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Twice Around the Sun

Today is my little boy’s second birthday. He was born at 0940 on Wednesday 17 June 2009, and so today is the day that the Earth completes two orbits of the Sun since his birth.

However at 0940 today the Earth will not quite have completed its two orbits of the Sun; it will have a little bit further to go. Around 1.3 million km further to go to be precise, and it’ll cover that distance in 12h 18m 20s…

Happy Second Birthday!

Our calendar year is divided up into 365 days, the closest whole number of days to the actually time it takes to Earth to orbit the Sun, called the sidereal year, which is equal to 365.256363004 days.

Therefore the year (the time it takes the Earth to orbit the Sun) isn’t exactly 365 days long, and so every four years we add on one extra day in February to get a 366 leap year to make up for the difference.

If we didn’t do this, and instead insisted that the year was always 365 days long, the seasons would begin to drift until midsummer’s day (21 June on our calendars) would fall in the middle of winter within 753 years, a problem for our descendents. *

So, since my son was born there have been 2 x 365 days marked off on our calendar (730 days), but in order for the Earth to make two complete orbits of the Sun we have to wait 2 x 365.256363004 = 730.512726008 days, or an extra 0.512726008 days, which equals 12h 18m 20s.

My son was born at 0940, and so he will be two sidereal years old at 2158 this evening.

If I was interested in the instant when the Sun returned to exactly the same point within the cycle of the seasons I would have to carry out the same calculation except this time using the tropical year of 365.24219 days. In this case two tropical years equals 730.48438 days, or an extra 0.48438 days, which equals 11h 37m 30s.

My son will be two tropical years old at 2117 this evening.

Happy birthday, little spaceman!

* We have to calculate the drift based on the tropical year, the length of time it takes for the Sun to return to the same place in the cycle of the seasons, which is equal to 365.24219 days. A basic 365 day year differs from this by 5h 48m 45s, which would result in the seasons drifting so that midsummer’s day falls in midwinter in 753 years.

Even the 365.25 day leap year differs from this tropical year by 11m 15s, resulting in a drift which happens much more slowly than 753 years, but it still happens, taking 23,383 years for midsummer’s day to fall in the middle of winter. To correct for this we fine-tune our leap year formula so that we do not add in an extra day in a year which is divisible by 100 unless it is also divisible by 400!

This makes the average length of a year 365.2425 days, which still differs from the tropical year by 26.8 seconds. This barely matters, and no further corrections to our calendar are needed since the seasonal drift in this case will take over 500,000 years to happen, and by that time the Earth’s year will have changed in length anyway!

Year Length of Year (days) Difference from Tropical Year (seconds)
Tropical Year 365.24219 0
Basic Year 365 20,925s (5h 48m 45s)
Simple Leap Year 365.25 675s (11m 15s)
Fine-tuned Leap Year 365.2425 26.8s
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