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Contribution of Ruđer Bošković in Determining Sun Rotation Elements i and ω Using Sunspot Observations

Roger Joseph Boscovich, in Croatian Ruđer Josip Bošković (Dubrovnik, Croatia, May 18th, 1711 – Milan, Italy, February 13th, 1787) was Croatian Jesuit priest, astronomer, polymath, physicist, geodesist, cartographer, philosopher, poet and diplomat. He established and equiped astronomical observatory in Brera, using guidelines he sought in Greenwich astronomical observatory when he visited London 1760 and he made the program of astronomical observations activities in Brera where he planned observations of Sunspots. His first dissertation De maculis solaribus (About Sunspots) 1736 describes geometric and trigonometric methods for determining period of Sun rotation and position of Sun using three positions of a Sunspot. This method is similar to his method for determine the traces of comets. In 1777 he observed for six days a regular middle sized Sunspot traced at the Sun surface. This observations and calculations were published 1785 in the section Sur les éléments de la rotation du soleil sur son axe déterminés par l'observation de ses taches of the 5th book Opera pertinentia ad opticam et astronomiam. Using geometric method Bošković calculated value of Sun rotation sidereal period 26.77 days, since then the value was 25.5 days. Also he calculated synodic period of the Sun 28.89 days. Today we know that the Sun plasma body with differential rotation and its rotation period lasts 25-29 days. Furthermore, Bošković created adjustment method with a condition that the sum of absolute values of deviations strives to a minimum – L1-norm, before the method of Carl Friedrich Gauss (1777–1855) who created adjustment method with a condition that the sum of square number of deviations strives to a minimum – L2-norm, usual today. In 1678 Jean Dominique Cassini (Cassini IV, 1748-1825) is the first one who determined the inclination angle i between planes of ecliptic and equator of Sun and ecliptic longitude ascending knot of Sun equator Ω and after him many others mentioned in this research. The research should find out 1. Can we calculate sun rotation elements i and Ω using 1777 observations of Bošković? 2. Which method suits better for the adjustment of calculated results of Sun rotation elements: L1–norm (Bošković method) or L2–norm (Gauß method)? 3. Could we use the 1777 Bošković observations of three positions of one sunspot for calculating i and Ω values with some cotemporary method. This research continues in the future with explanation of De maculis solaribus (Bošković 1736), translation of old French text Opuscule II. (Bošković 1785, 75-178), the explanation of the text, and recalculation of these results in order to find out if the published calculations of Bošković were well done. The Bošković observations are time series data which are discussed in order to filter out outlying and noisy data. Further research could include analysis of calculations of i and Ω using Sunspot observations J. D. Cassini and others compared with nowadays sunspot observations and calculation with nowadays methods.

Ruđer Bošković, Sunspot, Sun rotation elements, L1–norm, L2–norm, time series.

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