| A concept used in astronomy to describe the basic background pattern of stars, against which other objects can be seen to move. The idea originated in ancient times as a way to distinguish the wanderers (the five naked-eye planets and the sun and moon) and visitors (comets, novae, meteors, etc.) from the seemingly unchanging background of constellations and stars.
It is also the basis of a type of astrology popular in ancient Egypt, Arabia and parts of the ancient Greek world, but which has fallen into obscurity over the last 300 years or more. The brightest, most recognisable stars in the northern sky are linked with specific attributes and types of event.
First, the scientific stuff
The concept of fixed stars is slightly outdated, as we now know that all stars move at least a little bit relative to their neighbours. This motion is called their proper motion, and reflects the facts that stars have their own motions independent of the gross motion of the local galaxy, or of the nearby stellar clusters. In almost all stars, this motion is only visible through painstaking, accurate observations.
Barnard's star ( RA 17h 58m, Dec +04:41, in Ophiuchus) is so faint (mag 9.56) it is only visible through a moderate telescope, but this red dwarf star is the 'vette of the stellar world, moving at around 10.29 arc seconds per year. This means it will move a distance equivalent to the width of the moon's full disk in around 175 years.
Most stars have proper motions much slower than this, and such slow change has only become observable with the advent of modern optical equipment and photographic systems, which allow astronomers to observe photographs of the same patch of sky taken many years apart.
Beyond that, as the earth orbits around the sun, we see the night sky from a slightly different perspective at opposite ends of the year. Very close stars will appear to move in relation to the distant stars over a six-month period. This is a result of parallax. Just as moving your head causes the screen in front of you to appear to move in relation to the wall behind it, when the earth crosses the 300 million km or so from perihelion to aphelion, some close stars appear to move relative to the more distant fixed stars.
Astronomers have used this phenomenon to develop a unit of distance: the parsec, which is derived from the words "parallax-second" Thus a parsec is the distance at which a star would have a parallax of one arc second if the earth moved from its orbit, to the sun. It is equivalent to 3.26 light-years or 206,265 astronomical units (the distance from the earth to the sun) or 3.086 x 10^16 metres.
So the fixed stars form the background to the observable night sky, and have become a frame of reference for observations of objects which move--or appear to move--relative to that unchanging background.
Source:
http://www.fourmilab.ch/yoursky/help/proper.html
The astrological issues
The most comprehensive list of astrological fixed stars I can find includes 768 naked-eye stars, listed in the book, Astrophysical Directions by Michael and Margaret Erlewine, and published in 1977.
Download the list at http://www.winshop.com.au/annew/768a.htm
Another astrologer, William Lilly, from the Elizabethan period in the UK mentioned a list of about 50 fixed stars, again, they are all clearly recognisable naked-eye stars. Lilly is, apparently, "undergoing something of a revival" among modern astrologers, according to this website, which also lists some of the attributes associated with the various stars.
http://www.yourfreehoroscopes.com/zodiac/fixedstars.html
There is controversy within the astrological community over whether the stars at higher latitudes (notably Polaris, but also Algol) can have any influence over an astrological chart, but most appear to agree that if the fixed stars are taken into account, then their influence is limited to the strongest aspects, such as conjunction and possibly parallel.
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