Elementary Concepts of Astronomy—II (Pañcāṅga & Planetary Facts)
The Pañcāṅga (Indian Almanac)
The pañcāṅga is the traditional Indian almanac used for daily life, rituals, and electional astrology (muhūrta). It has five “limbs”: (1) tithi (lunar date), (2) vāra (day of the week), (3) nakṣatra (lunar asterism), (4) yoga, and (5) karaṇa. Of these, vāra is a function of the Sun alone; the other four depend on the Moon or the Moon–Sun relationship.
Lunar Months: Types & Durations
The Moon’s revolution around the Earth defines several “months,” each measured by a different reference:
- Sidereal month: Moon’s return to the same zodiacal longitude (stars); about 27.3217 mean solar days.
- Synodic month: Full cycle of lunar phases (New Moon to New Moon); about 29.5306 days.
- Nodical / Draconic month: Return to the same lunar node; about 27.2122 days.
- Anomalistic month: Return to perigee/apogee (same orbital anomaly); about 27.5546 days.
Indian Calendar Month Kinds & Intercalations
Traditional reckoning recognizes different month types (e.g., saura—solar; sāvana—by equal civil days; cāndra—lunar; and nakṣatra—asterism-based). Because lunar months are shorter than a solar year, an intercalary month (adhika-māsa) is inserted when there is no Sun’s ingress (saṅkrānti) inside a lunar month; rarely, a kṣaya-māsa (dropped month) occurs when two saṅkrāntis fall within one lunar month.
Pakṣa (Fortnight) & Phase Names
A lunar month is split into two fortnights: the śukla-pakṣa (bright half, waxing Moon) and the kṛṣṇa-pakṣa (dark half, waning Moon).
A 19-Year Recurrence (Metonic-type Cycle)
A 19-year cycle occurs in which the Moon’s phases recur on near-identical dates—useful for aligning lunar and solar calendars.
Moon’s Nodes (Rāhu & Ketu) and Eclipses
Lunar nodes are the two intersection points of the Moon’s orbit with the ecliptic; astrology calls the ascending node Rāhu and the descending node Ketu. The line of nodes regresses, completing a revolution in about 18 years and 10 days.
Eclipses occur when the Sun, Earth, and Moon align near these nodes at New or Full Moon: solar eclipses at New Moon, lunar eclipses at Full Moon. A lunar eclipse is likely if the Full Moon is within ~12° of a node (virtually certain within ~9°); a solar eclipse is likely if the New Moon is within ~18.5° (virtually certain within ~15°). The number of solar eclipses in a year can range from two to seven.
Tithi (Lunar Date)
A tithi is defined by the angular separation between the Moon and the Sun: each tithi spans 12° of elongation. There are 30 tithis in a month (15 per pakṣa). A working formula is: Tithi index = ⌊(Moon longitude − Sun longitude)/12°⌋ + 1.
Vāra (Days of the Week) & Hora Logic
Day-lords follow the ancient hora sequence. The seven visible planets are arranged by increasing velocity (Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon). Each day’s first hora belongs to that day’s lord; the next horas cycle through the same sequence. Because the day-lord is the planet fourth in order from the previous day’s lord, Sunday follows Saturday, Monday follows Sunday, etc.
Nakṣatra (Lunar Asterism)
Nakṣatra denotes the lunar asterism the Moon occupies on a given day. It is one limb of the pañcāṅga and is used heavily in muhūrta and natal analysis.
Yoga (Daily/Nitya Yogas)
Yoga is a pañcāṅga element used in day-to-day rituals and electional work. Such as: Viśkumbha, Prīti, Āyuṣmān, Saubhāgya, Śobhana, Atigaṇḍa, Sukarma, Dhṛti, Śūla, Gaṇḍa, Vṛddhi, Dhruva, Vyāghāta, Harṣaṇa, Vajra, Siddhi, Vyatīpāta, Variyāṇa, Parigha, Śiva, Siddha, Sādhya, Śubha, Śukla, Brahma, Indra, and Vaidhṛti. Yogas are applied widely in electional astrology and daily rites.
Karaṇa (Half-Tithi)
A karaṇa is half a tithi (6° of Moon–Sun separation). Thus, a lunar month comprises 60 karaṇas.
There are four fixed karaṇas that occur only once per month: Śakuni (assigned to the latter half of kṛṣṇa-caturdaśī), Catuṣpāda (first half of amāvasyā), Nāga (latter half of amāvasyā), and Kiṁstughna (first half of śukla-pratipadā). The remaining seven recurring karaṇas—Bava, Balava, Kaulava, Taitila, Gara, Vāṇija, Viṣṭi—repeat in a fixed order from the second half of the first śukla day through the first half of the 14th kṛṣṇa day.
Some Astronomical Facts about the Grahas
Sun (Sūrya)
- Nearest star and source of Earth’s heat/light; provides centripetal force balancing planetary motion.
- Approx. 1.392 million km in diameter (~109× Earth); mass ~323,000× Earth.
- Located near an arm’s edge of the Milky Way, ~30,000 light-years from galactic center.
Moon (Candra)
- Earth’s satellite; fastest “graha” used in pañcāṅga. Diameter ~3476 km; average distance ~384,400 km.
- Same face always toward Earth (rotation period equals orbital period ≈ 27.32 days); libration makes up to ~59% of lunar surface visible over time.
- Phases are due to Sun–Moon geometry; these phases underlie tithis.
Mercury (Budha)
- Nearest to the Sun; mean distance ~58 million km; diameter ~4870 km.
- Highly eccentric orbit; rotation ~58.65 days (≈ 2/3 of orbital period ~88 days).
- Maximum elongation from Sun is limited (inner planet).
Venus (Śukra)
- Dense cloud cover; very bright; mean distance ~108 million km; diameter ~12,000 km.
- Retrograde rotation (~242.6 days) opposite most bodies; orbital period ~224.7 days.
- Inner planet; cannot stray far from the Sun in the sky.
Mars (Maṅgala)
- Outer planet; mean distance ~227.8 million km; diameter ~6786 km.
- Highly elliptical orbit: distance from Earth at opposition varies (~56–100 million km), hence variable brilliance.
- Rotation ~1.026 days; sidereal period ~687 days (~1.881 years); two small satellites Phobos and Deimos.
Jupiter (Guru)
- Largest planet; mass exceeds that of all others combined; rapid rotation (~9h 50m) causes equatorial bulge (≈143,000 km) vs. polar (~133,000 km).
- Mean distance ~778 million km; orbital period ~11.86 years; very cold (~−140 °C clouds); many satellites.
Saturn (Śani)
- Mean distance ~1426 million km; rotation ~10h 14m; orbital period ~29.46 years; diameter >120,000 km.
- Cold, massive (~95× Earth), spectacular rings; many satellites.
Inner vs. Outer Planets
Inner (inferior) planets—Mercury and Venus—lie between Earth and Sun and never move far from the Sun in the sky (max elongations ≈ 27° for Mercury, ≈ 47° for Venus). Outer (superior) planets—Mars, Jupiter, Saturn—lie outside Earth’s orbit.
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