arXiv subjects

Mirko Husak

Publications and source records attributed to Mirko Husak.

3 recordsLinked to original sources

arXiv2025

Bo\v{s}kovi\'{c}'s Spherical Trigonometric Solution for Determining the Axis and Rate of Solar Rotation by Observing Sunspots in 1777

In September 1777 Ru\dj er Bo\v{s}kovi\'{c} observed and measured the sun-spot positions to determine the solar rotation elements. In 1785, among other methods, he described a trigonometric spherical solution for the determination of the position of the axis and rate of the solar rotation using three sunspot positions, but without equations. For the first time, we derive the equations that are applicable to modern computers for calculating the solar rotation elements, as they were described by Bo\v{s}kovi\'{c}. We recalculated Bo\v{s}kovi\'{c}'s original example using his measurements of sunspot positions from 1777 and the equations developed here, confirming his results from 1785. Bo\v{s}kovi\'{c}'s methodology of arithmetic means determines $i$, $\Omega$, and sidereal period $T'$ separately, while the planar trigonometric solution determines $i$ and $\Omega$ together. His spherical trigonometric solution calculates $i$, $\Omega$, and the sidereal period $T'$ in a single procedure. Keywords: Ru\dj er Bo\v{s}kovi\'{c}, Sunspots, Solar rotation, Spherical trigonometry

astro-ph.SR↗

arXiv2025

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

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.

astro-ph.SR↗

arXiv2022

On the Determination of the Solar Rotation Elements i, Ω and Period using Sunspot Observations by Ruđer Bošković in 1777

In September 1777, Ruđer Bošković observed sunspots for six days. Based on these measurements, he used his own methods to calculate the elements of the solar rotation, the longitude of the node, the inclination of the solar equator and the period. He published a description of the methods, the method of observation and detailed instructions for calculations in the second chapter of the fifth part of the Opera in 1785. In this paper, Bošković original calculations and repeated calculations by his procedure are published. By analysing the input quantities, procedures, and results, the input quantities of the error, and the calculation results are discussed. The reproduction of Bošković calculations is successfully reproduced and we obtained very similar results. The conclusion proposes a relationship of Bošković research with modern astronomy.

astro-ph.SR↗