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Interface: Planetary Nodes     Part I Date Published: 11/14/2002 by Michael Erlewine
Bio: Michael Erlewine

Author Michael Erlewine Besides being the author/astrologer behind our top-selling Astro*Talk, TimeLine, and Friends and Lovers report programs, Michael is the man who founded Matrix back in the late '70s. Michael and his brother Stephen Erlewine (Stephen is still head of all astrological programming for Matrix) built Matrix into the leading producer of astrology software.

For many years Michael lived in Ann Arbor, Michigan, where he was much in demand as a counseling astrologer specializing in relationship and vocational advice. He also taught astrology at local schools and colleges, working with groups of as many as 1,200 people.

Michael is also known for his entrepreneurial drive which, in addition to Matrix, led him to create the All Music Guide - the largest music database in the world - and the All Movie Guide, as well as several award-winning websites, including

Michael also founded the Heart Center Library, the largest astrological library in North America that is open to the public. He remains curator of the works contained in this library, tapping this resource for one of his pet projects - a complete astrological encyclopedia.

Today Michael lives in the northern Michigan community of Big Rapids with his wife of 33 years and his family. He still does occasional private astrological counseling as people from around the world continue to seek his advice.

Those interested in a personal reading by Michael may contact him at:




The interface concept came out of my interest in heliocentrics, in particular an inquiry into the mutual inclination (or lack thereof) of the various planes of our solar system, planes like that of the eclipic, equator, horizon, galaxy, supergalaxy, and so on. I was fascinated by the different attitudes or inclinations of the various astronomical planes, each to the others. What could this mean?

A whole series of coordinate systems exist, each with their own center and plane of reference. Still more interesting to me is that fact that these many systems are oriented to each other differently -- at different angles to one another. They are set in space like some grand crystal. To me, they were whole approaches to life, each with their own independent attitude or stance. I was fascinated that astrologers devoted their attention to the zodiac or ecliptic, but seemed to pay little or no attention to other planes like that of the horizon, prime vertical, and equator. Astrologers seem not to understand or care that points such as the ascendant, MC, vertex, etc. are not zodiac points alone, but are nodes representing the intersection of the zodiac with some other great plane. It takes two independent planes to create a node. This fact seems to have been lost.

Even within our own solar system, each of the great planetary orbits has its own plane and particular orientation or attitude. Each of these great orbital planes are oriented or inclined to the others. Trying to reduce all these intersecting planes, this grand planetary crystal, to the set of the most significant points was how the interface nodal technique came into being.

Astrologers use a variety of coordinate systems to look at life. The most well known, of course, is the zodiac or ecliptic system, but there are also the equatorial system of right ascension & declination, the horizon system of azimuth and altitude, the prime vertical system of longitude and amplitude, and still others. On a grander scale, there are other coordinate systems that are fascinating in their own right , including the local system of stars of which our Sun is a member, the galactic system, and even a supergalactic systems (of which I have written). All in all, we have the several major coordinate systems in common use by astrologers such as the ecliptic and half a dozen or so esoteric systems that are little used. Which brings us to Interface Analysis.

Interface Analysis is little more than a reduction of all the nine planet's inclinations and disinclinations to the particular series of zodiac points that represent both symbolically and physically the exact and only spots in the zodiac at which these various inclinations and disinclinations are exact, or, in perfect alignment.

When a planet moves into alignment with the orbital plane of a second planet, it is at one of its nodes (ascending or descending). We call these nodes 'Interface Points'.Thus, an inclination or nodal alignment (interface) refers to an exact planar alignment between two planets (where the two planes intersect to form a node) and this will emphasize (for better or for worse) the nature and function of the planets involved. On the other hand, planets at DIS-inclination (at 90-degree points in their orbit to the nodes or interface points) represent these same principles as they are when most mutually disinclined -- each to the other. Here is a brief summary of the astronomical basis for this concept.

The Basic Astronomy

What is a node? As we know, each planet orbits around the Sun in a large ellipse with the Sun in the center, at one focus. This orbital ellipse defines a plane passing through the center of the Sun (Figure 1). The planes of the orbits of the nine planets in our solar system do not happen to coincide, but instead, are inclined to one another, slightly. The line defined by the intersection of the planes of any two planetary orbits is called the line of nodes (Figure 2).

Our solar system has the Sun at its center and this is known as the heliocentric celestial sphere. (Figure 3). Since all of the planetary orbital planes pass through the center of the Sun, the planes all intersect the celestial sphere in what are called great circles. Therefore, each intersecting planetary plane has a distinct pair of nodes with each of the other planets -- the system of planetary nodes.

The planetary nodes of all the other planets with respect to the Earth (i.e. where their planes intersect the Earth's orbital plane -- ecliptic) and the inclinations of these planes to the Earth's orbital plane are known to astrologers, although they are not often used. There is, however, some reference in the astrological literature to a planet being at its node in the plane of the Earth. For instance: Uranus might be sighted as being at its northern or southern node, and yet seldom (almost never) do we find reference to the Earth being at this same nodal point (and in the Uranian plane), although this happens twice a year! At these times, the Earth moves into the Uranian plane and takes on some of the qualities of that planet. My point is that while astrologers have embraced and used the concept of planetary pairs when it comes to aspects, we have fallen short as regards the nodal pairs, although they are at least as physically valid. Astrologers have a plethora or riches when it comes to points and techniques available to them.

il now, almost no attention has been given to the fact that each pair of planetary orbits intersect one another to produce their own set of nodal intersections, that have nothing to do with the orbit of the Earth. It is this last category that is the particular subject of this article.

Earth is but one planet, albeit a very important one to us, in our solar system. What we are examining here (which are not so familiar, although easily computed) are the nodes where any two planets' orbital planes (irrespective of the Earth's plane) intersect. This article is concerned with the location of the entire system of planetary-pair nodal points (interface point) as they can be measured along the zodiac.

Locating the Nodes

Let's consider any two planets other than the Earth, such as Mars and Saturn. The planes of their orbits make great circles on the Celestial Sphere as does the plane of the Earth's orbit. Where these two great planes intersect one another are planetary nodes or interface points for this particular planetary pair. Notice that these points are located slightly above or below the zodiac plane, but not right in it. Since we have only our zodiac as our plane of reference, it is convenient to use this in order to point out activities in these other planes. Using spherical trigonometry, we have projected these points onto our ecliptic so that by watching either Mars or Saturn transit a given point in our zodiac (using the heliocentric ephemeris), we know that the planet (either Mars or Saturn) is simultaneously at its Interface and exactly in the plane of the second planet. The result is an easy way for us to tell when a planet is at a particular interface point, but using a standard heliocentric ephemeris. Now let's look at the system of interface points from a less technical viewpoint.

The Value of Nodal Points in Astrological Work

Let us briefly review the use of nodes in modern astrology:


As mentioned earlier, astrology is very nodal, more than you might imagine. This article concentrates on the planetary nodes. However, just in passing, you may wish to note that standard points like the Ascendant and Vertex are nothing more than nodes. It always takes the planes of two independent coordinate systems to create a node. And while astrologers are aware that points like the ascendant and vertex are zodiac points, many are not aware that the ascendant is brought to you by means of the independent plane of the local horizon. It is where they intersect to form a line of nodes. Still fewer know that the Vertex is made available by the intersecting prime vertical coordinate system (again, to the zodiac). In fact, most of the hot spots of astrology are where two coordinates systems come together to intersect and create an interesting set of nodes or points. So much of our astrology concerns itself only with the zodiac that there is little awareness of the many supporting systems of coordinates that are also in effect.

Lunar Nodes:
Representing the interrelationship of the orbital plane of the moon with that of the Earth, the lunar nodes are widely used and understood by practically all modern astrologers, both in the East and the West. There are several good texts available on these nodes.

Planetary Nodes:
The use of the planetary nodes in modern astrology is generally restricted to the nodes of the various planets as they intersect the orbital plane of the Earth (the zodiac or ecliptic). The planar interfacial angles of the other planets relative to each other (planetary nodes) have been practically ignored.

As an example of this ignorance, let me cite the continual reference in the astrological literature to a planet being at its node in the plane of the Earth. For instance: Uranus is often sighted as being at its northern or southern node -- and yet seldom (almost never) do we find reference to the Earth being at this same nodal point (and in the Uranian plane) although, as mentioned above, this happens two times a year. At these times, the Earth moves into the Uranian plane and takes on some of the qualities of that planet.

In brief, the primary reason why the planetary nodes are not more widely used and appreciated by astrologers is the failure to realize these points in their reciprocity. A nodal point, by definition, represents the mutual intersection of two independent (planetary orbital) planes. We have chosen to call these nodal points 'Interface Points', as this word emphasized the reciprocal nature of any single point. They point both ways. Realization of these nodal lines as planetary pairs that represent the nature of both planets involved will result in more wide-spread use of these interface points and their incorporation into the body of technique as practiced by the astrologers of today.

In summary, the structure of our solar system is in fact defined by the interrelationship of the various orbital planes of which it is composed. This interrelationship is conveniently expressed by the complete system of planetary nodes and their square points. In this introduction to the use of these nodes by astrologers, we will confine ourselves to activation of these nodal points by direct transit at the Interface node shared by any two planets and activation by transit to points square (at ninety degrees) from these interface nodal points. At these ninety degree, or square points, a planet reaches what is astronomically termed its greatest latitude (either north or south) to the plane of the second planet involved. These points of greatest latitude are those points where the planet is most highly disinclined to the plane of the second planet and simultaneously changes reference from one node and begins to move (in its orbit) toward a conjunction with the opposite node. Therefore, you will note that at these square points we have a changing-line of relationship, while at the interface nodal points themselves, we have the simple activation or direct function of the principles involved.

To repeat: activation of the interface points themselves, by transit, results in simple emphasis and clear function. For instance: one planet will be, by transit, in the plane of the second. The second planet (somewhere in its own orbit) is always in its own plane and yet, for a time (long or short, depending on the planets involved), the first planet is, by transit, exactly in this same plane and may be said to take on some of it's qualities, whether by resonance or some other undetermined means.

It is important to have in mind which plane is being activated and which planet is, by transit, active in that plane. Is Mars by transit in the plane of Saturn? or is Saturn transiting in the plane of Mars (or both -- which happens occasionally)? These distinctions, at first perhaps confusing, will become clear with some practice and you may be satisfied, to begin with, keeping simply in mind that the Saturn/Mars Interface is in activation.

Questions of Interpretation

The simple and very defined structure and interrelationship of these various points tend to dictate concerning questions of interpretation, and one advantage to this approach is that very little is left to the imagination which, for some astrologers, can be a decided blessing. The relationships are clear:

The northern (or ascending) node of a planet is that point where the planet transits a given plane in what is called a south to north direction (from under to above the given plane). The southern or descending node is a transit from north to south (above to below the given plane). Above and below are defined by the position of the north pole of the ecliptic. To review:

A given planet transits a node, at which time it is perfectly in the plane of the second planet and continues along its orbit (away from that node) until the point is reached of greatest latitude (whether north or south) in relation to the nodal interface in question. From that moment onward, the planet proceeds to move toward the opposite nodal point and once again directly to the opposite node and into the plane of the planet to be transited. Therefore, matters of interpretation are somewhat simplified and restricted (at least at first) to an analysis of the various quadrants: transit to the nodes and to the points of greatest disinclination (above and below) to these nodes.

Activation of the Interface Points themselves needs no lengthy introduction here since there are many fine texts available that spell-out every possible planetary combination. Students are referred to Reinhold. Ebertin's The Combination of Stellar Influences as one of the best of its kind, although sometimes a bit dark or heavy.

Although the planetary combinations are well known from other forms of astrology, we will spend some time here in the presentation of the principles involved in an understanding as to the use of the square, or changing-line points. These changing-line points, when activated, represent simultaneously two ideas:

  1. A planet at these points is as out-of-plane and therefore as disinclined as it can ever be to the plane of the second planet.
  2. At the same time the planet is changing its relationship to the nodal axis itself -- away from one node and toward the opposite node.

A close study of these points will reveal much as to changing (uneasy, dis-eased, etc.) and the more simple function of the planetary pairs (nodes) involved.

Consideration of all the planet's orbits simultaneously presents an ever-changing -- almost kaleidoscopic effect -- very similar to that obtained when rotating a fairly complex crystal in sunlight. Mutual harmonics and complex interrelationships are revealed that often highlight a single planet -- again and again. Therefore it is entirely possible, using only the interface points and their changing-lines, or square points to reveal a structure indicative of the whole-life force of the individual or event being examined. In practice, however, best results are obtained when interface analysis is combined along with other traditional heliocentric astrological techniques.

The Planes or Chakras

Although this is not meant to be an article on the interpretation of the various planets and the planes they describe, some brief mention of the principles involved in such an interpretation is warranted. The planes or levels described by the planets are exactly similar to what in the Eastern tradition are termed chakras, the centers of force and activity which make up the whole of our life. A particular individual, while a part of this whole system, is usually more active and concerned with one level of their lives than with the others (at least at any given time).

Interface analysis has proved to be a great help in locating the specific level (chakra or plane) and planet to which an individual naturally responds. Once this is revealed, information is easily forthcoming of direct interest to the individual concerning the particular plane of life and initiation in which they are finding themselves involved.

For a more complete description of these various planets or chakras -- please see my article "Astrology of the Heart: The Chakras" on this subject. The basic idea may be expressed here in one sentence: the key to the outer will always be in inner or in other words: the key to a given planet (chakra) will usually be that planet whose orbit is immediately within or inside the planet in question.

A perfect clear example: the planet immediately within the Earth's orbit is Venus and for all time the Earth has been ever concerned with Venus or love and, in fact, divine love has always been put forth by the world's spiritual lights as the very key to life on this planet. This is equally true for all planets from and including Saturn into the Sun. (The outer planets have a different significance). It should be understood that, although we live by virtue of our birth on this planet, we are not by that fact automatically in full realization of our Earth existence. In fact, initiation within inner planes (planets) is a gradual process of graduation by degrees. The majority of us have great difficulty working through (for instance) the Saturn (Satan), Jupiter (succession), and Mars (marriage) to even get in possession of the Earth (the Heart or child) much less graduating to the inner planes of Venus (divine love), Mercury (light of love), and on to the Sun (Self or 1000-petaled chakra).

As remote and "flowery" (or vague or abstract) as this language may seem to some readers, it is important to understand these various planes and to realize that we in fact find ourselves endlessly involved, evolving, and revolving through this life. At any one time a given individual will be taken up with concerns of a given plane. It becomes of great importance to the counseling astrologer to accurately indicate at what level and plane the life is being extended or occurring and to what plane the individual may be referred to for light and a clear idea as to the questions they may have.

In practice the role of the astrologer often involves directing and referring individuals to the level or chakra which happens to be the key to their current life's concerns. Interface analysis can help astrologers to more accurately and without personal bias determine the levels or planes to which a given individual responds as well as the key or level to be recommended as a way to inner planes. In the past, astrologers have often been limited and restricted in their practice to those chakras or planets in which they personally may have taken initiation (understand from personal experience) and they have primarily worked with those clients who exist on an outer planet or plane of initiation from their own level.

It is possible using Interface analysis for the astrologer to accurately determine and to direct a client to the appropriate level or plane regardless of whether he or she personally has (or has not) taken that initiation. To do this with accuracy demands a relatively absolute frame of reference to which all matters may be referred. The simple structure of our solar system is such a frame and when properly understood and rigorously applied much of what amounts to guesswork in the practice of astrology is removed.

The Astrologer of this Aquarian Age

I would like to mention briefly some benefits of a more personal and yet still absolutely useful nature. To cite a personal instance in the life of this author: In my natal heliocentric configurations, I have the planets Venus/Neptune/Jupiter mutually inclined to each other. A source of concern and confusion (especially in younger years) for me involved encounters with those with which I didn't by nature get along. Some folks took a dislike to me. I always wondered why and I spent an unwarranted amount of energy and time searching myself to discover what had I done to offend or to deserve such a reception.

It was most satisfying and fascinating to discover in the helio natal charts of these individuals who seemingly took offense to myself that they had one or more planets at the changing-line or square point to my natal Jupiter/Venus or Neptune. In other words, they were most definitely disinclined to the planets to which I was by nature perfectly inclined. Seeing this spelled out to me in these natal configurations has helped me to realize the simple fact of these inclinations/disinclinations and to let pass the opportunities to search and question myself as to the fault on either part for the event. On the other hand, I was startled to discover that in almost every instance, my closest personal friends all had the same planets at the same degree and that this degree was an Interface point that was perfectly complementary (inclined) to myself. This was (in my life) a rather remarkable discovery and one with the most practical kind of benefits to me as to the time and energy previously wasted in a useless self-examination. Enough said.

A System of Notation

It remains for us to discuss a convenient system of notation by which to represent these Interface points as they are found in a given chart. Such a system must include the planets themselves in their order from the Sun outwards. A vertical column (like the spinal column) is perhaps symbolically the most correct. (Figure 6)

Taking a particular natal or event chart (heliocentric only), we examine each planet's position and compare these positions to those in one of the tables at the end of this article. We will want to notate activity at both the Interface points and the square or changing-line points. To the right of the vertical column we notate all planets that by transit at an interface point. We draw the symbol for the planet (at the Interface point) next to the symbol of the planet in which plane the transit occurs.

For instance: If Mars is by transit at the interface Mars-Earth (IF Mars-Saturn), we draw the symbol for Mars next to that for the Earth in the printed column. We also then draw the symbol for Earth next to the printed symbol for Mars, but on the left-hand side of the vertical column. The left-hand side of the vertical column will represent the planes in which the transits occur, while the right hand side of the vertical column represents the planets activating these planes by transit.

By notating each Interface twice we get a better representation and indication as to which level and plane receives the most emphasis in a particular chart. The changing-line or square points are notated in a separate column at the extreme left hand side of each diagram and are separated by a line from the first three columns.

In this case, we notate the symbol for the transiting planet across from the symbol for the planet and plane to which it is disinclined. You will find that both simple and complex interrelationships emerge and become clear from these diagrams. Whole chains or "trees" interconnecting stand out that might otherwise pass unrealized. A future work, perhaps, might be devoted to a detailed analysis of these relationships, but the scope of this purely introductory work can but sketch the outlines involved in such a project.

I have included below the "trees" of several well known individuals. You will note that the tree for Baba Ram Das, who personally withstood public opinion concerning the greatly feared psychedelic drug LSD, has the Interface Jupiter-Pluto simultaneously activated by both Pluto and Jupiter. These planets are also in conjunction in this natal chart (helio). The tree for Howard Hughes has another mutual activation, in this case between Jupiter and Venus. And Beethoven's chart has an extraordinary emphasis on the planet Pluto (as does Baba Ram Das). You will also note that the planes or chakras most active in the Hughes chart are the middle-body chakras (Mars and Jupiter), while Baba Ram Das is more active in the outer planets . Beethoven sort of has the whole tree lit up. Points of disinclination show in Beethoven's chart some difficulty with the Mars principle (the marriage or emotions), while in the other diagrams Mercury and Earth are featured in DIS-inclination.

It remains for those of you who can respond to the ideas presented here to investigate for yourselves this fascinating subject and determine its usefulness in your particular work. In our understanding, what is revealed through this system of Interface points is exactly what is presented in the whole of chapter four of Revelations.


Baba Ram Das (Richard Alpert)

Equator Sun = O | O
Mercury = m | m
Venus = V +m | V
Earth = E | E
Mars = M | S-M
Jupiter = J | P-J-P
Saturn = S +m | P-S-P-M
Uranus = U | U-N
Neptune = N | U-N-P
Pluto = P +E | N-S-J-P-J-S
I-place = I | I


Howard Hughes

Equator Sun = O | O
Mercury = m | P-m
Venus = V +m | J-V-J
Earth = E | E
Mars = M | N-J-M
Jupiter = J | V-J-V-M
Saturn = S +m | S
Uranus = U | U
Neptune = N | N
Pluto = P +E| P-m
I-place = I | I



Equator Sun= O | O-V-M
Mercury = m | m-U
Venus = V +m | O-V
Earth = E | E-P
Mars = M | O-M
Jupiter = J | J-P
Saturn = S +m | U-S-P
Uranus = U | m-U-S
Neptune = N | N-P
Pluto = P +E | E-J-S-N-I-P
I-place = I | I


Note: Attempts to apply these points to the geocentric natal chart would be practical only with the outer planets, where the difference between geo and helio positions is plus or minus about three degrees, and with the Earth/Sun axis, which is identical in either coordinate system. It is time that modern astrologers exercise their understanding of the fact that we live simultaneously the lives of our solar system and Galaxy. We share a common fate. The heliocentric coordinate system may still be new to astrologers as a system of measurement, but the experience to which it refers is not new.

The religions of this world have long championed a more inclusive reality and each of us has for days or parts of days in our lives sustained awareness of this greater life. We have in fact arrived at a point where this experience can be measured and studied. As astrologers, we can point out to the world the opening in our times of the Age of Aquarius, of Group Work and mass Initiation. What more appropriate sign of this new age might we expect than a more holistic representation of this larger self to which we are true and an ability to refer and measure this self through coordinate systems of increasing inclusivity. The net result is not a desertion of the geo (body) perspective, but rather the enhancement of that perspective. "To see eternity in a grain of sand." As astrologers we are concerned with realizing eternity as it exists captured in the geocentric circumstances inherent in individual existence. We do not forsake the geo for the helio as some have suggested. We in fact live at once through all time and all space and: This is it! That all coordinate systems demonstrate this principle and exist only as they are convenient modes in which to measure and realize Eternity.

I include here a list of the interface points for the different epochs. These points do change, but the change is very slow. A variety of Matrix computer programs offer interface analysis as a built-in option, complete with interpretation. This interface concept was developed by Michael & Margaret Erlewine in the early 1970s. For those wishing to read more, reprints of the following are available from Matrix Software, 315 Marion Avenue, Big Rapids, MI 49307 Phone 616-796-3437 or email


"Interface: Planetary Nodes" by Michael & Margaret Erlewine and David W. Wilson, Heart Center Books, 1976.

"Interface Analysis" - by Michael Erlewine, NCGR Journal, 1977.

"Astrology of the Heart: The Planetary Chakras," available from Matrix Software, 315 Marion Avenue, Big Rapids, MI 49307

Basic Data: The Nodes to the Orbit of the Earth

Asending Nodes: Ordered by Ascending Node on Earth's Ecliptic

MERCURY 047.145944° + 4266.75"T + 0.626T2 +1.18528°T
MARS 048.786442° + 2775.57"T - 0.005"T2- 0.0192"T3 +0.77111°T
URANUS 073.489903° + 1838.25"T +0.49889°T
SUN'S EQUATOR 074.366667° + 5040.0"T +1.40000"T
VERBS 075.779647° + 3239.46"T + 1.476"T2 +0.89972°T
JUPITER 099.437861° + 3639.5"T +1.0l083°T
INVARIABLE PLANE 106.583611° + 3452.0"T +0.95888°T
PLUTO † 109.683462° + 5400.0"T +1.50000°T
SATURN 112.783567° + 3143.43"T +0.87278°T
NEPTUNE 130.678689° + 3966.54"T +1.09833°T

Inclinations: Ordered Relative to Ascending Node on Ecliptic

MERCURY          07.0028806° + 06.699"T -0.066"T2
MARS             01.8503333° - 02.43"T  +0.0454"T2
URANUS           00.7727222° + 02.00"T 
SUN'S EQUATOR    07.25° 
VENUS            03.3936306° + 03.621"T -0.0035"T2 
JUPITER          01.3086944° - 20.0"T 
INVARIABLE PLANE 01.5830556° - 18.0"T
PLUTO †           17.1698661° 
SATURN           02.4925833° - 16.0"T
NEPTUNE          01.7792499° - 33.0"T

EPOCH 1900.0 (all values this page)

Inclinations. Ordered Relative to the Plane of the Earth

PLUTO 17.2° Sun Earth Uranus } 9.9°
EQUATOR OF SUN 07.3 Mercury Pluto Earth } 0.2
MERCURY 07.0 Sun Pluto Neptune } 3.6
VENUS 03.4 Mars Pluto Mercury } 0.9
SATURN 02.5 I-plane Pluto Mercury } 0.6
MARS 01.9 Uranus Pluto Sun } 0.1
NEPTUNE 01.8 I-plane Pluto Mercury } 0.2
INVARIABLE PLANE 01.6 Jupiter Pluto Mercury } 0.3
JUPITER 01.3 I-plane Pluto Mercury } 0.5
URANUS 00.8 Jupiter Pluto Sun } 0.8
EARTH 00.0 Uranus Pluto Sun

Legend for columns 1 thru 5:

  1. Difference in inclination between planet and the earth's orbital plane.
  2. First differences for these.
  3. Planet to which listed planet is most mutually inclined.
  4. Planet to which the listed planet is least mutually inclined.
  5. Aside from Pluto, the planet to which the listed planet is least mutually inclined.

† The orbit of Pluto is still being defined. For purposes of this book it was necessary to select an approximate value for pluto's motion in a Julian century of 36525 days. The above value was selected although one should realize that this is only an approximation, good to within perhaps a degree of the value listed. See section on Invariable Plane as well.

Note: The above epoch for 1900, January 0.5 ET or Julian Day 2415020.0. The time interval from the epoch is denoted by T and is measured in Julian centuries of 36525 ephemeris days. All elements are the MEAN elements for above epoch except elements for Pluto which are osculating elements at the epoch 1950.0 or JED 2433282.423. See note above on Pluto.

Interface and Changing-Line formulae for Epoch 1900.0

First Planet       Second Planet
INTERFACE        INTERFACE   Changing-line  Changing-line

mercury-mars      1.33352    1.33543        1.33410
mercury-uranus    1.25563    1.25663        1.25570
mercury-Sun       1.35723    1.35473        1.35778
mercury-venus     1.32612    1.32749        1.32579
mercury-jupiter   1.24959    1.25043        1.24963
mercury-I-plane   1.24932    1.25010        1.24923
mercury-pluto     1.51641    1.51158        1.51744
mercury-saturn    1.23909    1.23953        1.23843
mercury-neptune   1.25998    1.26085        1.25976
mars-uranus       0.87411    0.87422        0.87412
mars-Sun          1.56595    1.56624        1.56853
mars-venus        0.94634    0.94628        0.94650
mars-jupiter      0.99312    0.99314        0.99310
mars-I-plane      0.97558    0.97554        0.97547
mars-pluto        1.52943    1.52887        1.53218
mars-saturn       0.90811    0.90801        0.90792
mars-neptune      1.08660    1.08659        1.08632
uranus-Sun        1.50559    1.50569        1.50808
uranus-venus      1.01518    1.01528        1.01564
uranus-jupiter    1.58331    1.58325        1.58336
uranus-I-plane    1.28076    1.28071        1.28082
uranus-pluto      1.53631    1.53635        1.53981
uranus-saturn     1.00323    1.00320        1.00335
uranus-neptune    1.30995    1.30981        1.30985
Sun-venus         1.83542    1.84245        1.83866
Sun-jupiter       1.49778    1.49935        1.49802
Sun-I-plane       1.51960    1.52146        1.51981
Sun-pluto         1.53338    1.53263        1.53575
Sun-saturn        1.57557    1.57707        1.57533
Sun-neptune       1.50486    1.50638        1.50476
venus-jupiter     0.94019    0.94029        0.94030
venus-I-plane     0.98782    0.98801        0.98795
venus-pluto       1.60418    1.60454        1.61376
venus-saturn      1.04765    1.04756        1.04737
venus-neptune     1.09119    1.09144        1.09123
jupiter-I-plane   0.64359    0.64341        0.64334
jupiter-pluto     1.53434    1.53453        1.53782
jupiter-saturn    0.67877    0.67856        0.67835
jupiter-neptune   1.20017    1.20004        1.19989
I-plane-pluto     1.55180    1.55219        1.55640
I-plane-saturn    0.69629    0.69605        0.69590
I-plane-neptune   1.36744    1.36713        1.36707
pluto-saturn      1.60345    1.61334        1.60480
pluto-neptune     1.55333    1.55834        1.55384
saturn-neptune    0.89809    0.89829        0.89841

The above listed numbers represent the amount of change(in the direction of the signs (counter-clockwise) that the Interface and each of its SQUARE points make in a Julian century of 365.25 days. They would be of use in calculating the approximate position of the various points for epochs not included among the Tables in this book. For instance, the first on the list Interface mercury-mars (from Table 1900.0 elsewhere in book) is 046°5607. Therefore: Formula = 046°5607 + 1°33352 per century advance (to be added for years after 1900.0 and subtracted for years prior to 1900.0)

Basic Data for Epoch 1900.0

mercury-mars    046.5607  136.5519 136.5583 -0.0719 +7.0025 +1.8489 5.1536
mercury-uranus  044.0525  134.0059 134.0481 -0.3798 +6.9925 +0.6729 6.3197
mercury-Sun     146.6179  236.4796 236.8832 +6.9083 -1.1413 +2.1888 3.3544
mercury-venus   025.2738  114.9755 115.1751 -2.6201 +6.4897 +2.1553 4.3389
mercury-jupiter 037.7196  127.5800 127.7071 -1.1525 +6.9065 +0.6199 6.2878
mercury-I/plane 034.8064  124.6260 124.7934 -1.5037 +6.8380 +0.4948 6.3453
mercury-pluto   133.0455  223.1063 225.0065 +6.9851 +0.4958 15.6043 15.225
mercury-saturn  026.4341  116.1487 116.4272 -2.4875 +6.5420 +0.1585 6.3896
mercury-neptune 032.6444  129.4350 122.6520 -1.7618 +6.7755 -0.2485 7.0273
mars-uranus     033.0860  123.0704 123.0809 -0.5009 +1.7812 +0.5884 1.1929
mars-Sun        082.4611  172.4887 172.5904 +1.0262 +1.5395 +7.1762 5.6376
mars-venus      101.4462  191.4750 191.5248 +1.4713 +1.1218 +3.0574 1.9363
mars-jupiter    004.0367  094.0068 094.0395 -1.3019 +1.3136 -0.1231 1.4371
mars-I-plane    175.7172  085.6885 085.7318 -1.4793 +1.1113 -0.5636 1.6755
mars-pluto      115.1813  205.2033 205.7095 +1.6956 +0.7405 17.0807 16.348
mars-saturn     157.4574  247.4330 247.5116 +1.7530 -0.5920 +1.7714 2.3645
mars-neptune    001.0265  090.9968 091.0537 -1.3701 +1.2434 -1.1350 2.3790
uranus-Sun      074.4706  164.4710 164.4722 +0.0132 +0.7726 +7.2500 6.4774
uranus-venus    076.4534  166.4540 166.4558 +0.0400 +0.7717 +3.3934 2.6217
uranus-jupiter  128.2772  218.2821 218.2898 +0.6313 +0.4455 +1.1463 0.7008
uranus-I/plane  130.8478  220.8526 220.8642 +0.6507 +0.4168 +1.4431 1.0264
uranus-pluto    111.2139  201.2190 201.3600 +0.4728 +0.6112 17.1629 16.552
uranus-saturn   127.2559  217.2609 217.2822 +0.6233 +0.4670 +2.4133 1.9567
uranus-neptune  156.1883  246.1896 246.2098 +0.7665 +0.0982 +1.6056 1.5075
Sun-venus       073.1336  163.1136 163.1243 -0.1569 +7.2483 +3.3900 3.8533
Sun-jupiter     069.1741  159.0905 159.1611 -0.6596 +7.2196 +1.1302 6.0898
Sun-I-plane     066.2905  156.1616 156.2689 -1.0239 +7.1766 +1.2072 5.9703
Sun-pluto       129.4036  219.8343 221.1218 +5.9519 +4.1248 16.0451 11.987
Sun-saturn      058.1673  147.9192 l48.1161 -2.0326 +6.9563 +1.4421 5.5177
Sun-neptune     061.1419  150.9355 151.1238 -1.6670 +7.0537-+0.6217 6.4348
venus-jupiter   062.3441  152.2985 152.3297 -0.7894 +3.3003 +1.0437 2.2568
venus-I plane   054.0782  144.0090 144.0571 -1.2561 +3.1521 +0.9633 2.1893
venus-pluto     116.9404  207.0400 207.6247 +2.2351 +2.5524 17.0418 14.474
venus-saturn    028.9005  ll8.8001 118.8890 -2.4734 +2.3168 +0.2653 2.0534
venus-neptune   044.2577  134.1680 134.2543 -1.7758 +2.8910 +0.1110 2.7814
jupiter-I plane 136.3489  226.3633 226.3678 +0.7861 +1.0463 +1.3740 0.3278
jupiter-pluto   110.4960  200.5017 200.5736 +0.2511 +1.2844 17.1679 15.884
jupiter-saturn  126.6866  216.6988 216.7119 +0.5993 +1.1634 +2.4194 1.2561
jupiter-neptune 176.4552  266.4618 266.4829 +1.2753 +0.2939 +1.2405 0.9469
I-plane-pluto   109.9878  199.9904 200.0140 +0.0940 +1.5803 17.1696 15.589
I-plane-saturn  123.3140  213.3261 213.3335 +0.4558 +1.5160 +2.4505 0.9346
I-plane-neptune 193.3314  283.3339 283.3540 +1.5805 +0.0898 +0.8169 0.7275
pluto-saturn    109.1754  199.1268 199.1686 -0.1570 17.1691 +2.4876 14.682
pluto-neptune   107.4070  197.1899 197.3869 -0.7032 17.1546 +1.6343 15.521
saturn-neptune  078.4410  168.3905 168.4143 -1.4068 +2.0572 +1.0892 0.9684

Legend for Above: Interface listed by planetary pair followed by position of node on earth's ecliptic. Next a list of the square points. 1 & 2. Square #1 refers to the first listed planet in the Interface pair at far left hand column...#2 to the second. Next follows list for latitude above or below the earth's ecliptic(+ or-) for each point. NOTE: It must be kept in mind that these values represent only one half of the axis and that values by longitude 180 degrees apart comprise the other half. Latitudes also are identical for the 180 degree point but take the opposite sign to the one listed above.(+ becomes - ... or vice versa)


© Copyright: Michael Erlewine





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