Lunar day around the Sun at the same time, the Moon must travel further to return to the same phase. On average, this synodic period lasts 29 days, 12 hours, 44 minutes, and 3 seconds. This is the mean figure since the speed of the Earth–Moon system around the Sun varies slightly during a year due to the eccentricity of its elliptical orbit, variances in orbital velocity, and a number of other periodic and evolving variations about its observed, relative, mean values, which are influenced by the gravitational perturbations of the Sun and other bodies in the Solar System. As a result,
Aryabhatiya to modern astronomy and mathematics. Aryabhata asserted that the Moon, planets, and asterisms shine by reflected sunlight, correctly explained the causes of eclipses of the Sun and the Moon, and calculated values for π and the length of the sidereal year that come very close to modern accepted values. His value for the length of the sidereal year at 365 days 6 hours 12 minutes 30 seconds is only 3 minutes 20 seconds longer than the modern scientific value of 365 days 6 hours 9 minutes 10 seconds. A close approximation to π is given as: "Add four to one