Ask Ethan: How long until our calendar needs replacing?

KEY TAKEAWAYS

  • Every year, Earth’s rotational period changes slightly, and over long enough times, so will the number of days in a year. 
  • Even with everything we’ve done to accurately compute those changes, our modern calendar will only last a few millennia more before further changes are needed. 
  • Eventually, leap years will go away entirely, and then we’ll start needing to remove days. In time, even total solar eclipses will cease.

Even with leap years and long-term planning, our calendar won’t be good forever. Here’s why, and how to fix it.

by Ethan Siegel

With every year that passes, we assume that two separate things will both line up. One is the seasonal year on Earth: the progression from winter to spring to summer to fall and back around again, coinciding with the periodic solstices and equinoxes as well. On the other hand, there’s also the astronomical year: where the Earth completes a full revolution around the Sun and returns to the same point in its orbit. The whole point of switching to the calendar we now use — the Gregorian Calendar — was to make sure that these two ways of tracking the passage of a year, using the Tropical Year (which aligns with the seasons) rather than the Sidereal Year (which aligns with Earth’s orbit).

But even by choosing the Tropical year, our calendar won’t in fact, always line up, even with our modern knowledge of timekeeping. That’s because the orbital properties of Earth itself are changing over time, and once enough time passes, we’ll have to modify our calendar to keep up. But how long do we have, and how will we need to modify it? That’s what Alisa Rothe wants to know, asking:

“[I read that] the Earth is slowing down in its orbit around the Sun. Does this mean that we will eventually have to add another day to our calendar year? How much time will pass before that becomes necessary? And in the same way, did a year used to contain fewer days 4.5 billion years ago?”

These are great questions. But to find out the answers, we have to look at all the changes that are happening together, to see which ones matter the most.

calendar
The presence or absence of a February 29 on the calendar determines with great significance whether the equinox shifts forwards or backwards in time from the prior year’s equinox. 2020 marked the first year since 1896 where the entire United States experienced a March 19 equinox. Leap days don’t occur every 4 years, and we’ll need to change their frequency to keep up with the calendar. (Credit: Getty Images)

Let’s start by answering a simpler question: right now, how good is the matchup between the “calendar year” and the actual Tropical Year?

The Tropical Year is the same whether you measure it from:

  • summer solstice to summer solstice,
  • winter solstice to winter solstice,
  • spring equinox to spring equinox,
  • autumnal equinox to autumnal equinox,

or any other point in time, based on the Sun’s position in the sky relative to Earth, as it was the year before. To calculate the tropical year, you have to fold in not just Earth spinning on its axis and revolving around the Sun, but also the precession of the equinoxes and all other orbital changes.

Basically, if you took a look at Earth’s axis and said, “this is how it’s oriented, with respect to the Sun, right at this moment,” a single Tropical Year would mark the very next time that the Earth’s axis returned to that exact same orientation. It’s not quite the same as a 360° revolution around the Sun, but off by a small amount. In terms of the amount of time it takes to make up one Tropical Year today, it’s precisely 365.2422 days. In more conventional terms, that’s 365 days, 5 hours, 48 minutes, and 45 seconds.

To travel once around Earth’s orbit in a path around the Sun is a journey of 940 million kilometers. The extra 3 million kilometers that Earth travels through space, per day, ensures that rotating by 360 degrees on our axis won’t restore the Sun to the same relative position in the sky from day to day. This is why our day is longer than 23 hours and 56 minutes, which is the time required to spin a full 360 degrees. (Credit: Larry McNish at RASC Calgary Centre)

The fact that our Tropical Year isn’t perfectly divisible into a whole number of days is the reason for our relatively complex system of leap years: years where we do (or don’t) insert an extra day into our calendar. Most years, we assign 365 days to our calendar, while on leap years, we add in a 366th day: February 29th.

Originally, we kept time using the Julian Calendar, which added that 366th day in every four years: on a leap year. This led to a long-term estimate of 365.25 days in a year, meaning that for every four years that passed on our calendar, we were moving out-of-sync with the actual Tropical Year by 45 minutes…

more…

https://bigthink.com/starts-with-a-bang/calendar/

F. Kaskais Web Guru

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