Spaṣṭa-Graha: True Position Calculations

The two corrections that turn a smooth average planet into the one you actually see

The mean planet is a smooth fiction; the real planet drifts away from it in the sky. Learn how Indian astronomers built the spaṣṭīkaraṇa, the two-step correction (manda and śīghra) that turns the mean position into the spaṣṭa-graha, the true, observed position.

The Sun's Gift to the Seeker

Near the end of the Kṛta Yuga, the first and golden age, the story goes, an asura named Maya hungered to know the hidden law of the moving heavens. He turned his whole devotion toward the Sun. The Sun, too fierce to be met face to face, sent a portion of his own light down in human form to the tireless seeker, and that emissary spoke aloud the Sūrya Siddhānta, the Sun's own doctrine of the planets. This is how the tradition dresses the origin of its most influential astronomy manual, and we should read it as the legend it is.

Strip away the myth, though, and a real and hard question is left standing, the very question Maya is said to have asked. The mean motion tells you where a planet should be if it moved at a perfectly even pace. But go outside and look, and the planet is not there. It sits stubbornly to one side, sometimes by several degrees, a gap wide enough to see with the naked eye. Why is the real planet not where the average says it should be, and by exactly how much? Answering that is the whole art of the spaṣṭa-graha, the true position.

Two Honest Reasons for the Gap

The Indian astronomers traced the difference between the mean planet and the real one to two separate causes, and treated each with its own correction.

The first is that a planet does not truly move at a constant speed along its path. It runs a little faster in one part of its circuit and slower in the opposite part. The correction for this uneven pace is the manda-phala, the "slow" correction, and it is the subject of the next lesson.

The second cause is subtler and, as we will see, more revealing. Part of what we see as a planet's motion is really, as we understand it today, a reflection of our own moving viewpoint and of the planet's relation to the Sun. This is what makes the outer planets occasionally seem to halt and slide backward. The correction for it is the śīghra-phala, the "fast" correction, and it is the subject of the lesson after.