# Solar cycle

To calculate Easter in the Julian calendar, it is first necessary to know the dates on which Sunday would fall in a given year. To do this, a solar cycle (Latin: circulus solaris, cyclus solaris) needs to be constructed. This solar cycle is composed of a continuously numbered series of 28 years, where all the years that form an identical match in week order are marked. In short, if two years start and end on different days of the week, they are not perfect matches. Now, this can only be done with the Julian calendar, not the Gregorian calendar, due to the inaccessibility of its centenary years—because of this, it’s pointless to use a solar cycle on a Gregorian calendar.

An ordinary year has 52 weeks, and an extra day if the year began on a Monday. It then follows that the next year begins on a Tuesday, and so on, and so forth. In this way, seven years would be enough calendar dates to cycle back to the same day of the week. However, by inserting leap years every fourth year (as in the Julian calendar), the date of the new week’s start is shifted by two days in the following year. Ultimately, this causes the whole cycle to last even longer, bringing the length up to 28 years (7 × 4).

Each value of the solar cycle in the Julian calendar can be assigned a Dominical letter—once again, in the Gregorian calendar this does not apply.

Calculation formula: solar_cycle = (year + 9) % 28
if the result is 0, the value of the solar circle is 28
Which can be shortened to solar_cycle = (year + 8) % 28 + 1

The beginning of the first cycle was set to the year 9 BC (which was supposed to be a leap year), because it began on a Monday. The French classicist, Josephus Justus Scaliger, asserted that the beginning of the first cycle was the year 328, which was the first leap year after the Council of Nicaea. Bear in mind that only integers are counted; the '%' character (modulo) indicates that the modulo, or the remainder, is the only thing we’re interested in. In this case, the remainder can be as large as 27.

Below you can find a table of solar cycle values ​​from the Year 0 (according to astronomical years) on to 5599. It is quite easy to use. Simply find the century in the column and the year in the row. The number you’re looking for will be at the intersection. So, for example, if we are interested in finding the value of the solar cycle for the year 1348, we’d find 1300 in the column and 48 in the row, then follow each to their intersection. In this example, the solar year for 1348 is 13.

years0
700
1400
2100
2800
3500
4200
4900
100
800
1500
2200
2900
3600
4300
5000
200
900
1600
2300
3000
3700
4400
5100
300
1000
1700
2400
3100
3800
4500
5200
400
1100
1800
2500
3200
3900
4600
5300
500
1200
1900
2600
3300
4000
4700
5400
600
1300
2000
2700
3400
4100
4800
5500
0  28  56  84  92513117521
1  29  57  85  102614218622
2  30  58  86  112715319723
3  31  59  87  122816420824
4  32  60  88  13117521925
5  33  61  89  142186221026
6  34  62  90  153197231127
7  35  63  91  164208241228
8  36  64  92  17521925131
9  37  65  93  186221026142
10  38  66  94  197231127153
11  39  67  95  208241228164
12  40  68  96  21925131175
13  41  69  97  221026142186
14  42  70  98  231127153197
15  43  71  99  241228164208
16  44  72  25131175219
17  45  73  261421862210
18  46  74  271531972311
19  47  75  281642082412
20  48  76  11752192513
21  49  77  218622102614
22  50  78  319723112715
23  51  79  420824122816
24  52  80  52192513117
25  53  81  622102614218
26  54  82  723112715319
27  55  83  824122816420