What people first learnt how to calculate palanetary orbits?

    It was not done using the decimal system

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    When people first discovered that planets orbited around the sun, they thought that the orbits would be in the shape of a circle. It wasn't until 1601 that Johannes Kepler, using precise measurements taken by the astronomer Tycho Brahe, determined that the planets actually orbit in ellipses around the sun. An ellipse looks like a circle that has been "squashed" slightly, like an oval, or like an egg. Kepler also found that when a satellite orbits in an ellipse, it moves faster when it is close to the object it is orbiting and slower when it is farther away.

    After discovering these two laws, Kepler went on to measure the 'eccentricity' of each planet's orbit. Eccentricity is a measure of how circular a satellite's orbit is. For a perfectly circular orbit the eccentricity is zero; elliptical orbits have eccentricities between zero and one.

    From Wikipedia:
    Ancient Indian astrology is based upon sidereal calculation. The sidereal astronomy is based upon the stars and the sidereal period is the time that it takes the object to make one full orbit around the Sun, relative to the stars. It can be traced to the final centuries BC with the Vedanga Jyotisha attributed to Lagadha, one of the circum-Vedic texts, which describes rules for tracking the motions of the Sun and the Moon for the purposes of ritual. After astronomy was influenced by Hellenistic astronomy (adopting the zodiacal signs or rāśis). Identical numerical computations for lunar cycles have been found to be used in India and in early Babylonian texts.

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