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Pappus of Alexandria (c.290-c.350): one of the last great mathematicians of antiquity, so far above his contemporaries and so little understood by them that there is little reference to his works by other Greek writers. His works are eight volumes of his Collection and commentaries on Euclid’s Elements and Ptolemy’s Almagest.

parallax: the apparent shifting of a closer celestial body (a planet or nearby star) against the background of far more distant stars caused by changing one’s point of view. If the two points of view are on opposite sides of the Earth, it is called a "geocentric" or "diurnal" parallax; if on opposite sides of the Earth’s orbit, it is called "heliocentric" or "annual" parallax. Since the distance between those points is known precisely (the diameter of the Earth or its orbit), and the angle of shift can be measured, the distance to the closer body can be determined by trigonometry. A bodies "parallax" is 1/2 of the angle of that apparent shift.

In 1672 Giovanni Cassini used a parallax base line from Paris to Cayenne, French Guiana to measure the distance to Mars, and in so doing measured the Earth-Sun distance (1 AU) for the first time. It wasn’t until 1835 that Friedrich Bessel obtained the first accurate measurement of a star’s parallax for the star 61 Cygni. With a parallax of 0.32 arc-seconds (1/11,000th of 1°), its parallax was almost 200 times below the threshold of Tycho Brahe’s ability to measure the position of stars.

parallel: an aspect between two planets that are the same angular distance north or south of the celestial equator (the Earth’s equator projected into space) and are on the same side of it; orb 1°. Two planets with the same "declination" are said to be in parallel (see "declination" and "contraparallel"). This aspect is said to act like the conjunction when two planets have the same declination and are on the same side of the celestial equator (in parallel), and like the opposition when two planets have the same declination and are on opposite sides of the celestial equator (in contraparallel).

parsec: 3.26 light years, or 19.2 trillion miles; defined as the distance to a body with a heliocentric parallax of one second, hence "par - sec" is short for "parallactic second." If a body appears to shift one second of arc against background stars when viewed from opposite points in the Earth’s orbit (182 days apart), its distance from the Earth is one parsec. The nearest star other than the Sun, Alpha Centauri C (Proxima Centauri) is 1.3 parsecs or 4.22 light years distant.

Part of Fortune (Pars Fortuna): if the Sun were moved onto the ascendant and the angle between the Sun and the Moon were left unchanged, the Moon’s new position is the Part of Fortune (i.e., it is the longitudes of the Moon + ascendant - Sun). It denotes success in worldly affairs.

penumbra (Latin paene "almost" + umbra "shadow"): that region of a celestial body’s shadow under which only a portion of the Sun’s light is blocked by the occluding body. During a solar eclipse on Earth, observer’s in the Moon’s penumbra experience only a partial eclipse of the Sun (see page 130).

peregrine: said of a planet that is not in dignity, debilitated, or in mutual reception, but seems to be independent of other planets; in questions of theft in horary astrology a peregrine planet in an angle or the second house is the thief.

perigee: the point in its orbit where an object is closest to the Earth (opposite of apogee).

perihelion: the point in its orbit where a body is closest to the Sun (opposite of aphelion); "perigee" is used for objects orbiting the Earth; "periapsis" for the closest point in orbit around other bodies.

period, orbital: the time for a body to make one complete orbit around another. A question naturally arises: ‘one complete orbit’ with respect to what? The answer is in the five types of orbital periods: sidereal, synodic, draconic, anomalistic and tropical that are defined and used in this text.

personal planets: the Sun, Moon, Mercury, Venus and Mars. These planets change positions fast enough to distinguish birth charts close in time from one another. They are also personal in that they relate to individual rather than to collective or social energy, as do the outer planets.

perturbation: an alteration or change in a body’s orbit due to the gravitational influence of another body upon it. The unexplained (accounting for all the then known solar system bodies) perturbations in Uranus’ orbit were responsible for the discovery of Neptune. Jupiter so strongly perturbs nearby bodies that no planets, only asteroids, formed between its orbit and that of Mars.

Placidian: the most popular house system in the English-speaking world; probably due to the serendipity of its being in the widely circulated 1820 "Raphael’s Almanac and Prophetic Messenger."

plane: an imaginary, infinite flat surface, like the meridian or horizon planes.

planet: on Aug. 24, 2006, the International Astronomical Union redefined a planet as an object that:

1) is in orbit around the Sun;

2) assumes a round shape due to sufficient mass;

3) has cleared its neighborhood of significantly sized bodies other than its own satellites;

4) is not a satellite of a planet or non-stellar body.

The result of this redefinition was that, since Pluto had NOT cleared its neighborhood of significantly sized bodies, it lost its astronomical status as a planet. Pluto has now been reclassified as one of three or four dwarf planets: Ceres the asteroid, Pluto a TNO (Trans-Neptunian object), Eris (2003 UB313, a recently discovered TNO larger than Pluto), and probably 2003 EL61 (a KBO also with a moon, about as large as Pluto). Astronomically there are now only eight planets in the solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Astrologically, however, Pluto is still interpreted as though it were a planet.

planetesimal: pieces of planets theorized to exist in protoplanetary disks or debris disks. Planets are thought to form from the accretion of colliding dust grains in the solar nebula; in this manner clumping dust grains form larger and larger bodies, until at about one kilometer in diameter they gravitationally attract each other. From this point on they can grow by mutual gravitational attraction into moon-sized planetesimals. Planetesimals are often defined as a limiting size for astronomical bodies, below which growth is caused by the Brownian motion or turbulence of the gas or dust cloud in which they reside, and above which growth is caused by gravitational attraction.

plasma: atoms in the gaseous state that have lost some or all of their electrons, usually by being heated or electrically excited. Stars are entirely composed of plasma, akin to the astrological element fire. The four states of matter—solid, liquid, gas, plasma—differ only in the degree in which their atoms vibrate relative to their bonding energy.

The measure of the average vibrational motion of the atoms or molecules of a substance is called its temperature. Thus the lowest possible temperature is when there is no atomic vibration at all. This is called absolute zero: 459 degrees below zero on the Fahrenheit scale, and the beginning (zero degrees) of the Kelvin scale of temperature. Curiously enough, the universe has a very low and uniform temperature in all directions. Known as the "3° Kelvin background radiation," this 3° temperature everywhere in outer space is an afterglow of the Big Bang cooled to almost nothing after 13.7 billion years, and the strongest evidence we have that a Big Bang occurred at all.

In a solid, the counterpart of the astrological element earth, the energy holding the constituent atoms together (their bonding energy") is stronger than the atom’s vibrational energy. This is what makes a solid a solid and gives it a fixed geometry. As a solid is heated, a point is reached at which the average vibrational energy of its constituent atoms equals or exceeds the energy holding them together. At this point the solid melts and becomes a liquid. A liquid is that state of matter, the counterpart of the astrological element water, in which the average vibrational energy of the constituent particles exceeds their bonding energy. If a liquid is continuously heated, there comes a point at which the average vibrational energy of the constituent particles so exceeds their bonding energy that they repel each other. At this point the liquid boils and becomes a gas—the counterpart of the astrological element air.

If the gas is heated even more, the vibrational energy of its constituent particles eventually becomes so great that its atoms begin to permanently kick off their outer electrons. A gas having lost some or all of its outer electrons is said to be ionized, and is known as a plasma—the counterpart of the astrological element fire.

plutino: an object beyond the orbit of Neptune with a 2:3 orbital resonance with Neptune. Plutinos are found in the inner part of the Kuiper belt, and make up about ¼ of the known KBOs (Kuiper Belt Objects). The largest plutinos include Pluto, its moon Charon, 1993 RO, 90482 Orcus, 28978 Ixion, 2003 VS2, 38628 Huya, and 2003 AZ84.

plutoid: a trans-Neptunian (beyond Neptune) dwarf planet or an object that is likely to be such a body and that has received a permanent name as a plutoid. The International Astronomical Union (IAU) developed this category of astronomical objects as a consequence of its 2006 resolution defining the word "planet". The IAU’s formal definition of ‘plutoid’ as of June 2008, is: "Plutoids are celestial bodies in orbit around the Sun at a semimajor axis greater than that of Neptune that have sufficient mass for their self-gravity to overcome rigid body forces so that they assume a hydrostatic equilibrium (near-spherical) shape, and that have not cleared the neighbourhood around their orbit. Satellites of plutoids are not plutoids themselves." As of 2008, Pluto, Eris, Haumea, and Makemake are the only objects classified as plutoids. Ceres is indeed a dwarf planet, but its orbit is not trans-Neptunian. As of April 2007, upwards of 70 more bodies may yet be determined to meet this definition.

precess: A spinning body to which an outside force is applied will tend to rotate in a direction perpendicular to both the outside force and to its spin axis. This resultant rotation is called precession, a movement seen both in spinning tops and in planets (please see page 42 for more).

precession of equinoxes (see pages 42-44): Since the Earth is not a perfect sphere (see "oblateness"), the Sun and the Moon pull on it unevenly. This non-uniform pull creates a net force causing the Earth’s spin axis to wobble or precess in space, the way a top’s axis pulled on by gravity circles the vertical as it slows down. Thus the Earth’s equator and its line of intersection with the ecliptic precess as well. Since this line of intersection is the line of the equinoxes, we get the "precession of the equinoxes." This wobble takes 25,788 years to complete one cycle, or 25,788÷12=2150 years/sign. A "great age" takes its name from the group of stars (constellation) through which the vernal equinox is currently precessing. Thus the Age of Pisces lasted from about the birth of Christ to about the mid-20th century, and the Age of Aquarius will last from about mid-20th century until about 4100.

prime vertical: the vertical circle passing through the center of the Earth and perpendicular to the horizon that also passes through the east and west points on the horizon. The prime vertical is also perpendicular to the meridian: the vertical circle passing through the north and south points on the horizon. The horizon and meridian planes quarter the local sky, and form the 12 houses when trisected by planes perpendicular to the prime vertical and passing through the horizon’s north–south line (see the figure on page 231).

progressed: planetary positions (or a whole chart) computed on the principle that one rotation of the Earth on its axis (one day) symbolizes one revolution of the Earth around the Sun (one year); said to signify inner development; distinct from transits said to represent exterior events.

proper motion: the true movement of a celestial body through space relative to the Sun and Solar System, and not due to the daily rotation of the Earth on its axis or its yearly revolution around the Sun (parallax). Barnard’s star at six light years distance has a proper motion of 10.6'' per year, the highest of all stars. Eris, the ninth largest natural body orbiting the Sun, has a proper motion of 19''/day, and Sedna, 42''/day. The Sun moves at 220 km/second about the center of the Milky Way. This can be taken as the rotational speed of the galaxy itself at the Sun’s distance from its center.

protoplanet: moon-sized planetary embryos within protoplanetary discs believed to have formed out of kilometer or larger planetesimals, whose subsequent collisions eventually form planets.

protoplanetary disc: a rotating disc of dense dust and gas surrounding a newly formed star in which planets can potentially form by accretion to planetesimal size, and then by gravitational attraction.

protostar: a stage in the development of a young star after its formative cloud of hydrogen, helium and dust has begun to contract, but before it reaches the main sequence and begins fusing hydrogen in its core.

protosun: a more familiar name for a protostar

Ptolemy, Claudius (87 to 150 A.D.): a Greek living in Alexandria, Egypt who codified the Greek geocentric view of the universe in his 12-volume The Almagest (The Greatest). Aristotle and Ptolemy’s perfect geocentric universe became the model for astronomers, astrologers, and, although it was pagan, for the Christian church for 2000 years until Nicolaus Copernicus (see pages 31-32).

putti (singular, putto): angelic creatures used by artists to allude to or to represent love, usually depicted as adorable chubby children or babies with tiny wings suggesting their celestial origin.

Pythagoras (c. 569-c. 475 B.C.): Nothing of Pythagoras’ writings has survived. His half religious, half scientific society followed a code of secrecy that has left him a mysterious figure. Early biographers attributed divine powers to Pythagoras and presented him as a godlike figure. Nevertheless, we know his primary teachings were that: reality, at its deepest level, is mathematical in nature; philosophy can be used for spiritual purification; the soul can rise to union with the divine; and that certain symbols have a mystical significance.




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