Programming interface to the Swiss Ephemeris - programmiastral.com

Note: However, as Michael Erlewine points out in his elaborate web page on this topic
(http://thenewage.com/resources/articles/interface.html), planetary nodes could be defined for any couple of planets. E.g.
there is also an intersection line for the two orbital planes of Mars and Saturn. 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.
2) There is a second definition that leads to different geocentric ephemerides. 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.g., instead of considering the points of the
Mars orbit that are located on the ecliptic plane, one might consider the points of the earth’s orbit that are located on the
orbital plane of Mars. 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.
3) Third, the planetary nodes could be defined as the intersection points of the plane defined by their momentary geocentric
position and motion with the plane of the ecliptic. Here again, the ecliptic latitude would change sign at the moment
when the planet were in conjunction with one of its nodes. This possibility has not been implemented in the Swiss
Ephemeris.
Possible definitions for apsides and focal points
The lunar apsides - the lunar apogee and lunar perigee - have already been dealt with 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.e. the two points on a planetary orbit that are closest to the sun
and most distant from the sun, resp. 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-Moon-
Barycenter (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.e. points on the orbit of the Sun where it is closest to and where it is farthest from the Earth. These points
form an opposition and are used by some astrologers, e.g. by the Dutch astrologer George Bode or the Swiss
astrologer Liduina Schmed. The ”perigee”, located at about 13 Capricorn, is called the "Black Sun", the other
one, in Cancer, is called the ”Diamond”.