One Moon.
Two measurements.

Astronomy Engine 2.1.19 supplies geocentric Sun and Moon positions. We rotate both into the ecliptic of date using its IAU 2006 precession and IAU 2000B nutation. The Sun includes the library’s light-time and aberration corrections; the Moon uses its lunar model with a one-step light-time correction.

Conventional Lahiri: the mean J2000 anchor is 23° 51′ 25.5324″. Full coordinate rotations transport that reference; nutation is added consistently before subtracting the ayanāṃśa from both tropical longitudes. This is distinct from a fixed 24° offset or True Citra.

One UTC instant drives the entire scene. UTC is converted to TT using published leap offsets and 32.184 seconds. Dates after 2026 assume no further leap seconds until the table is updated. Supported UTC dates: 1972–2100. At the range edges, the local clock may show an adjacent date. Leap-second entry itself is not supported.

In 4,510 matched-time reference samples across 1972–2100, observed maximum differences were 2.27″ for the Sun, 3.62″ for the Moon, and 0.00017″ for mean ayanāṃśa. Ten JPL position samples were within 2.29″. For 3,372 transition endpoints across the supported range, the largest time difference was 7.75 seconds. A separate check of 14 endings in the official 2026–27 Rashtriya Panchang matched its printed minute after rounding. These are sample comparisons, not guaranteed accuracy at every instant. Times are estimates; millisecond root finding does not imply millisecond astronomical accuracy.

The diagram remains a two-dimensional illustration, not a local sky map. Place is a label; city presets supply approximate coordinates, while device or manually entered coordinates specify the sunrise observer. Geocentric transitions do not depend on the observer’s coordinates. Sunrise-based vāra separately uses explicit coordinates and the retained IMD sunrise convention. IANA timezone rules determine the local dates and offsets shown, including daylight saving. Device coordinates are requested only when you choose “Use device location” and grant browser permission. Saved location settings stay in this browser. This mode does not calculate sunrise-based festival dates, eclipses, moonrise or an authoritative Panchang.

All angles are geocentric ecliptic longitudes: directions measured from Earth’s center around the ecliptic. We increase longitude counterclockwise in the spatial view.

Tithi: subtract the Sun’s longitude from the Moon’s and wrap into 0°–360°. Each of 30 intervals spans 12°. The first 15 form Śukla pakṣa; the next 15 form Kṛṣṇa pakṣa.

Nakshatra: divide the Moon’s sidereal longitude into 27 equal intervals of 13° 20′, beginning with Aśvinī. These equal longitude sectors are distinct from irregular constellation outlines. Each sector has four equal padas of 3° 20′: 108 around the full circle. Only the active sector’s four parts are emphasized in the ring.

Intervals include their starting boundary and exclude their ending boundary. Exact 0° begins tithi 1; exact 180° begins tithi 16. The stellar dots are illustrative, not catalogued star positions.

Tithi = ⌊wrap(Moon − Sun) / 12°⌋ + 1
Nakshatra = ⌊wrap(Moon) / (13° 20′)⌋ + 1

Teaching reference: 0° is fixed to the start of Aśvinī in an idealized stellar frame. The background points are illustrative, not a catalog of observed stars. No tropical-to-sidereal conversion, epoch calibration, or ayanāṃśa is applied; this is not a Lahiri or other calendar calculation.

Intervals include their starting boundary and exclude their ending boundary. At 12°, tithi 2 begins. At 13° 20′, Bharaṇī begins. At 360°, the ruler wraps to 0°.

Exact full Moon at 180° ends Pūrṇimā (tithi 15) and begins Kṛṣṇa Pratipadā (tithi 16). Exact new Moon at 0° ends Amāvāsyā (tithi 30) and begins Śukla Pratipadā (tithi 1). A phase instant and a tithi interval are different things.

Equal longitude sectors are a mathematical convention. Traditional star groupings and modern constellation boundaries have irregular shapes.

The model is flat, circular, and uniform: Moon 360° per 27.321661 simulated days; Sun 360° per 365.256363 days. These illustrative mean rates produce a phase cycle of about 29.53 days. Day 0 is an invented conjunction at 18°; it has no calendar date.

We omit orbital inclination, eccentricity, parallax, precession, nutation, eclipses, and atmospheric effects. The displayed illuminated fraction is (1 − cos elongation) / 2 under the coplanar, distant-Sun approximation.

The phase disk uses a north-up schematic with waxing light on the right and waning light on the left. Actual sky orientation depends on location and time. No observer location or timezone is assumed, because this mode does not calculate a local sky. The Moon’s phases are caused by viewing its sunlit half from different directions, not by Earth’s shadow.

Sky uses the bundled ephemeris and declared Lahiri reference. Learn keeps geometric experiments where an idealization makes the cause easier to see: a fixed Sun while the Moon moves, uniform cycles, and adjustable orbital tilt. These experiments do not represent a chosen real date. Observer-dependent events and festival rules remain outside this app’s scope.

The amber outer arc marks the Sun’s current 30° sidereal rāśi, using the same conventional Lahiri reference as the Moon. Entering the next sector is a saṅkrānti. The green inner ring follows the Moon’s nakshatra and pada instead. Earth remains fixed in this geocentric diagram.

The twelve equal rāśis are longitude divisions, not unequal constellation outlines. We show rāśi names, without assigning regional solar-month names or festival dates. The IMD Rashtriya Panchang 2026–27 explains the 30° divisions and lists the names on printed pages viii and xiv. The optional blue outer ring marks the Moon’s 30° rāśi; it follows the Moon, even when the Sun is nearby. The green ring marks the Moon’s nakshatra, with its current pada brighter. Geometric experiments remain in Learn.

• IMD · Rashtriya Panchang 2026–27 ↗Official minute-level endpoint sample; this is not full calendar validation.
• Astronomy Engine · code, model and MIT license ↗Version 2.1.19 is bundled locally with its license.
• Swiss Ephemeris · conventional Lahiri definitions ↗Independent validation reference only; Swiss software is not bundled.
• JPL Horizons · frames and apparent positions ↗Independent apparent inertial directions, transformed into the same ecliptic frame for comparison.
• IERS Bulletin C 72 · leap-second announcement ↗No leap second at the end of December 2026; future offsets require maintenance.
• U.S. Naval Observatory · Phases of the Moon ↗Longitude differences of 0°, 90°, 180°, and 270° define the principal phase instants.
• NASA · Moon phases ↗Sunlit geometry, waxing and waning, and why the orbital and phase cycles differ.
• IMD · Positional Astronomy Centre ↗Publisher of the Rashtriya Panchang and Indian Astronomical Ephemeris. Consult these for real calendar work; this prototype uses the explicitly declared teaching conventions above.

Jyotir Vidya · Indic Sky Lab is an educational learning app of The Bharatheeya Institute, developed by Aieun Labs. The independently checked v0.2 browser engine and sky interactions are retained from Indic Sky Lab.

Read the method, validation record, source provenance and complete third-party license notices →