Bošković's method for determining the axis and rate of solar rotation by observing sunspots in 1777

In 1777 Ruđer Bošković observed sunspots, determined their positions and the solar rotation elements by his own methods briefly described here. We repeat his calculations of the mean solar time, sunspot positions, and solar rotation elements using both the Bošković’s original equations and equations adapted for modern computers. We repeat the calculations using two values of the obliquity of the ecliptic, Bošković’s, and an interpolated one. Using his 1777 observations, Bošković obtained the solar equator’s inclination, ecliptic longitude of the ascending node, and sidereal and synodic rotation periods. We analyzed and compared these original Bošković results with our repeated calculations. Our results confirm the validity of Bošković’s methods and the precision of his calculations. Additionally, the paper presents the solar differential rotation determination using all 1777 observations by Ruđer Bošković.