Sky map आकाश मानचित्र

The astronomy and mathematics behind this map

How the positions on this page are computed

Every graha position here comes from the ephemeris this site runs on — a numerical model built on JPL’s DE431 planetary data — the same class of data NASA uses for spacecraft navigation — accurate to sub-arcsecond precision across many millennia. The classical texts below are the theory Vedic astrology inherited and still names its houses and daśās after; the raw longitudes themselves are computed, not looked up from a hand table.

The vernal equinox and the two zodiacs

The vernal equinox is the moment the Sun’s apparent path (the ecliptic) crosses the celestial equator heading north — astronomical spring, and the zero point of the tropical zodiac that Western astrology and the modern Gregorian calendar both use.

Because Earth’s axis slowly wobbles — precession, a roughly 25,772-year cycle first quantified by Hipparchus (c. 130 BCE) and later explained by Newtonian gravity — that equinox point drifts westward against the fixed stars by about 50.3 arcseconds a year. Vedic (sidereal, nirayana) astrology instead fixes its zero point to the star field itself, close to the star Citrā (Spica), so a growing gap opens between tropical 0° Aries and sidereal 0° Meṣa. That gap is the ayanamśa.

Ayanāṃśa: which one, and why it matters

Ayanāṃśa (ayana = course, aṃśa = portion) is the angular offset between the tropical and sidereal zero points — about 24° today, growing by roughly 50 arcseconds a year. Several schools anchor it to different reference points, so sidereal longitudes shift slightly depending which is used:

• Lahiri (Chitrapaksha) — Anchored opposite the star Citrā (Spica); adopted by the Government of India’s Calendar Reform Committee (1955) and used in the official Indian Ephemeris and Nautical Almanac. This site uses Lahiri.
• Raman — B. V. Raman’s revision, roughly 0.4° west of Lahiri.
• Krishnamurti (KP) — A small refinement of Lahiri used in the Krishnamurti Paddhati system.
• Fagan–Bradley — The Western sidereal-astrology standard, anchored to a different stellar reference.

Classical Indian planetary theory

Long before telescopes, Indian astronomer-mathematicians built complete numerical models for planetary motion, framed as revolutions within a mahāyuga:

• Sūrya Siddhānta — Surviving text roughly 4th–10th century CE (Ebenezer Burgess’s 1860 English translation is the standard reference). Gives mean and true planetary motion via epicyclic manda and śīghra corrections, the obliquity of the ecliptic (≈24°), and a solar year within about 3 minutes of the modern value.
• Āryabhaṭīya — Āryabhaṭa, 499 CE. Proposed Earth’s axial rotation as the cause of the sky’s apparent motion, computed π to four decimal places, and explained eclipses via Earth’s and the Moon’s shadows — while Rāhu and Ketu, the Moon’s orbital nodes, remain in everyday use in Vedic astrology today.
• Brāhmasphuṭasiddhānta — Brahmagupta, 628 CE. Refined planetary parameters and corrected several of Āryabhaṭa’s constants; also formalised the rules for zero and negative numbers used throughout this arithmetic, and was translated into Arabic in the 8th century, carrying Indian astronomy into the wider medieval world.
• Siddhānta Śromaṇi — Bhāskārācārya II, 1150 CE. The most refined of the classical texts — its sidereal year is accurate to within about a minute of the modern value, and it gestures toward instantaneous rates of motion (tātkālikagati).

References

• Burgess, E. (trans.), 1860 — Sūrya-Siddhānta: A Text-Book of Hindu Astronomy, Journal of the American Oriental Society.
• Colebrooke, H. T. (trans.), 1817 — Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bhāscara (includes the Brāhmasphuṭasiddhānta chapters on arithmetic and algebra).
• Government of India, Calendar Reform Committee, 1955 — Report of the Calendar Reform Committee (the Lahiri ayanāṃśa’s official adoption).
• Meeus, J., 1998 — Astronomical Algorithms (2nd ed.), Willmann-Bell — the standard modern reference for the formulae behind equinox, precession and planetary-position computation.
• Folkner, W. M. et al., 2014 — The Planetary and Lunar Ephemerides DE430 and DE431, IPN Progress Report 42-196, Jet Propulsion Laboratory (NASA) — the solar-system model this site’s ephemeris engine is built on.

This is offered as background on the mathematics and history behind the map, not as an argument for one ayanāṃśa or cosmology over another.