Features of Indian astronomy
Astronomy in India (jyotisha in its mathematical sense, ganita) grew from a practical need: keeping time for rituals, farming and travel. Key features:
- Naked-eye observation of the Sun, Moon, five visible planets and bright stars, measured with simple instruments like the gnomon (shanku) and water clocks.
- Mathematical models written in verse, using sines, epicycles and very long time cycles to compute positions.
- A Moon-based star frame: the 27 (sometimes 28) nakshatras.
- Exchange of ideas with Babylonian, Greek, Persian and Arab astronomers, and later with Europe.
Important astronomers and texts
- Vedanga Jyotisha (an early calendar text, around the first millennium BCE): a 5-year cycle of Sun and Moon.
- Aryabhata (Aryabhatiya, 499 CE): said the Earth spins on its axis, explained eclipses as shadows of the Earth and Moon, gave the year length very closely and a good value of π (3.1416).
- Varahamihira (6th c.): summarised five older systems (Pancha Siddhantika).
- Brahmagupta (628 CE): rules for planets and eclipses, and for zero in arithmetic.
- Bhaskara II (12th c.): Siddhanta Shiromani, planetary motion with early ideas of instant speed.
- Kerala school (14th–16th c., Madhava, Nilakantha): infinite series for sine and π; an improved planet model.
Nakshatras and the lunisolar calendar
The Sun's yearly path among the stars is the ecliptic. The Moon stays close to it. Dividing the full circle of 360° into 27 parts gives 13°20′ per nakshatra. The Moon takes about 27.3 days to circle the stars once, so it stays roughly one day in each nakshatra. Each nakshatra is named after a bright star or group, e.g. Ashvini, Rohini, Chitra, Revati.
The panchang ("five parts") gives for each day: tithi (lunar day), vara (weekday), nakshatra, yoga and karana.
- Tithi: the time for the Moon to gain 12° on the Sun. 360° ÷ 12° = 30 tithis in one lunar (synodic) month of about 29.5 days, split into a bright half (shukla paksha) and a dark half (krishna paksha).
- Lunar year: 12 months ≈ 354 days, about 11 days shorter than the solar year (≈ 365.25 days).
- Adhika masa: an extra month added about every 32–33 months, so months stay in the same season. This makes the calendar lunisolar.
- Solar months follow the Sun through the 12 rashis (30° each); for example Makar Sankranti marks the Sun entering Makara.
Many cultures built similar lunisolar calendars, including the Chinese and Hebrew calendars; the Islamic calendar is purely lunar and does not add months.
Ancient and modern prediction methods
| Ancient Indian method | Modern method | |
|---|---|---|
| Observation | Naked eye, gnomon, water clock, masonry instruments | Telescopes, radar, spacecraft, atomic clocks |
| Model | Earth at centre; mean motion plus corrections (epicycles, sine tables) | Sun-centred orbits, Newton's gravity and relativity, numerical integration |
| Eclipses | Computed from Sun-Moon positions and the Moon's node (Rahu/Ketu as the crossing points) | Computed to the second for any place on Earth |
| Accuracy | Good to minutes or hours; errors grew over centuries and texts were corrected (bija) | Fractions of a second; checked constantly |
The method is the same in spirit: observe → build a model → predict → check → correct. Astronomy (science) must be kept separate from astrology (predicting human fate), which is not supported by scientific tests.
Observatories: Jantar Mantar
Between about 1724 and 1735, Maharaja Sawai Jai Singh II built five observatories, called Jantar Mantar, at Delhi, Jaipur, Ujjain, Varanasi and Mathura (Mathura's no longer stands). He made the instruments huge, from stone and plaster, because bigger scales give finer readings.
- Samrat Yantra: a giant sundial. Its triangular wall (gnomon) points to the celestial pole; its shadow on curved quadrants gives local time. The Jaipur one is about 27 m high and reads time to about 2 seconds.
- Jai Prakash Yantra: two hollow half-spheres; a ring's shadow shows the Sun's position.
- Rama Yantra: cylinders to measure altitude and azimuth of stars.
- Misra Yantra (Delhi): a combined instrument for several tasks.
The Jaipur Jantar Mantar is a UNESCO World Heritage Site. Earlier, observatories such as Ujjain had long been centres of astronomy; Ujjain's meridian served as a prime meridian for Indian astronomers.
Try it
Look at the Moon on three nights in a row at the same time and note which bright star it is near. It moves about 13° east each night (about the width of your fist and a bit at arm's length). In the 3D, move the day slider by 1 and see the Moon jump one nakshatra.
Key formulas and definitions
- 1 nakshatra = 360° ÷ 27 = 13°20′
- 1 tithi = 12° gain of Moon over Sun; 30 tithis = 1 lunar month ≈ 29.53 days
- Lunar year ≈ 12 × 29.53 ≈ 354.4 days
- Solar year − lunar year ≈ 11 days → extra month about every 32.5 months
- Moon moves ≈ 13.2° per day against the stars; Sun ≈ 1° per day
- Rashi (zodiac sign) = 30°; 12 rashis = 360°
Worked examples
1. How many degrees does each nakshatra cover? Show the working.
360° ÷ 27 = 13.333…° = 13°20′.
2. The Moon is 66° ahead of the Sun. Which tithi is running?
66 ÷ 12 = 5.5, so 5 full tithis are complete and the 6th tithi (shashthi) is running.
3. About how many days does the lunar year fall behind the solar year in 3 years? What fixes it?
365.25 − 354.4 ≈ 10.9 days per year; × 3 ≈ 32.6 days, about one month. Adding one adhika masa fixes it.
4. The Moon moves about 13.2° a day. How many days to cross one nakshatra?
13.33° ÷ 13.2° per day ≈ 1.01 days, roughly one day.
5. Why did Jai Singh II build instruments tens of metres tall instead of small brass ones?
On a bigger scale each degree is a longer arc, so the shadow can be read more finely. Stone does not bend or wear like small brass parts, so readings stay steady.
Common mistakes
- Mixing up astronomy and astrology: astronomy measures and predicts sky motions; astrology claims sky positions decide human fate, which tests do not support.
- Thinking a tithi is a fixed 24-hour day: its length varies (about 19 to 26 hours) because the Moon's speed varies.
- Believing the lunar month is 27.3 days: that is the sidereal month (back to the same star); new moon to new moon is about 29.5 days.
- Thinking Jantar Mantar is one building: it is a set of separate instruments, and there were five observatories in different cities.