Hipparchus cycle

Hipparchus

The term Hipparchus cycle goes back to the Greek astronomer Hipparchus of Nicaea . Hipparchus established between 148 and 126 BC. After Hipparchus redefined the length of the solar year, taking precession into account , the Callippian calendar cycle was calculated too long compared to the solar year . The Hipparchus cycle found no practical application in calendar calculations. The reasons for this remain unclear and puzzling.

Basics

Comparison of the different definitions for the tropical year

Hipparchus determined the solar year to be 365.23398 days (365d 5h 36m 56sec) on the basis of his astronomical records. His calculations thus deviated from the actual length (365.24231 days; 365d 5h 48m 56sec) by only twelve minutes.

Hipparchus now adopted the basic system of the Callippi calendar, which he first quadrupled in length, and then deduct a full day. Hipparchus chose the cycle duration of 304 years on the basis of his calculated solar year value, which he had determined with a deviation of 1/300 compared to the Kallippian value of 365.25 days.

This resulted in an average calendar year with a length of 365.24671 days (365d 5h 55m 16sec), which is only a difference of about 17 minutes and 20 seconds compared to the solar year he calculated and six minutes and 20 seconds compared to the actual solar year.

Accuracy of the Hipparchus cycle

Compared to the actual solar orbit of the earth , there were increasing deviations over a longer time frame at the time of Hipparchus. Compared to the actual orbit of the sun, there was a deviation of one day in the first Hipparchus cycle after almost 227 years.

First Hipparchus cycle

Sun orbit of the earth

${\displaystyle {\begin{matrix}1\,{\text{Jahr}}&=&365{,}2423\,{\text{Tage}}\\304\,{\text{Jahre}}&=&111033{,}6592\,{\text{Tage}}\end{matrix}}}$

Comparative data

${\displaystyle {\begin{matrix}304\,{\text{Jahre}}&=&{}\quad 111035{,}0000\,{\text{Tage}}/{\text{Kalendersystem}}\\304\,{\text{Jahre}}&=&{}\quad 111033{,}6592\,\mathrm {Tage} /{\text{Sonnenumlauf}}\end{matrix}}}$

Calendar deviation

${\displaystyle {\begin{aligned}1{,}3408\,{\text{Tage}}\quad {\text{in}}\,&304\,{\text{Jahren}}\\1\,{\text{Tag}}\quad {\text{in}}\,&226{,}73031\,{\text{Jahren}}\end{aligned}}}$

Comparison of a cycle duration in the years from 1696 to 2000

In the course of the year the values ​​for the solar year changed due to the precession. A Hipparchus cycle that would have ended in 2000 shows the following comparative values:

Sun orbit of the earth

${\displaystyle {\begin{matrix}1\,{\text{Jahr}}&=&{}\ 365,24223\,{\text{Tage}}\\304\,{\text{Jahre}}&=&111033,6379\,{\text{Tage}}\end{matrix}}}$

Comparative data

${\displaystyle {\begin{matrix}304\,{\text{Jahre}}&=&{}\quad 111035{,}0000\,{\text{Tage}}/{\text{Kalendersystem}}\\304\,{\text{Jahre}}&=&{}\quad 111033{,}6379\,{\text{Tage}}/{\text{Sonnenumlauf}}\end{matrix}}}$

Calendar deviation

${\displaystyle {\begin{aligned}1{,}3621\,{\text{Tage}}\quad \mathrm {in} \,&304\,{\text{Jahren}}\\1\,{\text{Tag}}\quad \mathrm {in} \,&223{,}18479\,{\text{Jahren}}\end{aligned}}}$

See also

• Meton cycle

literature

• Otto Neugebauer : The Metonic and the Callippic Cycle In: Otto Neugebauer: A history of ancient mathematical astronomy . Springer, Berlin 2006 (reprint 1975), ISBN 3-540-06995-X , pp. 622-624.

Remarks

1. ↑ ^{a b} The solar year at that time was a little longer compared to today's value due to the precession (data from Jean Meeus ).