At the lunar nodes, the moon crosses the plane of the ecliptic and its ecliptic latitude changes sign. There are similar nodes for the planets, but their definition is more complicated. Planetary nodes can be defined in the following ways: 1 They can be understood as an axis defined by the intersection line of two orbital planes. Such non-ecliptic nodes have not been implemented in the Swiss Ephemeris.
Because such lines are, in principle, infinite, the heliocentric and the geocentric positions of the planetary nodes will be the same. There are astrologers that use such heliocentric planetary nodes in geocentric charts. The ascending and the descending node will, in this case, be in precise opposition. The planetary nodes can be understood, not as an infinite axis, but as the two points at which a planetary orbit intersects with the ecliptic plane.
For the lunar nodes and heliocentric planetary nodes, this definition makes no difference from the definition 1. However, it does make a difference for geocentric planetary nodes, where, the nodal points on the planets orbit are transformed to the geocenter. The two points will not be in opposition anymore, or they will roughly be so with the outer planets. The advantage of these nodes is that when a planet is in conjunction with its node, then its ecliptic latitude will be zero.
This is not true when a planet is in geocentric conjunction with its heliocentric node. And neither is it always true for inner the planets, for Mercury and Venus. Note: There is another possibility, not implemented in the Swiss ephemeris: E. If one takes these points geocentrically, the ascending and the descending node will always form an approximate square. This possibility has not been implemented in the Swiss Ephemeris.
Here again, the ecliptic latitude would change sign at the moment when the planet were in conjunction with one of its nodes. Possible definitions for apsides and focal points The lunar apsides - the lunar apogee and lunar perigee - have already been discussed further above. Similar points exist for the planets, as well, and they have been considered by astrologers. Also, as with the lunar apsides, there is a similar disagreement: One may consider either the planetary apsides, i. The former point is called the perihelion and the latter one the aphelion. For a geocentric chart, these points could be transformed from the heliocenter to the geocenter.
However, Bernard Fitzwalter and Raymond Henry prefer to use the second focal points of the planetary orbits. And they call them the black stars or the black suns of the planets. The heliocentric positions of these points are identical to the heliocentric positions of the aphelia, but geocentric positions are not identical, because the focal points are much closer to the sun than the aphelia. Most of them are even inside the Earth orbit. The Swiss Ephemeris supports both points of view.
Special case: the Earth The Earth is a special case. Instead of the motion of the Earth herself, the heliocentric motion of the Earth-MoonBarycenter EMB is used to determine the osculating perihelion. There is no node of the earth orbit itself. There is an axis around which the earth's orbital plane slowly rotates due to planetary precession. The position points of this axis are not calculated by the Swiss Ephemeris. Special case: the Sun In addition to the Earth EMB apsides, our software computes so-to-say "apsides" of the solar orbit around the Earth, i.
These points form an opposition and are used by some astrologers, e. The perigee, located at about 13 Capricorn, is called the "Black Sun", the other one, in Cancer, is called the Diamond. So, for a complete set of apsides, one might want to calculate them for the Sun and the Earth and all other planets. Mean and osculating positions There are serious problems about the ephemerides of planetary nodes and apsides. There are mean ones and osculating ones. Both are well-defined points in astronomy, but this does not necessarily mean that these definitions make sense for astrology. Mean points, on the one hand, are not true, i.
Osculating points, on the other hand, are based on the idealization of the planetary motions as two-body problems, where the gravity of the sun and a single planet is considered and all other influences neglected. There are no planetary nodes or apsides, at least today, that really deserve the label true. Mean positions Mean nodes and apsides can be computed for the Moon, the Earth and the planets Mercury Neptune.
They are taken from the planetary theory VSOP Mean points can not be calculated for Pluto and the asteroids, because there is no planetary theory for them. Although the Nasa has published mean elements for the planets Mercury Pluto based on the JPL ephemeris DE, we do not use them so far , because their validity is limited to a year period, because only linear rates are given, and because they are not based on a planetary theory.
Osculating nodes and apsides Nodes and apsides can also be derived from the osculating orbital elements of a body, the parameters that define an ideal unperturbed elliptic two-body orbit for a given time. Celestial bodies would follow such orbits if perturbations were to cease suddenly or if there were only two bodies the sun and the planet involved in the motion and the motion were an ideal ellipse. This ideal assumption makes it obvious that it would be misleading to call such nodes or apsides "true". It is more appropriate to call them "osculating".
Osculating nodes and apsides are "true" only at the precise moments, when the body passes through them, but for the times in between, they are a mere mathematical construct, nothing to do with the nature of an orbit. We tried to solve the problem by interpolating between actual passages of the planets through their nodes and apsides. However, this method works only well with Mercury. With all other planets, the supporting points are too far apart as to allow a sensible interpolation. There is another problem about heliocentric ellipses.
Neptune's orbit has often two perihelia and two aphelia i. As a result, there is a wild oscillation of the osculating or "true" perihelion and aphelion , which is not due to a transformation of the orbital ellipse but rather due to the deviation of the heliocentric orbit from an elliptic shape. Neptunes orbit cannot be adequately represented by a heliocentric ellipse. In actuality, Neptunes orbit is not heliocentric at all. The double perihelia and aphelia are an effect of the motion of the sun about the solar system barycenter. This motion is a lot faster than the motion of Neptune, and Neptune cannot react to such fast displacements of the Sun.
As a result, Neptune seems to move around the barycenter or a mean sun rather than around the real sun. In fact, Neptune's orbit around the barycenter is therefore closer to an ellipse than his orbit around the sun. The same is also true, though less obvious, for Saturn, Uranus and Pluto, but not for Jupiter and the inner planets. This fundamental problem about osculating ellipses of planetary orbits does of course not only affect the apsides but also the nodes.
As a solution, it seems reasonable to compute the osculating elements of slow planets from their barycentric motions rather than from their heliocentric motions. This procedure makes sense especially for Neptune, but also for all planets beyond Jupiter. It comes closer to the mean apsides and nodes for planets that have such points defined. For Pluto and all trans-Saturnian asteroids, this solution may be used as a substitute for "mean" nodes.
Note, however, that there are considerable differences between barycentric osculating and mean nodes and apsides for Saturn, Uranus, and Neptune. A few degrees! But heliocentric ones are worse. Anyway, neither the heliocentric nor the barycentric ellipse is a perfect representation of the nature of a planetary orbit. So, astrologers should not expect anything very reliable here either! The best choice of method will probably be: For Mercury Neptune: mean nodes and apsides. Osculating positions are given with Pluto and all asteroids.
This is the default mode. For the reasons given above, method 4 seems to make best sense. In all of these modes, the second focal point of the ellipse can be computed instead of the aphelion. To compute them, one must have the main-asteroid ephemeris files in the ephemeris directory. The size of such a file is about kb.
Galactic & Ecliptic Astrology
All other asteroids are available in separate files. The names of additional asteroid files look like:. These files cover the period BC - AD. A short version for the years AD has the file name with an 's' imbedded, ses. The numerical integration of the all numbered asteroids is an ongoing effort. In December , asteroids were numbered, and their orbits computed by the devlopers of Swiss Ephemeris. In January , the list of numbered asteroids reached , in January more than , 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: -. 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 DE JPL ephemeris.
Orbital elements, with a few exceptions, were taken from the asteroid database computed by E. Bowell, Lowell Observatory, Flagstaff, Arizona astorb. After the introduction of the JPL database mpcorb. 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 has shown a difference of only 0. We also compared our asteroid ephemerides with data from JPLs on-line ephemeris system Horizons which provides asteroid positions from 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. 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 , , , , and , 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. 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. 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 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. But the tables in AA are based on older computations, whereas we used recent orbital elements. AA , 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 AD and a few arc minutes in BC. As a result of close encounters with Saturn in Sept. Small uncertainties in today's orbital elements have chaotic effects before the year Do not rely on earlier Chiron ephemerides supplying a Chiron for Cesar's, Jesus', or Buddha's birth chart. They are completely meaningless. Pholus Pholus is a minor planet with orbital characteristics that are similar to Chiron's. It was discovered in Pholus' orbital elements are not yet as well-established as Chiron's.
Our ephemeris is reliable from AD through now. Outside the 20th century it will probably have to be corrected by several arc minutes during the coming years. 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. A database of fixed stars is included with Swiss Ephemeris.
The precision is about 0. Our data are based on the star catalogue of Steve Moshier. It can be easily extended if more stars are required. The database was improved by Valentin Abramov, Tartu, Estonia. He reordered the stars by constellation, added some stars, many names and alternative spellings of names. In Feb. In Jan. We include some astrological factors in the ephemeris which have no astronomical basis they have never been observed physically. As the purpose of the Swiss Ephemeris is astrology, we decided to drop our scientific view in this area and to be of service to those astrologers who use these hypothetical planets and factors.
However, their inventors, the German astrologers Witte and Sieggrn, considered them to be planets. And moreover they behave like planets in as far as they circle around the sun and obey its gravity. On the other hand, if one looks at their orbital elements, it is obvious that these orbits are highly unrealistic. Some of them are perfect circles something that does not exist in physical reality. The inclination of the orbits is zero, which is very improbable as well.
The revised elements published by James Neely in Matrix Journal VII show small eccentricities for the four Witte planets, but they are still smaller than the eccentricity of Venus which has an almost circular orbit. This is again very improbable. There are even more problems. An ephemeris computed with such elements describes an unperturbed motion, i.
This may th. Also, note that none of the real transneptunian objects that have been discovered since can be identified with any of the Uranian planets. The hypothetical planets can again be called with any of the three ephemeris flags. The solar position needed for geocentric positions will then be taken from the ephemeris specified.
Transpluto Isis This hypothetical planet was postulated by the French astronomer M. Sevin because of otherwise unexplainable gravitational perturbations in the orbits of Uranus and Neptune. However, this theory has been superseded by other attempts during the following decades, which proceeded from better observational data. They resulted in bodies and orbits completely different from what astrologers know as 'Isis-Transpluto'.
More recent studies have shown that the perturbation residuals in the orbits of Uranus and Neptune are too small to allow postulation of a new planet. They can, to a great extent, be explained by observational errors or by systematic errors in sky maps. In telescope observations, no hint could be discovered that this planet actually existed.
Rumors that claim the opposite are wrong. Moreover, all of the transneptunian bodies that have been discovered since are very different from Isis-Transpluto. Even if Sevin's computation were correct, it could only provide a rough position. To rely on arc minutes would be illusory. Neptune was more than a degree away from its theoretical position predicted by Leverrier and Adams. Moreover, Transpluto's position is computed from a simple Kepler ellipse, disregarding the perturbations by other planets' gravities. Moreover, Sevin gives no orbital inclination. This mainly results from the fact that its orbital elements are referred to epoch 5.
The article does not say which equinox they are referred to. Therefore, we fitted it to the Astron ephemeris which apparently uses the equinox of which, however, is rather unusual! Harrington This is another attempt to predict Planet X's orbit and position from perturbations in the orbits of Uranus and Neptune. It was published in The Astronomical Journal 96 4 , October , p. According to Harrington there is also the possibility that it is actually located in the opposite constellation, i. Taurus instead of Scorpio.
The planet has a mean solar distance of about AU and a period of about years. Nibiru A highly speculative planet derived from the theory of Zecharia Sitchin, who is an expert in ancient Mesopotamian history and a paleoastronomer. The elements have been supplied by Christian Woeltge, Hannover. This planet is interesting because of its bizarre orbit.
It moves in clockwise direction and has a period of years. Its orbit is extremely eccentric. It has its perihelion within the asteroid belt, whereas its aphelion lies at about 12 times the mean distance of Pluto. In spite of its retrograde motion, it seems to move counterclockwise in recent centuries. The reason is that it is so slow that it does not even compensate the precession of the equinoxes.
Vulcan This is a hypothetical planet inside the orbit of Mercury not identical to the Uranian planet Vulkanus. Orbital elements according to L. Note that the speed of this planet does not agree with the Kepler laws. It is too fast by 10 degrees per year.
A Brief Introduction to Astrology: the Planets - Astrodienst
Many Russian astrologers use it. Its distance from the earth is more than 20 times the distance of the moon and it moves about the earth in 7 years. Its orbit is a perfect, unperturbed circle. Of course, the physical existence of such a body is not possible. The gravities of Sun, Earth, and Moon would strongly influence its orbit. Waldemaths Black Moon This is another hypothetical second moon of the earth, postulated by a Dr. Its distance from the earth is 2. The orbital elements have been derived from Waldemaths original data.
There are significant differences from elements used in earlier versions of Solar Fire, due to different interpretations of the values given by Waldemath. After a discussion between Graham Dawson and Dieter Koch it has been agreed that the new solution is more likely to be correct. The new ephemeris does not agree with Delphine Jays ephemeris either, which is obviously inconsistent with Waldemaths data. This body has never been confirmed. With its km diameter and an apparent diameter of 2. The Planets X of Leverrier, Adams, Lowell and Pickering These are the hypothetical planets that have lead to the discovery of Neptune and Pluto or at least have been brought into connection with them.
Their enormous deviations from true Neptune and Pluto may be interesting for astrologers who work with hypothetical bodies. Leverrier and Adams are good only around the ies, the discovery epoch of Neptune. To check this, call the program swetest as follows:. You can do this from the Internet web page swetest. One can see that the error is in the range of 2 degrees between and and grows very fast beyond that period. Any suggestions how we could improve our sidereal calculations are welcome! Revilla, San Jose, Costa Rica, who gave us this precious bibliographic hint.
The problem of defining the zodiac One of the main differences between the western and the eastern tradition of astrology is the definition of the zodiac. Western astrology uses the so-called tropical zodiac in which 0 Aries is defined by the vernal point the celestial point where the sun stands at the beginning of spring.
The tropical zodiac is a division of the ecliptic into 12 zodiac signs that are all of equal size, i. Astrologers call these signs after some constellations that are found along the ecliptic, but they are actually independent of these constellations. Because the vernal point slowly moves through the constellations and completes a full cycle once in years, tropical Aries moves through all constellations along the ecliptic, staying in each one for roughly years. Currently, the vernal point, and the beginning of tropical Aries, is located in the constellation of Pisces. In a few hundred years, it will enter Aquarius, which is the reason why the more impatient ones among us are already preparing for the Age of Aquarius.
The so-called sidereal zodiac also consists of 12 equal-sized zodiac signs, but it is tied to the fixed stars.
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These sidereal signs, which are used in Hindu astrology and by some western Neo-Babylonian and Neo-Hellenistic astrologers, only roughly coincide with the sidereal constellations, which are of variable size. While the definition of the tropical zodiac is clear and never questioned, sidereal astrology has quite some problems in defining its zodiac. There are many different definitions of the sidereal zodiac, and they differ by several degrees.
At a first glance, all of them look arbitrary, and there is no striking evidence from a mere astronomical point of view for anyone of them. However, a historical study shows at least that all of them stem from only one sidereal zodiac. On the other hand, this does not mean that it be simple to give a precise definition of it. Sanskrit ayanmsha means part of a path; the Hindi form of the word is ayanamsa with an s instead of sh. The value of the ayanamsha of date is computed from the ayanamsha value at a particular start date e.
And planetary. The Swiss Ephemeris allows for about thirty different ayanamshas, but the user can also define his or her own ayanamsha. Positions were given relative to some sidereally fixed reference point. The main problem in fixing the zero point is the inaccuracy of ancient observations. Around F. In Raymond Mercier noted that the zero point might have been defined as the ecliptic point that culminated simultaneously with the star eta Piscium Al Pherg. Around , Cyril Fagan, the founder of the modern western sidereal astrology, reintroduced the old Babylonian zodiac into astrology, placing the fixed star Spica near Virgo.
As a result of rigorous statistical investigation astrological! Fagan and Bradley said that the difference between P. Hubers zodiac and theirs was only 1. But actually if Merciers value for the Huber ayanamsha is correct it was 7. According to a text by Fagan found on the internet , Bradley once opined in print prior to "New Tool" that it made more sense to consider Aldebaran and Antares, at 15 degrees of their respective signs, as prime fiducials than it did to use Spica at 29 Virgo.
Such statements raise the question if the sidereal zodiac ought to be tied up to one of those stars. Today, we know that the fixed stars have a proper motion, wherefore such definitions are not a good idea, if an absolute coordinate system independent on moving bodies is intended. But the Babylonians considered them to be fixed. For this possibility, Swiss Ephemeris gives an Aldebaran ayanamsha: 14 ayanamsha with Aldebaran at 15ta and Antares at 15sc around the year The Hipparchan tradition Raymond Mercier has shown that all of the ancient Greek and the medieval Arabic astronomical works located the zero point of the ecliptic somewhere between 10 and 22 arc minutes east of the star zeta Piscium.
This definition goes back to the great Greek astronomer Hipparchus. How did he choose that point? Hipparchus said that the beginning of Aries rises when Spica sets. This statement was meant for a geographical latitude of 36, the latitude of the island of Rhodos, which Hipparchus descriptions of rises and settings are referred to. However, there seems to be more behind it. Mercier points out that according to Hipparchus star catalogue the stars alpha Arietis, beta Arietis, zeta Piscium, and Spica are located in a very precise alignment on a great circle which goes through that zero point near zeta Piscium.
Moreover, this great circle was identical with the horizon once a day at Hipparchus geographical latitude of In other words, the zero point rose at the same time when the three mentioned stars in Aries and Pisces rose and when Spica set. This would of course be a nice definition for the zero point, but unfortunately the stars were not really in such precise alignment.
They were only assumed to be so. According to Merciers calculations, the Hipparchan zero point should have been between 12 and 22 arc min east of zePsc, but the Hipparchan ayanamsha, as given by Mercier, has actually the zero point 26 east of zePsc. This comes from the fact that Mercier refers to the Hipparchan position of zeta Piscium, which was at least rounded to 10 if otherwise correct.
If we used the explicit statement of Hipparchus that Aries rose when Spica set at a geographical latitude of 36 degrees, the precise ayanamsha would be for 27 June jd and zePsc would be found at 29pi12, which is too far from the place where it ought to be. Mercier also discusses the old Indian precession models and zodiac point definitions. He notes that, in the Srya Siddnta, the star zeta Piscium in Sanskrit Revat has almost the same position as in the Greek sidereal zodiac, i.
On the other hand, however, Spica in Sanskrit Citra is given the longitude 30 Virgo. This is a contradiction, either Spica or Revat must be considered wrong. Moreover, if the precession model of the Srya Siddnta is used to compute an ayanamsha for the date of Hipparchus, it will turn out to be , which is very close to the Hipparchan value. The same calculation can be done with the rya Siddnta, and the ayanamsha for Hipparchos date will be For the Siddnta Shiromani the zero point turns out to be Revat itself.
By the way, this is also the zero point chosen by Copernicus! So, there is an astonishing agreement between Indian and Western traditions! The same zero point near the star Revat is also used by the so-called Ushshash ayanamsha which is still in use.
It differs from the Hipparchan one by only 11 arc minutes. The tropical and the sidereal zero points were at exactly the same place. Did astronomers or astrologers react to that event? They did! Under the Sassanian ruler Khusrau Anshirwn, in the year , the astronomers of Persia met to correct their astronomical tables, the socalled Zj al-Shh.
These tables are no longer extant, but they were the basis of later Arabic tables, the ones of alKhwrizm and the Toledan tables. This cycle happened to end in the year , and the conjunction of Jupiter with the Sun took place only one day after the spring equinox. And the spring equinox took place precisely 10 arcmin east of zePsc. This may be a mere coincidence from a present-day astronomical point of view, but for scientists of those days this was obviously the moment to redefine all astronomical data.
Mercier also shows that in the precession model used in that epoch and in other models used later by Arabic Astronomers, precession was considered to be a phenomenon connected with the movement of Jupiter, the calendar marker of the night sky, in its relation to the Sun, the time keeper of the daily sky. Such theories were of course wrong, from the point of view of todays knowledge, but they show how important that date was considered to be. The same zero point then reappears with a precision of 1 in the Toledan tables, the Khwrizmian tables, the Srya Siddhnta, and the Ushshash ayanamsha.
Besides the synchronicity of the Sun-Jupiter conjunction and the coincidence of the two zodiacs, it is funny to note that the cosmos helped the inaccuracy of ancient astronomy by rounding the position of the star zePsc to precisely 10 arc minutes east of the zero point! All Ptolemean star positions were rounded to 10 arc minutes. Suryasiddhanta and Aryabhata The explanations above are mainly derived from the article by Mercier. However, it is possible to derive ayanamshas from ancient Indian works themselves. The planetary theory of the main work of ancient Indian astronomy, the Suryasiddhanta, uses the so-called Kaliyuga era as its zero point, i.
This era is henceforth called K0s. This is also the zero date for the planetary theory of the ancient Indian astronomer Aryabhata, with the only difference that he reckons from sunrise of the same date instead of midnight. We call this Aryabhatan era K0a. Now, Aryabhata mentioned that he was 23 years old when exactly years had passed since the beginning of the Kaliyuga era. If years with a year length as defined by the Aryabhata are counted from K0a, we arrive at the 21st March, AD, At this point of time the mean Sun is assumed to have returned to the beginning of the sidereal zodiac, and we can derive an ayanamsha from this information.
There are two possible solutions, though: 1. We can find the place of the mean Sun at that time using modern astronomical algorithms and define this point as the beginning of the sidereal zodiac. As Aryabhata believed that the zodiac began at the vernal point, we can take the vernal point of this date as the zero point. The same calculations can be done based on K0s and the year length of the Suryasiddhanta.
The resulting date of Kali is the same day but about half an hour later: Algorithms for the mean Sun were taken from: Simon et alii, Numerical expressions for precession formulae and mean elements for the Moon and the planets, in: Astron. Based on Suryasiddhant: ingress of mean Sun into Aries at point of mean equinox of date.
Based on Suryasiddhanta again, but assuming ingress of mean Sun into Aries at true position of mean Sun at the same epoch 21 Mar , Based on Aryabhata, ingress of mean Sun into Aries at point of mean equinox of date. Based on Aryabhata again, but assuming ingress of mean Sun into Aries at true position of mean Sun at the same epoch. This ayanamsha definition is the most common one in modern Hindu astrology. It was first proposed by the astronomy historian S. Dixit came to the conclusion that, given the prominence that Vedic religion gave to the cardinal points of the tropical year, the Indian calendar, which is based on the zodiac, should be reformed and no longer be calculated relative to the sidereal, but to the tropical zodiac.
However, if such a reform could not be brought about due to the rigid conservatism of contemporary Vedic culture, then the ayanamsha should be chosen in such a way that the sidereal zero point would be in opposition to Spica. In this way, it would be in accordance with Grahalaghava, a work by the 16th century astronomer Ganea Daivaja that was still used in the 20th century by Indian calendar makers.
This standard is mandatory not only for astrology but also for astronomical ephemerides and almanacs and calendars published in India. It was named after the Calcuttan astronomer and astrologer Nirmala Chandra Lahiri, who was a member of the Reform Committee. However, as has been said, it was Dixit who first propagated this solution to the ayanamsha problem.
And last but not least, the same ayanamsha definition seems to have been used in Babylon and Greece, as well. While the information given above in the chapters about the Babylonian and the Hipparchan traditions are based on analyses of old star catalogues and planetary theories, a study by Nick. The standard definition of the Indian ayanamsha Lahiri ayanamsha was originally introduced in by the Indian Calendar Reform Committee ' 00" on the 21 March , Ephemeris Time.
Astrology For Dummies Cheat Sheet
The definition was corrected in Indian Astronomical Ephemeris , page , footnote: "According to new determination of the location of equinox this initial value has been revised to and used in computing the mean ayanamsha with effect from '. The value ' 00". The Lahiri standard position of Spica is in the year , and in In the year , when the star was conjunct the autumnal equinox, its position was It was in the year AD that its position was precisely The motion of the star is a result partly of its proper motion and partly of planetary precession, which has the ecliptic slightly change its orientation.
But what method exactly was used to define this ayanamsha? According to the Indian pundit AK Kaul, an expert in Hindu calendar and astrology, Lahiri wanted to place the star at , but at the same time arrive at an ayanamsha that was in agreement with the Grahalaghava, an important work for traditional Hindu calendar calculation that was written in the 16th century. Kaul to Dieter Koch on 1 March In , 12 years after the standard definition of the Lahiri ayanamsha had been published by the Calendar Reform Committee, Lahiri published another ayanamsha in his Bengali book Panchanga Darpan.
There, the value of mean ayanamsha is given as The idea behind this modification was obviously that he wanted to have the star exactly at for recent years, whereas with the standard definition the star is wrong by almost an arc minute. It therefore seems that Lahiri did not follow the Indian standard himself but was of the opinion that Spica had to be at exactly true chitrapaksha ayanamsha. At the moment, the Swiss only supports the official standard. However, it is rather trivial to calculate the positions of a planet and the star and then subtract the star from the planet.
Swiss Ephemeris versions below 1. It made a difference of only 0. If the reader finds errors in this documentation or is able to contribute important information, his or her feedback will be greatly appreciated. Usually ayanamshas are defined by an epoch and an initial ayanamsha offset. However, if one wants to make sure that a particular fixed star always remains at a precise position, e. Spica at , it does not work this way. The correct procedure here is to calculate the tropical position of Spica for the date and subtract it from the tropical position of the planet: 27 True chitrapaksha ayanamsha: Spica is always exactly at or 0 Libra in ecliptic longitude not polar!
Sources: Burgess, E. Lahiri, N. Saha, M. The sidereal zodiac and the Galactic Center As said before, there is a very precise definition for the tropical ecliptic. It starts at one of the two intersection points of the ecliptic and the celestial equator. Similarly, we have a very precise definition for the house circle which is said to be an analogy of the zodiac. It starts at one of the two intersection points of the ecliptic and the local horizon.
Unfortunately there is no such definition for the sidereal zodiac. Or can a fixed star like Spica be important enough to play the role of an anchor star? One could try to make the sidereal zero point agree with the Galactic Center. The Swiss astrologer Bruno Huber has pointed out that the Galactic Center enters a new tropical sign always around the same time when the vernal point enters the next sidereal sign. Around the time, when the vernal point will go into Aquarius, the Galactic Center will change from Sagittarius to Capricorn.
Huber also notes that the ruler of the tropical sign of the Galactic Center is always the same as the ruler of the sidereal sign of the vernal point at the moment Jupiter, will be Saturn in a few hundred years. A correction of the Fagan ayanamsha by about 2 degrees or a correction of the Lahiri ayanamsha by 3 degrees would place the Galactic Center at 0 Sagittarius.
Astrologically, this would obviously make some sense. Therefore, we add an ayanamsha fixed at the Galactic Center: 17 Galactic Center at 0 Sagittarius The other possibility in analogy with the tropical ecliptic and the house circle would be to start the sidereal ecliptic at the intersection point of the ecliptic and the galactic plane. At present, this point is located near 0 Capricorn.
However, defining this point as sidereal 0 Aries would mean to break completely with the tradition, because it is far away from the traditional sidereal zero points. Other ayanamshas There are a few more ayanamshas, whose provenance is not known to us. Seven Ray Institute. It is based on an inference that the Age of Aquarius starts in the year I decided to use the 1st of July simply to minimise the possible error given that an exact date is not given.
Conclusions We have found that there are basically three definitions, not counting the manifold variations: 1. It could have been Aldebaran at 15 Taurus and Antares at 15 Scorpio. In search of correct algorithms A second problem in sidereal astrology after the definition of the zero point is the precession algorithm to be applied. This algorithm is unfortunately too simple. At best, it can be considered as an approximation. The precession of the equinoxes is not only a matter of ecliptical longitude, but is a more complex phenomenon. It has two components: a The soli-lunar precession: The combined gravitational pull of the Sun and the Moon on the equatorial bulge of the earth causes the earth to spin like a top.
As a result of this movement, the vernal point moves around the ecliptic with a speed of about This cycle lasts about years. The gravitational influence from the planets causes it to wobble. As a result, the obliquity of the ecliptic currently decreases by 47 per century, and this movement has an influence on the position of the vernal point, as well. This has nothing to do with the precessional motion of the earth rotation axis; the equator holds an almost stable angle against the ecliptic of a fixed date, e.
Because the ecliptic is not fixed, it cannot be correct just to subtract an ayanamsha from the tropical position in order to get a sidereal position. Let us take, e. It is obviously measured on the ecliptic of This value is also measured on the ecliptic of But the whole ayanamsha is subtracted from a planetary position which is referred to the ecliptic of the epoch t.
This does not make sense. As an effect of this procedure, objects that do not move sidereally, e. Longitude Latitude 2 sag 07' The effect can be much greater for bodies with greater ecliptical latitude. Exactly the same kind of thing happens to sidereal planetary positions, if one calculates them in the traditional way.
It is only because planets move that we are not aware of it. The traditional method of computing sidereal positions is geometrically not sound and can never achieve the same degree of accuracy as tropical astrology is used to. There is nothing against this method from a geometrical point of view. But it has to be noted, that this system is not really fixed either, because it is still based on the moving ecliptic, and moreover the fixed stars have a small proper motion, as well.
If we follow this method, the position of the galactic center will always be the same 2 sag 06' For, if we want everything referred to the ecliptic of a fixed date t0, we will have to choose that date very carefully. Its ecliptic ought to be of special importance.
The ecliptic of or the one of are obviously meaningless and not suitable as a reference plane. And how about that 18 March , on which the tropical and the sidereal zero point coincided? Although this may be considered as a kind of cosmic anniversary the Sassanians did so , the ecliptic plane of that time does not have an eternal value. It is different from the ecliptic plane of the previous anniversary around the year BC, and it is also different from the ecliptic plane of the next cosmic anniversary around the year AD.
This algorithm is supported by the Swiss Ephemeris, too. It can be used for computations of the following kind: a Astronomers may want to calculate positions referred to a standard equinox like J, B, or B, or to any other equinox. See explanations in the next chapter. The algorithm can be applied to the Sassanian ayanamsha or to any user-defined sidereal mode, if the ecliptic of its reference date is considered to be astrologically significant.
It shows the dimensions of the inherent inaccuracy of the traditional method. For the planets and for centuries close to t0, the difference from the traditional procedure will be only a few arc seconds in longitude. Note that the Sun will have an ecliptical latitude of several arc minutes after a few centuries.
For the lunar nodes, the procedure is as follows: Because the lunar nodes have to do with eclipses, they are actually points on the ecliptic of date, i. Therefore, we first compute the nodes as points on the ecliptic of date and then project them onto the sidereal zodiac. This procedure is very close to the traditional method of computing sidereal positions a matter of arc seconds. However, the nodes will have a latitude of a couple of arc minutes. For the axes and houses, we compute the points where the horizon or the house lines intersect with the sidereal plane of the zodiac, not with the ecliptic of date.
Here, there are greater deviations from the traditional procedure. As a matter of fact, there are some possibilities in this direction. The mechanism of the planetary precession mentioned above works in a similar way as the mechanism of the luni-solar precession. The movement of the earth orbit can be compared to a spinning top, with the earth mass equally distributed around the whole orbit. The other planets, especially Venus and Jupiter, cause it to move around an average position. But unfortunately, this long-term mean Earth-Sun plane is not really stable, either, and therefore not suitable as a fixed reference frame.
The period of this cycle is about years. The angle between the long-term mean plane and the ecliptic of date is at the moment about , but it changes considerably. This cycle must not be confused with the period between two maxima of the ecliptic obliquity, which is about years and often mentioned in the context of planetary precession. This is the time it takes the vernal point to return to the node of the ecliptic its rotation point , and therefore the oscillation period of the ecliptic obliquity. This plane is extremely stable and probably the only convincing candidate for a fixed zodiac plane.
This method avoids the problem of method 3. No particular ecliptic has to be chosen as a reference plane. The only remaining problem is the choice of the zero point. This algorithm must not be applied to any of the predefined sidereal modes, except the Sassanian one. You can use this algorithm, if you want to research on a better-founded sidereal astrology, experiment with your own sidereal mode, and calibrate it as you like. More benefits from our new sidereal algorithms: standard equinoxes and precessioncorrected transits Method no.
This is sometimes useful when Swiss Ephemeris data ought to be compared with astronomical data, which are often referred to a standard equinox. There are predefined sidereal modes for these standard equinoxes: 18 J 19 J 20 B Moreover, it is possible to compute precession-corrected transits or synastries with very high precision. An astrological transit is defined as the passage of a planet over the position in your birth chart. Usually, astrologers assume that tropical positions on the ecliptic of the transit time has to be compared with the positions on the tropical ecliptic of the birth date.
But it has been argued by some people that a transit would have to be referred to the ecliptic of the birth date. With the new Swiss Ephemeris algorithm method no. This is more precise than just correcting for the precession in longitude see details in the programmer's documentation swephprg. 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. 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. 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 planets 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 m e. 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. 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. This corresponds to a geographic displacement by a few 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 meters. 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.
Heliacal Events of the Moon, Planets and Stars 5. Introduction From Swiss Ephemeris version 1. 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. 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. Contrast between studied object and sky background The observers 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. Aspect determining visibility The theory behind this visibility criterion is explained by Schaefer [, ] and the implemented by Reijs  and Koch . The general ideas behind this theory are explained in the following subsections. 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. This is common functions performed by Swiss Ephemeris. Geographic location The location of the observer determines the topocentric coordinates incl. Meteorological circumstances The meteorological circumstances are very important for determining the visibility of the celestial object. 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.
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. Functions to determine the heliacal events Two functions are seen as the spill of calculating the heliacal events: 5.
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. 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. Three months later, on 14 May , it did a second morning first heliacal rising. The heliacal setting or evening last took place on 14 June The function cannot detect morning lasts of Mars and following second heliacal risings.
The function only provides the heliacal rising of 25 Nov. 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.
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. Curtis listed under References. 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. Future developments The section of the Swiss Ephemeris software is still under development. The acronychal events of superior planets and stars will be added.
References - Caldwell, J. Curtis, Venus Visible at inferior conjunction, in : Popular Astronomy vol.
The default is "s", although this may be changed in future so should not be relied on. These signs are actually the unit of angular measurement, used for measuring ecliptic longitude. The abbreviations are also different than those of the constellations. Note also that if you want a suffix such as for arcseconds you must add that suffix on afterward by yourself.
The second argument specifies whether to use ephemeris time true or universal time false or omitted. This is equal to local sidereal time minus right ascension. This value will be NaN if the object is directly overhead. You must give either. If you do not give. Output:  If a house system is specified, elements 1 to 12 or 1 to 36 for method "G" contain the ecliptic longitude of that house, in degrees. The filename can be a string, buffer, or a number; if a number it is just the DE number of the ephemeris to use. It has no function unless the calculation functions specify that you are using.
JPL as the current ephemeris. Normally the result is using universal time. Use Object. The input has the same format as with the. Only stars can be used with this function; not planets. This feature is meant only for testing and there is no guarantee of its working. The format of the argument given is deliberately undocumented. If a number, it is something from the. If a string, it is a fixed star, and the result will include a comma, with the traditional name before the comma and the nomenclature name after the comma.
Sun if you want to refer to our Sun. Also, "fixed stars" are not actually fixed. For a fixed star, the input can be one of five formats: - A string representing a number. In this case, it is a line number in sefstars. The first star listed in the file that has that prefix possibly as the entire name is used. The return value has the same format as this. Give the start and end dates for the search; if only one date is given, does a search forever in the future or past ; if no dates are given, calculates the next or previous occultation from now.
If omitted, use geocentric calculation. If omitted, it is geocentric. The default is the Moon. Any number from. I am unsure that the signed mode is actually work properly, currently. Options can be:. Return value is an object with properties:. This includes the solar system planets, including Pluto now considered a dwarf planet , as well as Sun and Moon even though they are not planets.
There is also TrueNode and MeanNode for the ascending lunar node angular points where the orbit of the Moon crosses the ecliptic; there are two such points, and the descending node is degrees away; TrueNode is the osculating node element , even though that is not a physical object. The planet name should be capitalized. You can use. See the comments in seorbel. Pluto, the same positions will be calculated. There is also. Input options are:. Default is 5. Default is zero. You can subtract the number of the wanted prime meridian if you do not want the official prime meridian to be in use.
The z coordinate is currently unused and is always zero. Valid options are:. The default setting is to compute refraction at sea level. The default is 0. The effect is not visible; it will continue to work regardless. The path settings will still be set and will not be reset. Searches after the time specified by the second argument by default, the current time. Other numbers should not be used because their meaning may change in future versions. The default is the Royal Observatory.
The default is zero. Specify -6 for civil twilight used for aviation, automobile headlights, and various other laws , for nautical twilight for sailors navigation and military , and for astronomical twilight for observing the stars. If omitted but the temperature is included, attempt to estimate it.
If omitted, don't include refraction in the calculation.
Related ephemeris astrology definition
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