Chapter 8 — Fixed Stars #

What you will learn #

In this chapter, you will discover why “fixed” stars are not really fixed, how the library calculates their positions taking into account precession and proper motion, how to search for a star by name (even with spelling mistakes), and how to use fixed stars in astrological calculations.

8.1 Stars are not so fixed #

The ancients called them “fixed stars” to distinguish them from planets (“wandering stars”), which visibly move from night to night. But stars move too — just much, much more slowly.

Precession: the whole sky rotates #

The largest effect is not the movement of individual stars, but that of our reference point. The Earth’s axis wobbles slowly like a spinning top, completing a cycle in about 26,000 years. This phenomenon — the precession of the equinoxes — causes the vernal point (0° Aries) to shift by about 50 arcseconds per year relative to the stars.

In practice, all stars shift by about 1° every 72 years in ecliptic longitude. Regulus, which 2000 years ago was in the heart of Leo, is today at almost 0° Virgo.

Proper motion: every star has its path #

Besides precession (which moves all stars in the same way), each star has its own proper motion — its actual displacement in space. The speed depends on the star’s distance and actual velocity:

Sirius: 1.33"/year — in 2000 years it has moved by almost half a degree
Arcturus: 2.28"/year — one of the fastest proper motions among bright stars
Regulus: 0.25"/year — relatively “still”
Barnard’s Star: 10.36"/year — the absolute record, but it is invisible to the naked eye

For the bright stars used in astrology, proper motion is almost always negligible over scales of a few centuries. But for historical calculations (ancient birth charts, stars in ancient Egypt) it becomes important.

The library accounts for both precession and proper motion when calculating a star’s position. You can also manually propagate proper motion with propagate_proper_motion:

import libephemeris as ephem

# Propagate Sirius's proper motion from the Hipparcos catalog (J1991.25) to J2000
# RA and Dec in degrees, proper motion in arcsec/year
ra_sirio = 101.2872  # RA J1991.25 in degrees
dec_sirio = -16.7161  # Dec J1991.25 in degrees
pm_ra = -0.5461   # proper motion in RA (includes cos(dec)), arcsec/year
pm_dec = -1.2232   # proper motion in Dec, arcsec/year

J1991_25 = 2448349.0625  # Hipparcos catalog epoch
J2000 = 2451545.0         # J2000.0 epoch

ra_2000, dec_2000 = ephem.propagate_proper_motion(
    ra_sirio, dec_sirio,
    pm_ra, pm_dec,
    J1991_25, J2000
)

print(f"Sirius at J2000.0: RA = {ra_2000:.4f}°, Dec = {dec_2000:.4f}°")

Sirius at J2000.0: RA = 101.2858°, Dec = -16.7191°

In daily practice, you will almost never need this function: fixstar2_ut does everything automatically — precession, proper motion, nutation, and aberration included.

8.2 The star catalog #

The library includes an internal catalog of about 100 stars, based on data from ESA’s Hipparcos satellite (1989–1993). Hipparcos measured the position, proper motion, and magnitude of over 118,000 stars with unprecedented precision (about 1 thousandth of an arcsecond).

The catalog covers all the important stars for astrology and observational astronomy: the 15 Behenian fixed stars (stelle di Agrippa), the four “royal” stars (Aldebaran, Regulus, Antares, Fomalhaut), the brightest stars in the sky, and the most used zodiacal stars.

Calculating a star’s position #

The main function is fixstar2_ut. Pass it the star’s name, the Julian Day, and the calculation flags:

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)

# Position of Regulus
nome, pos, flag, err = ephem.fixstar2_ut("Regulus", jd, ephem.SEFLG_SPEED)

if not err:
    lon = pos[0]  # ecliptic longitude
    lat = pos[1]  # ecliptic latitude
    vel = pos[3]  # speed in longitude (degrees/day)

    segni = ["Ari", "Tau", "Gem", "Cnc", "Leo", "Vir",
             "Lib", "Sco", "Sgr", "Cap", "Aqr", "Psc"]
    segno = segni[int(lon / 30)]
    gradi = lon % 30

    print(f"{nome}")
    print(f"Position: {gradi:.2f}° {segno}")
    print(f"Latitude: {lat:.4f}°")
    print(f"Speed: {vel:.6f}°/day")
else:
    print(f"Error: {err}")

Regulus,alLeo
Position: 0.17° Vir
Latitude: 0.4657°
Speed: -0.000071°/day

The function returns four values:

nome — the full name of the star in the "Name,Nomenclature" format (e.g. "Regulus,alLeo" where alLeo stands for “alpha Leonis”)
pos — a tuple of 6 values: (longitude, latitude, distance, lon_speed, lat_speed, dist_speed). The distance is fixed at 100,000 AU (stars are effectively at an infinite distance for our calculations)
flag — the returned flags (usually identical to those passed)
err — an error string, empty if everything went well

The main stars of astrology #

Here are the most used stars in astrological tradition, with their approximate position in 2024:

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)

stelle = [
    "Aldebaran",    # Bull's Eye — "Watcher of the East"
    "Regulus",      # Lion's Heart — "Watcher of the North"
    "Antares",      # Scorpion's Heart — "Watcher of the West"
    "Fomalhaut",    # Mouth of the Southern Fish — "Watcher of the South"
    "Sirius",       # The brightest star in the sky
    "Algol",        # The "Demon Star" — beta Persei
    "Spica",        # The ear of wheat of Virgo
    "Betelgeuse",   # Orion's shoulder
    "Rigel",        # Orion's foot
    "Vega",         # The star of Lyra
    "Polaris",      # The North Star
    "Canopus",      # The second brightest in the sky
]

segni = ["Ari", "Tau", "Gem", "Cnc", "Leo", "Vir",
         "Lib", "Sco", "Sgr", "Cap", "Aqr", "Psc"]

for star in stelle:
    nome, pos, flag, err = ephem.fixstar2_ut(star, jd, 0)
    if not err:
        lon = pos[0]
        segno = segni[int(lon / 30)]
        gradi = lon % 30
        nome_corto = nome.split(",")[0]
        print(f"{nome_corto:12s}  {gradi:5.1f}° {segno}")

Aldebaran      10.1° Gem
Regulus         0.2° Vir
Antares        10.1° Sgr
Fomalhaut       4.2° Psc
Sirius         14.4° Cnc
Algol          26.5° Tau
Spica          24.2° Lib
Betelgeuse     29.1° Gem
Rigel          17.2° Gem
Vega           15.7° Cap
Polaris        28.9° Gem
Canopus        15.3° Cnc

Magnitude: how bright is it? #

Magnitude indicates the apparent brightness of a star. The scale is counterintuitive: lower numbers mean brighter stars. Sirius has a magnitude of −1.46 (very bright), while stars barely visible to the naked eye have a magnitude of about 6.

import libephemeris as ephem

# Magnitude of some stars
for star in ["Sirius", "Vega", "Polaris", "Algol"]:
    nome, mag, err = ephem.fixstar2_mag(star)
    if not err:
        nome_corto = nome.split(",")[0]
        print(f"{nome_corto:12s}  magnitude {mag:+.2f}")

Sirius        magnitude -1.46
Vega          magnitude +0.03
Polaris       magnitude +1.98
Algol         magnitude +2.12

Equatorial coordinates #

If you need Right Ascension and Declination (to point a telescope, for example), add the SEFLG_EQUATORIAL flag:

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)

nome, pos, flag, err = ephem.fixstar2_ut(
    "Sirius", jd, ephem.SEFLG_EQUATORIAL
)

if not err:
    ra = pos[0]   # Right Ascension in degrees
    dec = pos[1]  # Declination in degrees

    # Convert RA to hours, minutes, seconds
    ra_ore = ra / 15.0
    ore = int(ra_ore)
    minuti = int((ra_ore - ore) * 60)
    secondi = ((ra_ore - ore) * 60 - minuti) * 60

    print(f"Sirius: RA = {ore}h {minuti}m {secondi:.1f}s, Dec = {dec:+.4f}°")

Sirius: RA = 6h 46m 12.6s, Dec = -16.7520°

8.3 Fixed stars in astrology #

In astrological tradition, fixed stars have a special role. They are not used like planets (with daily aspects and transits), but are considered significant when a planet or an angle of the birth chart is in conjunction — meaning at the same ecliptic longitude — with an important star.

The four royal stars #

The most powerful are the four “royal stars” or “watchers of the sky”, one for each quadrant of the zodiac:

Aldebaran (~10° Gemini in 2024) — the Bull’s Eye, watcher of the vernal equinox. Associated with courage, military honor, and success through integrity.
Regulus (~0° Virgo) — the Lion’s Heart, watcher of the summer solstice. The “most astrological” star: associated with power, fame, and leadership. It is almost exactly on the ecliptic (latitude 0.46°), which makes it particularly significant.
Antares (~10° Sagittarius) — the Scorpion’s Heart, watcher of the autumnal equinox. “The rival of Mars” (anti-Ares), associated with intensity, passion, and destruction-regeneration.
Fomalhaut (~4° Pisces) — the Mouth of the Southern Fish, watcher of the winter solstice. Associated with idealism, spirituality, and dreams.

Conjunction with a planet #

In stellar astrology, the orb (the maximum distance to consider an influence active) is much tighter than for planets: generally 1° for first-magnitude stars, 30’ for others. Here is how to check if a planet is conjunct a star today:

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)

# Stars to check (the four royal stars + some important ones)
stelle_da_cercare = [
    "Aldebaran", "Regulus", "Antares", "Fomalhaut",
    "Sirius", "Spica", "Algol", "Vega"
]

pianeti = [
    (ephem.SE_SUN,     "Sun"),
    (ephem.SE_MOON,    "Moon"),
    (ephem.SE_MERCURY, "Mercury"),
    (ephem.SE_VENUS,   "Venus"),
    (ephem.SE_MARS,    "Mars"),
    (ephem.SE_JUPITER, "Jupiter"),
    (ephem.SE_SATURN,  "Saturn"),
]

# Calculate planets' positions
pos_pianeti = {}
for body_id, nome_p in pianeti:
    pos, _ = ephem.calc_ut(jd, body_id, ephem.SEFLG_SPEED)
    pos_pianeti[nome_p] = pos[0]  # ecliptic longitude

# Check conjunctions
orbe = 1.0  # 1 degree of tolerance

for star in stelle_da_cercare:
    nome_s, pos_s, _, err = ephem.fixstar2_ut(star, jd, 0)
    if err:
        continue

    lon_s = pos_s[0]
    nome_corto = nome_s.split(",")[0]

    for nome_p, lon_p in pos_pianeti.items():
        # Angular distance (handling the 360°→0° "jump")
        diff = abs(lon_p - lon_s)
        if diff > 180:
            diff = 360 - diff

        if diff <= orbe:
            print(f"★ {nome_p} conjunct {nome_corto}! "
                  f"(distance: {diff:.2f}°)")

No conjunctions within 1° found on this date.

8.4 Searching for a star: names, designations, and fuzzy search #

The library is very flexible in how it accepts star names. You can use:

Traditional name — the simplest and most intuitive way:

ephem.fixstar2_ut("Sirius", jd, 0)
ephem.fixstar2_ut("Regulus", jd, 0)
ephem.fixstar2_ut("Betelgeuse", jd, 0)

Bayer designation — the Greek letter + the constellation, used in astronomical catalogs. Alpha Leonis = the brightest star in Leo:

ephem.fixstar2_ut("Alpha Leonis", jd, 0)     # = Regulus
ephem.fixstar2_ut("Beta Persei", jd, 0)       # = Algol
ephem.fixstar2_ut("Alpha Canis Majoris", jd, 0)  # = Sirius

Nomenclature code — the abbreviated version of the Bayer designation, in the format used internally (e.g. alLeo = alpha Leonis):

ephem.fixstar2_ut("alLeo", jd, 0)   # = Regulus
ephem.fixstar2_ut("bePer", jd, 0)   # = Algol

HIP number — the Hipparcos catalog number, for those working with astronomical data:

ephem.fixstar2_ut("HIP 49669", jd, 0)  # = Regulus
ephem.fixstar2_ut("32349", jd, 0)       # = Sirius (HIP 32349)

Partial search — if you only remember the beginning of the name:

ephem.fixstar2_ut("Reg", jd, 0)    # finds Regulus (if not ambiguous)
ephem.fixstar2_ut("Alde", jd, 0)   # finds Aldebaran

Phonetic search: forgives spelling mistakes #

Star names come from Arabic, Latin, and Greek, and transliterations vary. The library includes a phonetic search system that finds the right star even if you misspell it:

# All these find Betelgeuse:
ephem.fixstar2_ut("Betelgeuse", jd, 0)   # correct spelling
ephem.fixstar2_ut("Betelgeuze", jd, 0)   # with z (German variant)
ephem.fixstar2_ut("Betelgeux", jd, 0)    # truncated

# And these find Fomalhaut:
ephem.fixstar2_ut("Fomalhaut", jd, 0)    # correct spelling
ephem.fixstar2_ut("Formalhaut", jd, 0)   # with an extra r

The phonetic system normalizes the name by removing double consonants, unifying similar vowels, and comparing the “consonant skeleton” of the name. It works well for common spelling variants, but returns an error if the search is ambiguous (multiple stars match the same pattern).

The returned name format #

When the search is successful, the first returned value is the full name in the "Name,Nomenclature" format:

nome, pos, flag, err = ephem.fixstar2_ut("Sirius", jd, 0)
print(nome)  # "Sirius,alCMa" → alpha Canis Majoris

nome, pos, flag, err = ephem.fixstar2_ut("Algol", jd, 0)
print(nome)  # "Algol,bePer" → beta Persei

Sirius,alCMa
Algol,bePer

The part after the comma is the abbreviated Bayer designation: al = alpha, be = beta, ga = gamma, and so on. The constellation code follows the standard three-letter IAU abbreviation (Leo, Per, CMa, Vir, Ori…).

Summary #

In this chapter, we learned how to work with fixed stars.

Key concepts:

“Fixed” stars move: precession shifts all stars by ~50"/year in ecliptic longitude, and proper motion adds an individual displacement for each star
The library includes a catalog of ~100 stars based on Hipparcos satellite data, with sub-milliarcsecond precision
In astrology, fixed stars matter when a planet or angle is in conjunction (within ~1°) with an important star
The four royal stars (Aldebaran, Regulus, Antares, Fomalhaut) are considered the most powerful
Magnitude indicates brightness: lower numbers = brighter star (Sirius = −1.46, naked eye limit ≈ 6)
The search is flexible: traditional name, Bayer designation, HIP number, partial search, and even phonetic search for misspelled names

Functions introduced:

fixstar2_ut(nome, jd, flag) — calculates the ecliptic (or equatorial with SEFLG_EQUATORIAL) position of a star, accepting names in many formats
fixstar2_mag(nome) — returns the visual magnitude of a star
propagate_proper_motion(ra, dec, pm_ra, pm_dec, from_jd, to_jd) — manually propagates a star’s proper motion between two epochs