UKRAINIAN
Astronomical School’s Report, 2017, Volume 13, Issue 1, Pages 35–39
The structure of the calendar solar cycle
Mikhalchuk V.V.
Abstract
In the Julian calendar there is the solar cycle duration of 28 years through which the distribution of the days of the week on numbers of all months of the year is completely repeated. The same regularity is also observed and in the 28-years Julian periods of the Gregorian calendar which are not containing the centuries years, which numbers are not divided without remainder by 400. Except for 28-years period, there are still smaller periods of the full repeatability of days of week in one year. The knowledge of the periods of the full repeatability of the days of the week in the years of the solar cycle has the practical value as allows using the calendars of the past years. In the literature are absent the information about these periods, therefore arises the problem about the determination of periods of the full repeatability of the days of the week in years and regularity of their alternation inside the solar cycle. This article is devoted to the solution of this problem for the calendar consisting of 28-years Julian periods. In this article the 28-years Julian period is divided into 7 Julian four-year periods. It allows obtaining the formula for finding the sum of differences between the duration of calendar year and the duration of an integer of weeks in the Julian calendar from the beginning of the 28-years cycle for all years of the everyone Julian four-year period. The rule of selecting the years in which there is the complete coincidence of days of week is introduced. The analysis of structure of the solar cycle, performed in this article, it is shown, that inside the solar cycle for the Julian calendar the full repeatability of all days of week in simple years can happen to periods of 6 and 11 years, and in leap-years – only with period of 28 years. Regularity of alternation of these periods in various years of anyone Julian four-year period is established. For each year the sum of the periods of the full recurrence of all days of the week is 28 years. Inside any 28-years solar cycle for every simple year always there are more 2 simple years with the full repeatability of all days of week, and in leap-years days of week are not repeated. The obtained regularity of alternation of years with the full repeatability of all days of the week inside the solar cycle allows using the calendars of the past years. It is shown, that during any 28-years solar cycle it is possible to use in three years the same calendar of simple year and only in one year – the calendar of leap-year. On the basis of the established periodicity the table of the full repeatability of all days of week for each year inside the solar cycle composed.
Keywords: calendar; solar cycle
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