiss Ephemeris CD-ROM.

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