Lunar month circular, the speed of Earth's progression around the Sun varies during the year. Thus, the angular rate is faster nearer periapsis and slower near apoapsis. The same is so for the Moon's orbit around the Earth. Because of these variations in angular rate, the actual time between lunations may vary from about 29.18 to about 29.93 days. The long-term average duration is days (29 d 12 h 44 min 2.8016 s). The synodic month is used to calculate eclipse cycles. It is customary to specify positions of celestial bodies with respect to the vernal equinox. Because of Earth's precession of
Aryabhata 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days) is an error of 3 minutes and 20 seconds over the length of a year (365.25636 days). As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on its own axis. His model also gave corrections (the "śīgra" anomaly) for the speeds of the planets in the sky in terms of the mean speed of the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model, in which the