jyotisha and the sky
How did ancient Indian astronomers calculate planetary positions without telescopes?
The instruments they used
Without telescopes, astronomers relied on what they could see and measure directly. A gnomon, called a Shanku, was a simple upright rod. By watching its shadow through the day, observers could track the sun's movement, find true north, and measure the time of year. An armillary sphere, called a Gola yantra, was a set of rings arranged to model the sky. It let astronomers sight along the paths of the sun, moon, and planets. Water clocks measured time carefully enough to record when a planet rose or set. These tools were simple by modern standards, but in skilled hands they produced observations good enough to build real mathematical models from.
The mathematics behind it
The real power was in the mathematics. Texts like the Surya Siddhanta, the Aryabhatiya, and the Brahmasphutasiddhanta laid out detailed methods for calculating where a planet would be on any given day. They used epicyclic models, meaning they described a planet as moving in a small circle whose centre itself moved along a larger circle. This let them account for the way planets seem to speed up, slow down, and sometimes appear to move backward in the sky. Trigonometry was central to all of this. The Kerala school later developed infinite series for sine and cosine, ideas that in Europe came much later. Aryabhata's calculations leaned toward a picture where the earth rotates, which put his numbers for planetary periods very close to what modern astronomy confirms.
How accurate were they
Accurate enough to predict eclipses reliably. Eclipse prediction requires knowing the positions of the sun and moon to a fine degree, and the texts managed this well. Their values for the length of the year and the periods of the planets were close to modern measurements. They were working without any optical instruments, so small errors crept in, but the mathematical framework was strong enough to correct for many of them through careful calculation.
Why it still matters
These methods are not just history. The traditional Hindu calendar, used today to set festival dates and auspicious times, still draws on the mathematical frameworks developed in these texts. Jyotisha, the broader tradition of Indian astronomy and astrology, treats this body of knowledge as living and practical. Scholars of the history of science continue to study these texts because some of the mathematical ideas in them appeared in India well before they appeared elsewhere.