## Fixing Star Positions

It is clear that with the aid of these circles -we are able to fix any position of a star, anywhere in the heaven, the same way as we fix all points oti out own earth.

The data necessary to accomplish this are:

1) The distance of a star E measured on the declination circle (Fig. 3) from the plane of the Equator sets its Decimation ED measured from single EOD and the complementing distance to 90* of the star from the pole, its pole distance EON. Bur the angle, which is formed with the Plane of the Horizon and that of the Equator (in Fig. 4 AQ for the poinr M), is called the Equalond Altitude. (Seepage 10).

This altitude is complemented to 90' by the Pole Altitude FMH.. From this follows, that the angle, made by the vertical line of a. point with the Plane of the Equator MO A, must be equal to the Pole Altitude.

2) The distance, measured on the parallel circles of a star from the first declination circle, is called Right Ascension. The circle of declination which passes through the Spring Equinox- is the first Declination Circle. From the way the place of a star is given ia relation to the plane of the World Equator and the World Poles, which come to lie through the center of the vertically lying World Axis, we can also define the place of the star in relation to the Plane of the Horiion as well as the Zenith and Nadir. They lie in the Center of a. line running through the fo-raer. Furthermore, we can define this star's place through the Azimuth, i.e. rhe Arc of the Horizon from the South Point to the Vertical Circle of the Star, and as said already, with the aid of the Altitude, i.e. the Arc of the Vertical Circle fixed to the Horizon,

A third and similar calculation can be made in relation, to the Ecliptic also called the Plane of the Sun's Path, and its Poles.

WHAT IS THE ECLIPTIC?

The entire period of the Declination of the Sun, takes about 3<S5J4 ^H''5 which includes the increase of the northern declination up to a certain limit, (23'27'N), its decrease ta iero, its following increase southward to a definite

limit (2 3"27'S) and its consequent decrease back to ztto, thus reaching again the point of beginning. During that time Che Right Ascension rnov« from Oh to 24h. At the end of this time the Sun is found very near the same point or place In the heaven ¡us at the beginning of the movement. The path described by the Sun during this time in the heaven we can find, when we enter from- day to day on. an artificially made heavenly bowl the values found through accual observation of this Declination and Right Ascension. We find thac this path appears to be one of the greatest circles which cuts the Equator at a certain angle. This arc (Fig. 5, page 10) BCDE, called Sun's path or Ecliptic, forms "with the Equator AQ an angle of about 23*27', CFQ, and this angle is called the Mean Obliquity of the Ecliptic. The Ecliptic is divided into 12 equal pacts, -whereby each pare contains 30*. These parts are called the signs of the Zodiac. Each monch, approximately,. the Sun passes through one of these signs. Of course, we muse not forget that actually oar earth is found opposite to the sign in which the Sun seems to be. When the geocentric place of the Sun is in Aries, the heliocentric place of the earth (as seen from" the center point of the Sun) must be in the sign of Libra. Whenever the Sun has passed through one complece round, one year has elapsed. Consider that after such time has passed, the Sun returns again to the same fixed star. We call this period a Sidereal Year.

We use the Ecliptic with its poles, the same as the Equator and its poles, to determine the places -of the stars. Through a star, whose place shall be defined that way, we imagine to have laid a half-circle, which reaches from the North Pole of tie Ecliptic to its South Pole. It cuts vertically the Ecliptic. Such i circle is called a Latitude Circle. That pare of the circle which is contained between Ecliptic and the Scar in question is called the Latitude of the StJr. This Latitude may be north or south, depending upon whether the star or planet is to the notth or to- the south of the Ecliptic. The Latitude can extend from 0 to 90". The star has 0" latitude -when it is found exactly in the Ecliptic and 90* Latitude if the star would be exactly in the Pole of the Ecliptic. However, a star is not fixed by Latitude alone. We need also its Longitude. Longitude is that arc of the Ecliptic, which lies between the Aries point and that point of the Ecliptic through which the Latitude circle crosses, which passes through the Star. Th£ measurement must always be made from West to East and be started at the Aries point (0* T)• The point of the Spring Equinox (Aries point), as well as the Fall Equinox (Libra point), belong to both, the Equator and Ecliptic. In Fig 6 let S be the Star placed in the Heavenly Sphere, PCP'" the World Axis, and EE' the Equator, erected vertically on CP; T^hen we place through the World Axis the Hour Circle Pem and O assumed to be the Spring Equinox, then we have Om according to our definition as the Right Ascension and Em as the Declination of the Star. If we imagine the Circle of the Ecliptic AOA' on which the apparent movement of the Sun occurs and draw upon it the Vertical Axis QEQ' and when we finally lay through the Star the Arc of the Biggest Circle QSn, then On is the Longituda in the Heaven and "Sn" is the Latitude of the Star S. (See illustration on page 10).

The biggest circle, placed vertically on the Ecliptic, QSn, Is called the LatiluJe Circle and the points Q and Q' arc the Poles of the Ecliptic. The Right Ascension is always given in houri, minutes and teconds, while the Longitude is always given in degrees and minutes (") from 0* to 360" or in 30" units with the zodiacal signs attached, such as we use exclusively tn astrological work.

1) When Longitude and Latitude are known, any star or planet is fixed.

2) When Right Ascension and Declination ate known the star or planet 3s fixed also.

Therefore, bow, that Longitude has no direct relation to Declination, neither has Right Ascension, to Latitude.

Beca.u.5c the plane of the Heavenly Equator falls together with the plane of the Earth's Equator, the Ecliptic, when put on to the earth's globe in out imagination, will cut this Earth Equator under the same angle is it will-cut the Heavenly Equator. When we imagine the plane of the Ecliptic laid horizontally, then the Axis of die Earth stands slanting, in telation to it, and it differs from a vertical Line in the same degree, as that under which Equator and Ecliptic cut each other. The angle is 23'26'48".

The motion of the Slot in the Ecliptic is onLy an apparent motion, since it is actually the earth that moves in the Ecliptic around the Sun. It is not only the earth that moves in the Ecliptic around the Su.n. All the other planets move :a it too! The Sun is the center around which their motion occurs. The actual distance of che planets among themselves, as well as from the Sun, varies considerably, else there would have occurred many collisions already. The path of the Ecliptic is not completely round but has che shape of an etlipje.

We consider the distance from Sun to the earth as 1, Table II shows the comparative distances of the other planets from the Sun.

The time of rotations from one fixed point, such as fro err the 0" Aries point; back to the very same point in the Zodiac for the various p La nets is shown on Table II, and is called the "Sidereal period, measured in tropical years." Decimals are used, which can be rucried ¡mo days with aid of Table IV. (See page 11 & 14).

The time given in this Table for Mercury and Venus represents their (notions around the Sua, when viewed from the Sun. Ia our astrological -wotk we sometimes -use this type of motion to figure wheat or cotton prices or the prices of some other commodities, in some cases also for stocks, but the methods which are taught in this -work consider only geocentric positions of the planets. ?These two planets from a geocentric view (as seen from the earth) take about one year's time to get around the Zodiac.