PX158 - B3 - measuring time

a day

• sidereal day : a full rotation of the earth $\approx 23h56min$
• solar day : time taken for the sun to return to the same part of the sky $\equiv 24hours$
  • for the solar day to be equal to the sidereal day, it must be: $\frac{24}{365}hours\approx 4mins$ longer

calendars

the sumerians

• a calendar with $360days=12months\times 30days$
• introduced a leap month every four years to make up for the true length of the year $\approx 365.25days$

the romans

• introduced the julian calendar, which had $365days$ a year
• added a leap day every four years
• but the earth's orbital period is $365.24219days$

the present

• in $1582$, pope gregory introduced a modification whereby some leap days are skipped to make up for the difference — the gregorian calendar
• not all countries adopted this at the same time, resulting in differences of $10days$ in different systems