How Graha Asta and Udaya Are Calculated

Asta begins with a solar proximity rule

A planet close to the Sun in the sky is difficult or impossible to see in twilight. Indian astronomical and astrological writing describes its disappearance as asta, lope, or moudhya, and its reappearance as udaya. The underlying observation is concrete: a small angular distance from the Sun puts a planet in a bright part of the sky. The traditional rule and the modern visibility problem are related, but they are not identical calculations.

The Sūrya Siddhānta in Ebenezer Burgess’s 1860 translation devotes chapter IX to heliacal risings and settings. Verses 6–9 give threshold values for the five star-planets and say that smaller distances leave them hidden by the Sun’s brilliance. A readable Sanskrit and English presentation of verses 9.6–10 shows 11° for Jupiter, 15° for Saturn, and 17° for Mars. It distinguishes 8° and 10° cases for Venus and 12° and 14° cases for Mercury. These values are the historical center of this calculator.

The five limits used here

For Mercury and Venus, the translated verses describe different setting and rising cases around the Sun. Modern almanac pages often summarize those pairs as a larger limit in forward motion and a smaller one in retrograde motion. This calculator follows that explicit modernized mapping and prints the motion and limit at each boundary. It does not hide the choice inside a generic “combustion” result.

Worked boundary examples

Suppose Jupiter’s apparent longitude is 84.3° and the Sun’s is 73.7°. Their smaller longitude gap is 10.6°. Because Jupiter’s limit is 11°, the model classifies that instant as Asta. If the gap later reaches 11.2°, it is outside the modeled interval. The same subtraction must be wrapped around 0°: a planet at 3° and the Sun at 354° are 9° apart, not 351° apart.

Mercury shows why its motion label matters. A 13° gap lies inside the 14° direct limit but outside the 12° retrograde limit. Near the close solar conjunctions that generate Asta, Mercury’s direct or retrograde state normally remains stable across a boundary. The result nevertheless prints that state and threshold so a rare edge case remains visible.

How the browser finds each boundary

Astronomy Engine 2.1.19 supplies apparent geocentric vectors for the Sun and each selected planet. The browser converts those vectors to true ecliptic longitude of date. It subtracts the two longitudes, wraps the difference into the interval from −180° through +180°, and takes the absolute value. West or east of the Sun is retained from the sign of the wrapped difference.

Apparent motion is estimated from the planet’s longitude three hours before and three hours after a trial instant. A negative centered difference is labeled retrograde; a positive difference is direct. The appropriate limit is then selected. The year search advances in twelve-hour steps. Whenever the Asta state changes, binary refinement narrows the transition to a window no wider than fifteen seconds. The published table rounds the civil and UTC clocks to the minute.

An interval can cross New Year. The search therefore extends 220 days on both sides of the selected local year before pairing an Asta start with the next Udaya end. This margin covers the much longer Mars intervals in the supported 2026–2027 range. “Days in year” clips the duration to the selected local-year boundaries; “full interval” measures between the actual Asta and Udaya instants.

Why ayanāṃśa does not set the Asta instant

Subtracting one ayanāṃśa from both the planet and the Sun leaves their difference unchanged. The Asta boundary therefore does not depend on whether the common zodiac frame is tropical or sidereal. This page still shows an approximate Lahiri sidereal longitude and rāśi at each boundary because they provide useful Vedic position labels. Another ayanāṃśa can shift that printed rāśi degree or a position very near a sign edge without moving the planet–Sun separation event itself.

Longitude separation and local visibility

A true heliacal visibility calculation asks whether the planet is bright enough and high enough in twilight for a particular observer. It uses the local horizon, the Sun’s altitude, the planet’s altitude and brightness, atmospheric extinction, and sometimes an empirical visibility criterion. Ecliptic longitude separation alone does not contain those quantities. Even an equal longitude gap can produce different observing conditions in two seasons or at two latitudes.

The classical chapter contains a broader procedure for rising and setting, while this browser feature deliberately isolates its published angular limits and applies them to modern apparent geocentric longitudes. That makes the result inspectable and useful as a traditional coordinate calendar. It should not be read as a claim that a planet is physically invisible everywhere between the two printed instants.

Why another almanac can give different dates

Drik Panchang’s current Planets Combustion directory places Asta/Udaya beside its planetary transit and retrograde families and links separate annual pages for Moon, Mars, Mercury, Jupiter, Venus, and Saturn. Its planet pages say that their event times use modern algorithms and the observer’s location. They also mention the same traditional degree values when describing approximate calculations. A location-aware visibility method, a longitude-only threshold, a different ephemeris, rounding, or a civil-day convention can all produce different boundaries.

This calculator covers Mercury through Saturn. The Moon is omitted because its rapid crescent visibility, lunar phase, and traditional east/west rules deserve a separate model; the Purnima and Amavasya calendar already supplies exact conjunction instants and tithi context. Uranus and Neptune are omitted because the five limits in verses 9.6–9 address the traditional naked-eye star-planets.

Reading one row

“Asta begins” is the transition from a separation above the applicable limit to one at or below it. “Udaya ends” is the reverse transition. The local line uses the fixed UTC offset entered in the form; the UTC line identifies the same instant without a civil-zone assumption. The side label says whether the planet’s longitude is east or west of the Sun. The motion and degree limit expose the rule that was active. The final rāśi degree is an approximate Lahiri label for the planet, separate from the planet–Sun gap.

A fixed offset cannot follow daylight-saving or historical civil-time changes. For a place that changes offset during the year, calculate each season with the applicable offset or use the UTC column. The astronomical event remains one instant; only the local representation changes.

Sources and further reading

• Burgess, Translation of the Sûrya-Siddhânta (1860), chapter IX, preserves the historical heliacal rising and setting method in a public-domain scan.
• Sūrya Siddhānta 9.6–10 presents the Sanskrit verses and an English rendering of the five degree limits.
• Drik Panchang, Planets Combustion shows the current public feature family and its separate annual graha pages. This site calculates an independent, narrower longitude model.
• Astronomy Engine 2.1.19 documents the locally bundled ephemeris used for apparent geocentric positions.