Sun's retrograde motion and violation of even-odd cycle rule in sunspot activity

The sum of sunspot numbers over an odd-numbered 11-yr sunspot cycle exceeds that of its preceding even-numbered cycle, and it is well known as Gnevyshev and Ohl rule (or G-O rule) after the names of the authors who discovered it in 1948. The G-O rule can be used to predict the sum of sunspot numbers of a forthcoming odd cycle from that of its preceding even cycle. However, this is not always possible because occasionally the G-O rule is violated. So far, no plausible reason is known either for the G-O rule or for the violation of this rule. Here, we show the epochs of the violation of the G-O rule are close to the epochs of the Sun's retrograde orbital motion about the centre of mass of the Solar system (i.e. the epochs at which the orbital angular momentum of the Sun is weakly negative). Using this result, it is easy to predict the epochs of violation of the G-O rule well in advance. We also show that the solar equatorial rotation rate determined from sunspot group data during the period 1879-2004 is correlated/anticorrelated to the Sun's orbital torque before/after 1945. We have found the existence of a statistically significant similar to 17-yr periodicity in the solar equatorial rotation rate. The implications of these findings for understanding the mechanism behind the solar cycle and the solar-terrestrial relationship are discussed.