Chapter 11 — The Sidereal Zodiac and Ayanamshas #
What you will learn #
In this chapter, you will discover why two different zodiacs exist (tropical and sidereal), what caused them to diverge over millennia, what the ayanamsha is, why there are over 40 different ways to calculate it, and how to use the library to work with the sidereal zodiac used in Indian Vedic astrology.
11.1 Two zodiacs: tropical and sidereal #
The same sky, two different measures #
In Chapter 1, we saw that the zodiac is a division of the ecliptic into 12 sectors of 30° each. But where does the counting start? Here lies the problem — and one of the deepest divisions in the history of astrology.
The tropical zodiac (used in the West) starts the count from the vernal equinox (spring equinox): the point where the Sun crosses the celestial equator moving north, around March 20. This point is defined as 0° Aries, regardless of which stars are in that direction.
The sidereal zodiac (used in India and Vedic astrology) starts the count from a point linked to the fixed stars. The zero point is anchored to a reference star (usually Spica, fixed at 0° Libra = 180°).
About 2000 years ago, the two zodiacs coincided almost perfectly. But since then, they have shifted relative to each other, and today the difference is about 24 degrees.
Why they diverge: the precession of the equinoxes #
The cause is precession: the Earth’s axis slowly wobbles like a spinning top, completing a cycle in about 26,000 years. This causes the vernal equinox point to shift by about 50 arcseconds per year relative to the stars.
In practice:
- The tropical zodiac “follows” the equinox, and therefore shifts relative to the stars
- The sidereal zodiac “follows” the stars, and therefore shifts relative to the equinox
The practical effect is significant: if in your tropical (Western) natal chart the Sun is at 15° Aries, in the sidereal (Vedic) chart it will be at about 21° Pisces — almost an entire sign of difference.
import libephemeris as ephem
# Comparison: Sun's position in tropical and sidereal
jd = ephem.julday(2024, 4, 8, 12.0)
# Tropical position (default)
pos_trop, _ = ephem.calc_ut(jd, ephem.SE_SUN, ephem.SEFLG_SPEED)
# Lahiri Ayanamsha
ephem.set_sid_mode(ephem.SE_SIDM_LAHIRI)
ayan = ephem.get_ayanamsa_ut(jd)
# Sidereal position = tropical - ayanamsha
lon_sid = (pos_trop[0] - ayan) % 360
signs = ["Ari", "Tau", "Gem", "Cnc", "Leo", "Vir",
"Lib", "Sco", "Sgr", "Cap", "Aqr", "Psc"]
s_trop = signs[int(pos_trop[0] / 30)]
g_trop = pos_trop[0] % 30
s_sid = signs[int(lon_sid / 30)]
g_sid = lon_sid % 30
print(f"Tropical Sun: {g_trop:.1f}° {s_trop}")
print(f"Sidereal Sun: {g_sid:.1f}° {s_sid}")
print(f"Ayanamsha (Lahiri): {ayan:.4f}°")
Tropical Sun: 19.1° Ari
Sidereal Sun: 24.9° Psc
Ayanamsha (Lahiri): 24.1961°
11.2 What is the ayanamsha #
The ayanamsha (from Sanskrit ayana = solstice, amsha = portion) is simply the difference in degrees between the tropical zero point and the sidereal zero point at a given moment:
sidereal longitude = tropical longitude − ayanamsha
Today the ayanamsha is about 24°, and grows by about 50.3" per year (the precession rate). In a few millennia, the two zodiacs will coincide again — and then diverge again in the other direction.
Calculating the ayanamsha #
import libephemeris as ephem
ephem.set_sid_mode(ephem.SE_SIDM_LAHIRI)
# Ayanamsha in different epochs
for year in [0, 500, 1000, 1500, 2000, 2024, 2100]:
jd = ephem.julday(year, 1, 1, 0.0)
ayan = ephem.get_ayanamsa_ut(jd)
print(f"Year {year:5d}: ayanamsha = {ayan:+7.2f}°")
Year 0: ayanamsha = +356.04°
Year 500: ayanamsha = +2.97°
Year 1000: ayanamsha = +9.92°
Year 1500: ayanamsha = +16.88°
Year 2000: ayanamsha = +23.86°
Year 2024: ayanamsha = +24.19°
Year 2100: ayanamsha = +25.25°
You will notice that the ayanamsha is negative in antiquity (the sidereal zodiac was “ahead” relative to the tropical one) and positive today (the tropical is “ahead”).
Using the SEFLG_SIDEREAL flag #
Instead of calculating the ayanamsha and subtracting it manually, you can ask the library directly to return positions in sidereal coordinates:
import libephemeris as ephem
jd = ephem.julday(2024, 4, 8, 12.0)
# Set the sidereal system
ephem.set_sid_mode(ephem.SE_SIDM_LAHIRI)
# Calculate directly in sidereal
pos_sid, _ = ephem.calc_ut(
jd, ephem.SE_SUN,
ephem.SEFLG_SIDEREAL | ephem.SEFLG_SPEED
)
signs = ["Ari", "Tau", "Gem", "Cnc", "Leo", "Vir",
"Lib", "Sco", "Sgr", "Cap", "Aqr", "Psc"]
sign = signs[int(pos_sid[0] / 30)]
degrees = pos_sid[0] % 30
print(f"Sidereal Sun (Lahiri): {degrees:.2f}° {sign}")
Sidereal Sun (Lahiri): 24.95° Psc
The flag SEFLG_SIDEREAL (65536) can be combined with any other flag: SEFLG_SPEED, SEFLG_EQUATORIAL, etc.
11.3 The schools of ayanamsha #
The problem: nobody agrees #
If the ayanamsha were a simple matter of fact, there would be no discussion. But the problem is: where exactly was the zero point 2000 years ago? There was no celestial GPS. Different astronomers and astrologers have proposed slightly different answers, based on different stars, different ancient texts, or different calculations. The difference between the most popular schools is a few degrees — enough to shift a planet into a different sign.
The library supports 47 ayanamsha systems. Here are the most important ones:
Indian Ayanamshas (the most used) #
Lahiri (SE_SIDM_LAHIRI, value 1) is the most widespread: it is the official standard of the Indian government, adopted in 1955 by the Indian Calendar Reform Committee (N.C. Lahiri). It fixes Spica (Citra in Sanskrit) at 180° of sidereal longitude. It is used by the vast majority of Vedic astrologers.
Krishnamurti (SE_SIDM_KRISHNAMURTI, value 5) is used in the KP (Krishnamurti Paddhati) system, a very popular predictive method in South India. It is very similar to Lahiri, with a difference of only a few arcminutes.
Raman (SE_SIDM_RAMAN, value 3) was proposed by B.V. Raman, one of the most influential Indian astrologers of the 20th century. It differs from Lahiri by about 1.5°.
Lahiri variants: there are also SE_SIDM_LAHIRI_1940 (43), SE_SIDM_LAHIRI_VP285 (44), and SE_SIDM_LAHIRI_ICRC (46), which differ by a few arcseconds and reflect different interpretations of the original data.
Western Sidereal Ayanamsha #
Fagan-Bradley (SE_SIDM_FAGAN_BRADLEY, value 0) was developed by Cyril Fagan and Donald Bradley in the 1950s for Western sidereal astrology. It differs from Lahiri by about 1°. It is rarely used outside a narrow circle of Western sidereal astrologers.
Ayanamshas based on true stars #
True Citra (SE_SIDM_TRUE_CITRA, value 27) fixes the true position (with proper motion) of Spica at exactly 180°. Unlike Lahiri, which uses a polynomial formula calculated once and for all, True Citra recalculates the real position of Spica at each date, tracking its proper motion.
True Revati (SE_SIDM_TRUE_REVATI, value 28) fixes the star Revati (zeta Piscium) at 359°50’.
True Pushya (SE_SIDM_TRUE_PUSHYA, value 29) fixes the star Pushya (delta Cancri) at 106°.
Galactic Ayanamshas #
For those looking for a “cosmic” zero point, there are several systems based on the position of the galactic center or the galactic equator:
Galactic Center 0 Sag (SE_SIDM_GALCENT_0SAG, value 17) places the galactic center at 0° Sagittarius.
Babylonian Ayanamshas #
For historical research on Babylonian astronomy: SE_SIDM_BABYL_KUGLER1 (9), SE_SIDM_BABYL_KUGLER2 (10), SE_SIDM_BABYL_KUGLER3 (11), SE_SIDM_BABYL_HUBER (12), SE_SIDM_BABYL_ETPSC (13), SE_SIDM_BABYL_BRITTON (38).
Comparison between ayanamshas #
import libephemeris as ephem
jd = ephem.julday(2024, 4, 8, 12.0)
systems = [
(ephem.SE_SIDM_LAHIRI, "Lahiri"),
(ephem.SE_SIDM_FAGAN_BRADLEY, "Fagan-Bradley"),
(ephem.SE_SIDM_RAMAN, "Raman"),
(ephem.SE_SIDM_KRISHNAMURTI, "Krishnamurti"),
(ephem.SE_SIDM_TRUE_CITRA, "True Citra"),
(ephem.SE_SIDM_TRUE_REVATI, "True Revati"),
(ephem.SE_SIDM_GALCENT_0SAG, "Galactic 0 Sag"),
]
print(f"Ayanamsha on {8}/04/2024:\n")
for mode, name in systems:
ephem.set_sid_mode(mode)
ayan = ephem.get_ayanamsa_ut(jd)
print(f" {name:20s} {ayan:.4f}°")
# The name of a system
name = ephem.get_ayanamsa_name(ephem.SE_SIDM_LAHIRI)
print(f"\nName: {name}")
Ayanamsha on 8/04/2024:
Lahiri 24.1961°
Fagan-Bradley 25.0793°
Raman 22.7498°
Krishnamurti 24.0993°
True Citra 24.1843°
True Revati 20.3779°
Galactic 0 Sag 27.1850°
Name: Lahiri
11.4 Custom Ayanamsha #
If none of the 47 predefined systems meets your needs, you can define your own custom ayanamsha with SE_SIDM_USER:
import libephemeris as ephem
# Define a custom ayanamsha:
# "On January 1st, 2000 (J2000.0), the ayanamsha is 23.5°"
J2000 = 2451545.0
ephem.set_sid_mode(
ephem.SE_SIDM_USER,
t0=J2000, # reference epoch
ayan_t0=23.5 # ayanamsha value at that epoch
)
# Now calculate the ayanamsha for any date
jd = ephem.julday(2024, 4, 8, 12.0)
ayan = ephem.get_ayanamsa_ut(jd)
print(f"Custom ayanamsha in 2024: {ayan:.4f}°")
# And use SEFLG_SIDEREAL for positions
pos, _ = ephem.calc_ut(jd, ephem.SE_SUN,
ephem.SEFLG_SIDEREAL | ephem.SEFLG_SPEED)
print(f"Custom sidereal Sun: {pos[0]:.4f}°")
Custom ayanamsha in 2024: 23.8390°
Custom sidereal Sun: 355.3029°
The library uses the IAU 2006 precession polynomials to calculate how the ayanamsha changes over time starting from the value you specified.
11.5 Practical calculations in sidereal #
Vedic birth chart #
Here is how to calculate a complete birth chart in Lahiri sidereal — the format used in Vedic astrology (Jyotish):
import libephemeris as ephem
# Date: August 15, 1947, 00:00 IST — Independence of India
# IST = UT + 5:30, so UT = 18:30 on August 14
jd = ephem.julday(1947, 8, 14, 18.5)
lat, lon = 28.6139, 77.2090 # New Delhi
# Set Lahiri sidereal
ephem.set_sid_mode(ephem.SE_SIDM_LAHIRI)
signs = ["Mesha", "Vrishabha", "Mithuna", "Karka",
"Simha", "Kanya", "Tula", "Vrischika",
"Dhanus", "Makara", "Kumbha", "Meena"]
# Planets in sidereal
planets = [
(ephem.SE_SUN, "Surya "),
(ephem.SE_MOON, "Chandra"),
(ephem.SE_MARS, "Mangal "),
(ephem.SE_MERCURY, "Budha "),
(ephem.SE_JUPITER, "Guru "),
(ephem.SE_VENUS, "Shukra "),
(ephem.SE_SATURN, "Shani "),
(ephem.SE_MEAN_NODE,"Rahu "),
]
print("Sidereal birth chart (Lahiri):\n")
for body_id, name in planets:
pos, _ = ephem.calc_ut(jd, body_id,
ephem.SEFLG_SIDEREAL | ephem.SEFLG_SPEED)
sign = signs[int(pos[0] / 30)]
degrees = pos[0] % 30
print(f" {name} {degrees:5.1f}° {sign}")
# Ketu = opposite to Rahu
rahu_pos, _ = ephem.calc_ut(jd, ephem.SE_MEAN_NODE,
ephem.SEFLG_SIDEREAL | ephem.SEFLG_SPEED)
ketu_lon = (rahu_pos[0] + 180) % 360
sign_k = signs[int(ketu_lon / 30)]
degrees_k = ketu_lon % 30
print(f" Ketu {degrees_k:5.1f}° {sign_k}")
Sidereal birth chart (Lahiri):
Surya 28.0° Karka
Chandra 4.0° Karka
Mangal 7.5° Mithuna
Budha 13.7° Karka
Guru 25.9° Tula
Shukra 22.6° Karka
Shani 20.5° Karka
Rahu 5.1° Vrishabha
Ketu 5.1° Vrischika
The Nakshatras #
In Vedic astrology, the zodiac is also divided into 27 Nakshatras (lunar mansions) of 13°20’ each. Each Nakshatra has a name, a meaning, and a ruling planet. The Moon takes about one day to traverse each of them.
import libephemeris as ephem
nakshatra_names = [
"Ashwini", "Bharani", "Krittika", "Rohini", "Mrigashira",
"Ardra", "Punarvasu", "Pushya", "Ashlesha", "Magha",
"Purva Phalguni", "Uttara Phalguni", "Hasta", "Chitra",
"Swati", "Vishakha", "Anuradha", "Jyeshtha", "Mula",
"Purva Ashadha", "Uttara Ashadha", "Shravana", "Dhanishtha",
"Shatabhisha", "Purva Bhadrapada", "Uttara Bhadrapada", "Revati"
]
# Rulers in the Vimshottari Dasha sequence
rulers = [
"Ketu", "Venus", "Sun", "Moon", "Mars",
"Rahu", "Jupiter", "Saturn", "Mercury",
"Ketu", "Venus", "Sun", "Moon", "Mars",
"Rahu", "Jupiter", "Saturn", "Mercury",
"Ketu", "Venus", "Sun", "Moon", "Mars",
"Rahu", "Jupiter", "Saturn", "Mercury"
]
jd = ephem.julday(2024, 4, 8, 12.0)
ephem.set_sid_mode(ephem.SE_SIDM_LAHIRI)
# Moon's Nakshatra
moon, _ = ephem.calc_ut(jd, ephem.SE_MOON,
ephem.SEFLG_SIDEREAL | ephem.SEFLG_SPEED)
nak_num = int(moon[0] / (360 / 27)) # 13°20' per Nakshatra
nak_pos = moon[0] % (360 / 27) # position in the Nakshatra
# Pada (quarter) — each Nakshatra has 4 padas of 3°20'
pada = int(nak_pos / (360 / 108)) + 1 # 1-4
print(f"Sidereal Moon: {moon[0]:.2f}°")
print(f"Nakshatra: {nakshatra_names[nak_num]} (n. {nak_num + 1})")
print(f"Pada: {pada}")
print(f"Ruler: {rulers[nak_num]}")
Sidereal Moon: 351.24°
Nakshatra: Revati (n. 27)
Pada: 2
Ruler: Mercury
The Moon’s Nakshatra at birth is fundamental in Vedic astrology: it determines the Dasha (the system of planetary periods that governs the person’s life).
11.6 The extended version: get_ayanamsa_ex_ut #
For advanced calculations where you need to specify additional flags or want the return flag, use get_ayanamsa_ex_ut:
import libephemeris as ephem
ephem.set_sid_mode(ephem.SE_SIDM_LAHIRI)
jd = ephem.julday(2024, 4, 8, 12.0)
# Simple version
ayan_simple = ephem.get_ayanamsa_ut(jd)
# Extended version (also returns the flag)
retflag, ayan_ex = ephem.get_ayanamsa_ex_ut(jd, ephem.SEFLG_SWIEPH)
print(f"Ayanamsha (simple): {ayan_simple:.6f}°")
print(f"Ayanamsha (extended): {ayan_ex:.6f}°")
Ayanamsha (simple): 24.196111°
Ayanamsha (extended): 24.196111°
Summary #
In this chapter, we explored the sidereal zodiac, which is fundamental to Vedic astrology.
Key concepts:
- There are two zodiacs: the tropical (zero point = equinox) and the sidereal (zero point linked to the stars). Today they differ by about 24°.
- The divergence is caused by the precession of the equinoxes: the Earth’s axis wobbles with a period of ~26,000 years, shifting the vernal point relative to the stars.
- The ayanamsha is the difference in degrees between the two zodiacs: sidereal longitude = tropical longitude − ayanamsha.
- There are over 47 ayanamsha systems because there is no agreement on where the zero point was 2000 years ago.
- Lahiri is the most widely used (Indian government standard), Fagan-Bradley is used for Western sidereal astrology, and True Citra uses the real position of Spica.
- In Vedic astrology, the 27 Nakshatras divide the sidereal zodiac into sectors of 13°20’, each with a meaning and a ruling planet.
Functions introduced:
set_sid_mode(sid_mode, t0=0.0, ayan_t0=0.0)— sets the ayanamsha system. UseSE_SIDM_USERwitht0andayan_t0for a custom ayanamsha.get_ayanamsa_ut(jd)— returns the ayanamsha in degrees for a date in UT.get_ayanamsa_ex_ut(jd, flags)— extended version that also returns the return flag.get_ayanamsa_name(sid_mode)— returns the readable name of an ayanamsha system (e.g."Lahiri").SEFLG_SIDEREAL(65536) — flag to add tocalc_utto get positions directly in sidereal coordinates.