Bo\v{s}kovi\'c's method for determining the axis and rate of solar rotation by observing sunspots in 1777

TL;DR

This paper revisits Bošković's 1777 sunspot observations to validate his methods for determining solar rotation, confirming their accuracy and providing modern analysis of his data.

Contribution

The study reproduces and verifies Bošković's original calculations using modern computational methods and compares results with different obliquity values, enhancing historical solar rotation data analysis.

Findings

Bošković's methods are validated with modern calculations.

The original and reproduced results show high consistency.

Solar differential rotation was determined from 1777 observations.

Abstract

In 1777 Ru{\dj}er Bo\v{s}kovi\'c 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 Bo\v{s}kovi\'c's original equations and equations adapted for modern computers. We repeat the calculations using two values of the obliquity of the ecliptic, Bo\v{s}kovi\'c's, and an interpolated one. Using his 1777 observations, Bo\v{s}kovi\'c obtained the solar equator's inclination, ecliptic longitude of the ascending node, and sidereal and synodic rotation periods. We analyzed and compared these original Bo\v{s}kovi\'c results with our repeated calculations. Our results confirm the validity of Bo\v{s}kovi\'c's methods and the precision of his calculations. Additionally, the paper presents the solar differential rotation determination using all 1777 observations by Ru{\dj}er Bo\v{s}kovi\'c.