Clocks of the Universe with Mihir Kulkarni

What is today’s date?  Well, depending on which calendar you use, that could be an interesting discussion.  On Friday evening, September 21, 2018—based on the Gregorian calendar that we currently use in the US and much of the world—Mihir Kulkarni, graduate student in astronomy at Columbia University, explained the science and history of calendars throughout the world and throughout history.

We take calendars for granted in everyday life.  A day is 24 hours and a year is 365 days most of the time.  But it’s actually far more complicated than that.

As Kulkarni explained, a synodic day (or solar day) is the amount of time it takes the Earth to complete a rotation about its axis with respect to the sun, which is about 4 minutes longer than a sidereal day, which is the amount of time it takes to complete a rotation with respect to the background stars.

Slide By: Mihir Kulkarni

It gets worse. A year is defined as the amount of time it takes for the Earth to make a complete orbit around the sun.  But how do you measure that?  If you measure the year against the background stars, a sidereal year is 365.25636 days. A tropical year is defined as the time it takes the Earth to travel along the ecliptic from one vernal equinox to the next, which equates to 365.24189 days, shorter than the sidereal year by almost 20 minutes.  A lunar year consists of 12 lunar months (a lunar month being the time between identical lunar phases), which equates to 354 or 355 days.  There are even lunisolar calendars (such as the Hebrew and some Indian calendars), where a month is a lunar month, but additional months are added periodically to keep the calendar consistent with the solar year.

Slide By: Mihir Kulkarni

What causes these differences?  Kulkarni explained that two major factors are the obliquity of Earth’s axis and the eccentricity of Earth’s orbit.  The obliquity refers to the (slightly variable) 23.5° tilt of Earth’s axis relative to the plane of Earth’s orbit around the Sun, which creates the differences between the ecliptic and the equator (thereby creating our seasons).  If the Earth’s axis were perfectly perpendicular to its orbital plane (i.e., zero obliquity) then the Sun would cross the Meridian at noon every day of the year (which is not the case).

The second of these complicating factors refers to the fact that Earth’s orbit is an ellipse rather than a perfect circle.  Referencing Johannes Kepler, Kulkarni noted that under Kepler’s second law, the Earth moves faster in its orbit when it is closer to the Sun, and slower when it is farther.

Finally, there is the precession of the Earth’s axis as it orbits the Sun.  Like a spinning top, although the Earth maintains the 23.5° axial tilt, the direction in which the Earth’s poles point changes, or precesses over the course of 26,000 years.  Right now the North Star is Polaris. In 3000 B.C. it was Thuban rather than Polaris, and in 1000 B.C. it was Kochab.  In 13,000 A.D. Vega will be our North Star.  As Kulkarni explained, this is the reason for the differences between the sidereal year and the tropical year.  If we do not wish our seasons to slowly migrate through the calendar, we need to use the tropical calendar (which we don’t).

Slide By: Mihir Kulkarni

So what’s the date today, really?

Many have tried to answer this question.  Notably Julius Caesar in 46 BC (whenever that means).  Under the Julian calendar, a day is exactly 24 hours, there are 365 days per year except for Leap years with 366 days.  The moon orbit around Earth is not taken into account.  The difference between a Julian year and a tropical year is one day per 128 years, which causes the equinoxes (and the seasons as well) to shift under the Julian calendar to earlier and earlier dates.  This eventually created a problem for the Catholic church as Kulkarni’s chart demonstrates:

Slide By: Mihir Kulkarni

By the XVIth century, it was clear that this couldn’t continue, and Pope Gregory XIII therefore instituted the Gregorian calendar.  To catch up with the tropical year, the day after October 4, 1582 was defined as October 15, 1582!  A slight change was made to Leap years:  if the year is divisible by 100 then it must also be divisible by 400 to be a Leap year.  (So for example, 1700 AD was not a Leap year.)  Although this was a significant improvement, allowing us to still use the Gregorian calendar to this day, not every country adopted the Gregorian calendar immediately.  As Kulkarni recounted, the Catholic countries were of course the first to do so.  But Protestant Britain and its colonies made the catchup from September 2, 1752 to September 14, 1752, a century and a half later.  And Russia changed only in 1918, meaning that the “October Revolution” which took place on October 25, 1917, actually took place in November using the Gregorian calendar!  If you think international differences in Daylight Savings Time dates are a problem, imagine what it must have been like living with these discrepancies!

But the Gregorian calendar is still “off” relative to the tropical calendar by 1 day every 3200 years.  If we are sufficiently lucky to survive long enough, we will eventually need another calendar reform.

Kulkarni finished by mentioning still another time system:  Unix time.  A Unix day has 84,600 seconds, or exactly 24 hours.  But since 1970, Leap seconds have been periodically inserted to keep in synch with the Gregorian calendar.

Incidentally, if you are interested in learning more about calendar systems, you might consider enrolling in the AAA’s course Clocks, Calendars, Coordinates and Orbits, offered from time to time by our own David Kiefer!

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