Patterns the planets draw, with Āryabhaṭa’s periods beside the modern ones. Pick a planet and watch: every line, loop and petal comes from the two orbits alone.
Earth and Venus go round the Sun at different speeds. Draw a line between them every few days for eight years and a five-petalled rose appears, because 8 Earth years are almost exactly 13 Venus years. Mercury, Mars, Jupiter and Saturn draw their own patterns. Āryabhaṭa, in 499 CE, gave each planet's revolutions in a yuga of 1,577,917,500 days: for Venus that is one every 224.70 days, against the modern 224.70. This page draws the patterns with JavaScript.
Each planet comes nearest to Earth about once per synodic period: Earth laps Mars every 780 days, Jupiter every 399 and Saturn every 378. Mars, Jupiter and Saturn are nearest when opposite the Sun and up all night; Mercury and Venus are nearest when between us and the Sun, lost in its glare. This section works out the next dates with JavaScript.