American in Spain

Days Getting Longer

December 22, 2006

May I be the first to wish you a Happy Winter Solstice! Finally, some hope of respite from the darkness we were thrust into in October with the end of our arbitrarily-imposed daylight savings time. However, it's not the amount of daylight, as affected by our latitude and location in orbit around the sun, that I want to talk about. It's the actual length of the day, the amount of time it takes for the Earth to make one rotation.

I recently found this awesome article, called Tides, the Earth, the Moon, and why our days are getting longer, which explains what it says it does:

This missive explains the following:

  1. Why the Moon always shows the same face to the Earth.
  2. Why the Moon's rotation period is the same as the length of time it takes to orbit the Earth (same as number 1, but phrased differently).
  3. Why there are two tides a day.
  4. Why the Earth's rotation rate is slowing.

Before reading the article I had forgotten why there are two tide cycles per day, and why there is a high tide on the side opposite the moon as well. That's pretty fascinating in itself. I was also aware that the official time keepers were having to add leap seconds to our atomic clocks, but I didn't understand why. This article clearly explains why, just as we see the same face of the Moon at all times, eventually the Earth's rotation will slow down until the Moon sees the same face of Earth at all times, and it will take a lunar month (27.3 current earth-days) for our beloved planet to make one rotation, effectively making the Moon's orbit geosynchronous.

So how long will this slowing process take? That's what I want to know. I made a very simplified, and obviously wrong, calculation based on the fact that the length of the day is currently increasing at a rate of 0.7 seconds per year. If this rate of angular deceleration continues, it will take...

(27.3 - 1) * 24 * 60 * 60 / 0.7 = 3,246,171.4 years

...for the Earth's rotation to slow down to that of a lunar month. Three million years is hardly a blip on geological time scales, so this is clearly wrong. Obviously, as the article mentions, the rate of deceleration will decrease as it approaches the "lunar earth day" asymptote. Still, I wonder how long it will actually take...

I've emailed Philip Plait, the guy that runs that Bad Astronomy website, to ask if he knows the actual value, or how to calculate it.

Anyway, it's fun to think about. Can you imagine it being dark for 14 days and then light for 14 days?

May your solstice festivities be merry!