The Surya Siddhanta, an ancient Indian astronomical text, is recognized for containing the roots of modern trigonometry. It introduced essential trigonometric functions such as sine (jya), cosine (kojya), and inverse sine (otkram-jya), and is acknowledged for presenting some of the earliest and most accurate trigonometric tables—centuries before similar advancements in Greece or elsewhere.
While Greek mathematician Hipparchus is often called the "father of trigonometry" for compiling early trigonometric tables, modern scholarship suggests that the Surya Siddhanta’s methods predate and outperform those early tables. The text is attributed to Mayasura, and some researchers refer to him as the "father of trigonometry" due to his foundational contributions in defining and applying trigonometric functions within the Surya Siddhanta. The sine tables in Surya Siddhanta, with intervals as fine as 3.75°, were more accurate and comprehensive than those of Hipparchus or Ptolemy, and its methods deeply influenced later Islamic and European mathematics.
The Surya Siddhanta is not just the root of Indian trigonometry, but a reference point for the discipline globally, and Mayasura (author of Surya Siddhanta) is increasingly credited as a true pioneer of trigonometry rather than Hipparchus alone.
The Surya Siddhanta contains several astronomical calculations and constants that, despite being thousands of years old, align remarkably well with modern scientific data. These calculations demonstrate a sophisticated understanding of celestial mechanics, particularly in the determination of planetary cycles and orbital positions.
1. Sidereal Revolutions of Planets
One of the most impressive feats of the Surya Siddhanta is its calculation of the time it takes for planets to complete a full orbit (sidereal revolution). When comparing the text's data to modern values, the accuracy is often within a fraction of a percent.
| Planet | Surya Siddhanta (Days) | Modern Value (Days) |
| Sun (Year) | 365.2587 | 365.2563 |
| Mercury | 87.969 | 87.969 |
| Venus | 224.698 | 224.700 |
| Mars | 686.997 | 686.979 |
| Jupiter | 4,332.32 | 4,332.58 |
| Saturn | 10,765.77 | 10,759.21 |
2. Planetary Aphelia (Apogees)
The text calculates the longitudes of the aphelia (the point in an orbit farthest from the Sun) for various planets. For a reference date of 499 A.D., the Surya Siddhanta's values are nearly identical to those calculated using modern astronomical rules
Sun: The text gives 77° 14', while modern rules calculate it at 77° 15'
. Mars: The text gives 130° 0', compared to the modern value of 128° 23'
. Jupiter: The text gives 171° 16', very close to the modern 170° 22'
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3. Trigonometric Functions (Sine Tables)
To perform these complex celestial calculations, the Surya Siddhanta utilized an early form of trigonometry. It contains a table of sines (jya) and versed sines (utkramajya) calculated for every 3° 45' of an arc
4. Lunar and Solar Eclipses
The text provides detailed algorithms for predicting the occurrence, duration, and magnitude of both solar and lunar eclipses
Lunar Diameter: The Surya Siddhanta estimates the moon's diameter with enough precision that its calculations for the "half-duration" of an eclipse and the "total obscuration" remain technically sound frameworks for observation
. Parallax: It accounts for parallax (the apparent change in position of an object when viewed from different points), which is essential for the accurate prediction of solar eclipses
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5. Earth’s Diameter and Circumference
The book estimates the Earth's diameter to be approximately 1,600 yojanas
Read... O my Hindus of Bharat - we have lost many centuries to mimic the Western civilization.
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