Swiss ephemeris 4 Computer ephemeris for developers of astrological software 4

Apparent versus true planetary positions

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3. Apparent versus true planetary positions

The Swiss ephemeris provides the calculation of apparent or true planetary positions. Traditional astrology works with apparent positions. ”Apparent” means that the position where we see the planet is used, not the one where it actually is. Because the light's speed is finite, a planet is never seen exactly where it is. (see above, 2.1.3 ”The details of coordinate transformation”, light-time and aberration) Astronomers therefore make a difference between apparent and true positions. However, this effect is below 1 arc minute.

Most astrological ephemerides provide apparent positions. However, this may be wrong. The use of apparent positions presupposes that astrological effects can be derived from one of the four fundamental forces of physics, which is impossible. Also, many astrologers think that astrological ”effects” are a synchronistic phenomenon (the ones familiar with physics may refer to the Bell theorem). For such reasons, it might be more convincing to work with true positions.

Moreover, the Swiss Ephemeris supports so-called astrometric positions, which are used by astronomers when they measure positions of celestial bodies with respect to fixed stars. These calculations are of no use for astrology, though.

  1. 4. Geocentric versus topocentric and heliocentric positions

More precisely speaking, common ephemerides tell us the position where we would see a planet if we stood in the center of the earth and could see the sky. But it has often been argued that a planet’s position ought to be referred to the geographic position of the observer (or the birth place). This can make a difference of several arc seconds with the planets and even more than a degree with the moon! Such a position referred to the birth place is called the topocentric planetary position. The observation of transits over the moon might help to find out whether or not this method works better.

For very precise topocentric calculations, the Swiss Ephemeris not only requires the geographic position, but also its altitude above sea. An altitude of 3000 m (e.g. Mexico City) may make a difference of more than 1 arc second with the moon. With other bodies, this effect is of the amount of a 0.01”. The altitudes are referred to the approximate earth ellipsoid. Local irregularities of the geoid have been neglected.

Our topocentric lunar positions differ from the NASA positions (s. the Horizons Online Ephemeris System by 0.2 - 0.3 arc sec. This corresponds to a geographic displacement by a few 100 m and is about the best accuracy possible. In the documentation of the Horizons System, it is written that: "The Earth is assumed to be a rigid body. ... These Earth-model approximations result in topocentric station location errors, with respect to the reference ellipsoid, of less than 500 meters."

The Swiss ephemeris also allows the computation of apparent or true topocentric positions.

With the lunar nodes and apogees, Swiss Ephemeris does not make a difference between topocentric and geocentric positions. There are manyfold ways to define these points topocentrically. The simplest one is to understand them as axes rather than points somewhere in space. In this case, the geocentric and the topocentric positions are identical, because an axis is an infinite line that always points to the same direction, not depending on the observer's position.

Moreover, the Swiss Ephemeris supports the calculation of heliocentric and barycentric planetary positions. Heliocentric positions are positions as seen from the center of the sun rather than from the center of the earth. Barycentric ones are positions as seen from the center of the solar system, which is always close to but not identical to the center of the sun.

  1. 5. Heliacal Events, Eclipses, Occultations, and Other Planetary Phenomena

    1. 5.1. Heliacal Events of the Moon, Planets and Stars

      1. 5.1.1. Introduction

From Swiss Ephemeris version 1.76 on, heliacal events have been included. The heliacal rising and setting of planets and stars was very important for ancient Babylonian and Greek astronomy and astrology. Also, first and last visibility of the Moon can be calculated, which are important for many calendars, e.g. the Islamic, Babylonian and ancient Jewish calendars.

The heliacal events that can be determined are:

  • Inferior planets

    • Heliacal rising (morning first)

    • Heliacal setting (evening last)

    • Evening first

    • Morning last

  • Superior planets and stars

    • Heliacal rising

    • Heliacal setting

  • Moon

    • Evening first

    • Morning last

The acronychal risings and settings (also called cosmical settings) of superior planets are a different matter. They will be added in a future version of the Swiss Ephemeris.

The principles behind the calculation are based on the visibility criterion of Schaefer [1993, 2000], which includes dependencies on aspects of:

  • Position celestial objects  
    like the position and magnitude of the Sun, Moon and the studied celestial object,

  • Location and optical properties observer 
    like his/her location (longitude, latitude, height), age, acuity and possible magnification of optical instruments (like binoculars)

  • Meteorological circumstances 
    mainly expressed in the astronomical extinction coefficient, which is determined by temperature, air pressure, humidity, visibility range (air quality).

  • Contrast between studied object and sky background 
    The observer’s eye can on detect a certain amount of contract and this contract threshold is the main body of the calculations

In the following sections above aspects will be discussed briefly and an idea will be given what functions are available to calculate the heliacal events. Lastly the future developments will be discussed.
      1. 5.1.2. Aspect determining visibility

The theory behind this visibility criterion is explained by Schaefer [1993, 2000] and the implemented by Reijs [2003] and Koch [2009]. The general ideas behind this theory are explained in the following subsections.
        1. Position of celestial objects

To determine the visibility of a celestial object it is important to know where the studied celestial object is and what other light sources are in the sky. Thus beside determining the position of the studied object and its magnitude, it also involves calculating the position of the Sun (the main source of light) and the Moon. This is common functions performed by Swiss Ephemeris.
        1. Geographic location

The location of the observer determines the topocentric coordinates (incl. influence of refraction) of the celestial object and his/her height (and altitude of studied object) will have influence on the amount of airmass that is in the path of celestial object’s light. 
        1. Optical properties of observer

The observer’s eyes will determine the resolution and the contrast differences he/she can perceive (depending on age and acuity), furthermore the observer might used optical instruments (like binocular or telescope).
        1. Meteorological circumstances

The meteorological circumstances are very important for determining the visibility of the celestial object. These circumstances influence the transparency of the airmass (due to Rayleigh&aerosol scattering and ozone&water absorption) between the celestial object and the observer’s eye. This result in the astronomical extinction coefficient (AEC: ktot). As this is a complex environment, it is sometimes ‘easier’ to use a certain AEC, instead of calculating it from the meteorological circumstances.

The parameters are stored in the datm (Pressure [mbar], Temperature [C], Relative humidity [%], AEC [-]) array.

        1. Contrast between object and sky background

All the above aspects influence the perceived brightnesses of the studied celestial object and its background sky. The contrast threshold between the studied object and the background will determine if the observer can detect the studied object.
      1. 5.1.3. Functions to determine the heliacal events

Two functions are seen as the spill of calculating the heliacal events:
        1. Determining the contrast threshold (swe_vis_limit_magn) 

Based on all the aspects mentioned earlier, the contrast threshold is determine which decides if the studied object is visible by the observer or not.
        1. Iterations to determine when the studied object is really visible (swe_heliacal_ut) 

In general this procedure works in such a way that it finds (through iterations) the day that conjunction/opposition between Sun and studied object happens and then it determines, close to Sun’s rise or set (depending on the heliacal event), when the studied object is visible (by using the swe_vis_limit_magn function).
        1. Geographic limitations of swe_heliacal_ut() and strange behavior of planets in high geographic latitudes

This function is limited to geographic latitudes between 60S and 60N. Beyond that the heliacal phenomena of the planets become erratic. We found cases of strange planetary behavior even at 55N.

An example:

At 0E, 55N, with an extinction coefficient 0.2, Mars had a heliacal rising on 25 Nov. 1957. But during the following weeks and months Mars did not constantly increase its height above the horizon before sunrise. In contrary, it disappeared again, i.e. it did a “morning last” on 18 Feb. 1958. Three months later, on 14 May 1958, it did a second morning first (heliacal rising). The heliacal setting or evening last took place on 14 June 1959.

Currently, this special case is not handled by swe_heliacal_ut(). The function cannot detect “morning lasts” of Mars and following “second heliacal risings”. The function only provides the heliacal rising of 25 Nov. 1957 and the next ordinary heliacal rising in its ordinary synodic cycle which took place on 11 June 1960.

However, we may find a solution for such problems in future releases of the Swiss Ephemeris and even extend the geographic range of swe_heliacal_ut() to beyond +/- 60.

        1. Visibility of Venus and the Moon during day

For the Moon, swe_heliacal_ut() calculates the evening first and the morning last. For each event, the function returns the optimum visibility and a time of visibility start and visibility end. Note, that on the day of its morning last or evening first, the moon is often visible for almost the whole day. It even happens that the crescent first becomes visible in the morning after its rising, then disappears, and again reappears during culmination, because the observation conditions are better as the moon stands high above the horizon. The function swe_heliacal_ut() does not handle this in detail. Even if the moon is visible after sunrise, the function assumes that the end time of observation is at sunrise. The evening fist is handled in the same way.

With Venus, we have a similar situation. Venus is often accessible to naked eye observation during day, and sometimes even during inferior conjunction, but usually only at a high altitude above the horizon. This means that it may be visible in the morning at its heliacal rising, then disappear and reappear during culmination. (Whoever does not believe me, please read the article by H.B. Curtis listed under “References”.) The function swe_heliacal_ut() does not handle this case. If binoculars or a telescope is used, Venus may be even observable during most of the day on which it first appears in the east.

      1. 5.1.4. Future developments

The section of the Swiss Ephemeris software is still under development. The acronychal events of superior planets and stars will be added. And comparing other visibility criterions will be included; like Schoch’s criterion [1928], Hoffman’s overview [2005] and Caldwall&Laney  criterion [2005].
      1. 5.1.5. References

- Caldwell, J.A.R., Laney, C.D., First visibility of the lunar crescent,, 2005, viewed March, 30th, 2009 

- H.B. Curtis, Venus Visible at inferior conjunction, in : Popular Astronomy vol. 18 (1936), p. 44; online at

- Hoffman, R.E., Rational design of lunar-visibility criteria, The observatory, Vol. 125, June 2005, No. 1186, pp 156-168. 

- Reijs, V.M.M., Extinction angle and heliacal events,, 2003, viewed March, 30th, 2009 

- Schaefer, B., Astronomy and the limit of vision, Vistas in astronomy, 36:311, 1993 

- Schaefer, B., New methods and techniques for historical astronomy and archaeoastronomy, Archaeoastronomy, Vol. XV, 2000, page 121-136 

- Schoch, K., Astronomical and calendrical tables in Langdon. S., Fotheringham, K.J., The Venus tables of Amninzaduga: A solution of Babylonian chronology by means of Venus observations of the first dynasty, Oxford, 1928.

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