42 calculation contracts · released 2026-08-18
Celestial calculations, with every convention exposed
This library defines what each number means, how Maha calculates it, which inputs and versions reproduce it, how uncertainty affects boundaries, and where astronomical geometry ends. It is a calculation authority layer—not an automated interpretation matrix.
Continuous value first
Longitude, time, separation, and uncertainty remain primary. Sign, house, tithi, or aspect labels are derived classifications.
Versioned method
Every result needs its ephemeris, frame, timescale, coordinate origin, software version, and convention choices.
No validity laundering
An accurate calculation can support reproducibility without establishing that an astrological interpretation predicts reality.
Civil time and observer
12 references
Converting local civil time to UTC
Why a local date and clock reading require a named timezone, historical rule set, and ambiguity policy before chart calculation.
IANA timezone identifiers and chart reproducibility
Why America/Chicago carries more information than a fixed UTC offset for modern and historical chart calculations.
Daylight-saving folds: one clock time, two instants
How Maha handles repeated local times when clocks move backward and the same wall-clock label occurs twice.
Daylight-saving gaps: local times that never occurred
Why software must reject or explicitly repair a wall-clock time skipped by a forward clock transition.
Historical timezone uncertainty
How to represent dates for which political rules, local mean time, clock adoption, or the original record are uncertain.
Leap seconds and celestial timestamps
Why UTC is not a uniform count of SI seconds and which bulletin must be retained for reproducible conversion.
UTC, TAI, TT, TDB, and UT1
A concise map of the time scales that appear in civil records, ephemerides, Earth rotation, and reference-frame transformations.
Julian Date conventions
How calendar timestamps become continuous day counts without losing calendar, timescale, or noon-origin assumptions.
Delta T and Earth-rotation uncertainty
Why historical calculations distinguish uniform terrestrial time from irregular Earth rotation.
Observer latitude and longitude
The terrestrial coordinate contract behind ascendants, houses, rise and set times, and topocentric positions.
Elevation, horizon, and rise/set calculations
When observer elevation matters and why geometric, standard refracted, and local terrain horizons are different models.
Geocentric versus topocentric positions
Why the observing origin must be named before two longitude or altitude results can be compared.
Ephemeris and uncertainty
5 references
Ephemeris and software versioning
The minimum version record required to reproduce planetary positions after libraries and reference data change.
Geometric, astrometric, and apparent positions
Three position types that can carry different correction sets even when they share a coordinate frame.
Light time, aberration, and gravitational deflection
Why corrected sky positions require more than a target vector and why each correction must be declared independently.
Numerical precision, rounding, and uncertainty
How Maha prevents printed digits from being mistaken for measurement or model certainty.
Reproducibility digests and calculation provenance
How canonical inputs, provider responses, software versions, and outputs become a tamper-evident calculation record.
Coordinates and zodiac frames
11 references
Ecliptic versus equatorial coordinates
Why longitude/latitude and right ascension/declination cannot be compared without a frame transformation.
Reference frame, epoch, and equinox
The three labels required to understand what a celestial coordinate is measured against.
Precession and longitude of date
How long-term motion of Earth’s orientation changes equinox-based coordinates and the tropical–sidereal offset.
Nutation and true versus mean coordinates
Why “true of date” and “mean of date” use different treatments of short-period Earth-orientation motion.
Tropical zodiac longitude
The equinox-anchored 0–360° coordinate used before any sidereal ayanāṁśa is applied.
Sidereal zodiac longitude
Why “sidereal” is incomplete without a named zero-point convention and numerical ayanāṁśa.
Lahiri ayanāṁśa convention
Maha’s exact Lahiri conversion contract, independent validation envelope, and boundary behavior.
Longitude normalization and angular difference
The modular arithmetic needed to prevent errors around 0°/360° and choose the shortest signed separation.
Zodiac sign boundary sensitivity
When a sign label should be marked unstable because model or input uncertainty overlaps a 30° boundary.
Retrograde, station, and direct-motion labels
How daily finite differences and instantaneous speed can disagree near a planetary station.
Mean versus true lunar node
The declared node convention behind Rahu and Ketu and why node placements differ across software.
Angles and houses
7 references
Ascendant calculation
The eastern ecliptic–horizon intersection, its dependence on place and Earth rotation, and Maha’s polar branch correction.
Midheaven and meridian intersection
What the MC geometrically represents and why it is not always the highest ecliptic point or the tenth whole-sign cusp.
Whole-sign house assignment
Maha’s production house convention: the entire sidereal ascendant sign is house one and subsequent signs follow in order.
Equal-house convention
How equal houses differ from whole-sign houses even though both use twelve 30° sectors.
Placidus house convention
Why a quadrant house system requires more inputs and has different high-latitude behavior from sign-based houses.
Polar latitude limitations in house calculation
What remains calculable when the Sun does not rise or set and some quadrant cusp systems have no conventional solution.
House-boundary sensitivity
How uncertain event times and coordinates propagate into house assignment and when house statements should be withheld.
Lunar calendar and aspects
7 references
Tithi calculation
How the Sun–Moon elongation becomes one of thirty lunar-day divisions without depending on ayanāṁśa.
Nakṣatra and pāda calculation
How Lahiri sidereal lunar longitude is divided into 27 equal nakṣatras and four quarters each.
Pañcāṅga yoga calculation
How the normalized sum of sidereal Sun and Moon longitudes becomes one of 27 equal yoga divisions.
Karaṇa calculation
How half-tithi elongation intervals map onto the repeating and fixed karaṇa sequence without premature rounding.
Sunrise-based day boundary
Why a Pañcāṅga weekday and daylight fraction may differ from the UTC or midnight-to-midnight civil calendar.
Aspect geometry and orb conventions
How exact angular separations become named aspects only after a declared angle list and maximum-orb policy are applied.
Applying and separating aspects
The extra motion calculation needed to determine whether two bodies are moving toward or away from exact angular contact.