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I've read (in Gates to the Hebrew calendar p.128 and other sources) that the Earth orbits the Sun in 365.256 days, but each 1000 years the year becomes shorter by 5.5 seconds.

"The accurate length of the year is 365 days, 5 hours, 48 minutes, and 45.216 seconds. However this time is going and becoming shorter by 5.5 seconds each 1000 years.

Does this mean that in 10000 years it'll become shorter by 55 seconds, and in 100 years it'll become shorter by 9.16 minutes? What's the explanation for the year shortening with time?

[N.b. I've not read the first book mentioned above and the cite is a translation was presented by a lecturer from which I took notes. Therefore, it could be that the original book contains the explanation. I have no way to check it and that's why I'm seeking here the explanation]. 

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  • $\begingroup$ Mind giving sources for all these claims? $\endgroup$ Apr 14 '20 at 23:26
  • $\begingroup$ According to my notes, I copied this information to my computer from a translated cite of the book "Gates to the Hebrew calendar" p.128 [1]: google.com/… $\endgroup$ Apr 14 '20 at 23:59
  • $\begingroup$ Here is the full cite: "The accurate length of the year is 365 days, 5 hours, 48 minutes, and 45.216 seconds. However this time is going and becoming shorter by 5.5 seconds each 1000 years" $\endgroup$ Apr 15 '20 at 0:07
  • $\begingroup$ Other sources that might be helpful: aviation_dictionary.enacademic.com/6939/tropical_year and this one: aa.quae.nl/en/antwoorden/kalenders.html#v578 $\endgroup$ Apr 15 '20 at 10:52
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    $\begingroup$ Note that "365 days, 5 hours, 48 minutes, and 45.216 seconds" is 365.24219 days rather than 365.256 days. Your question conflates sidereal years (365.256 days) with tropical years (365.24219 days). $\endgroup$ Apr 15 '20 at 11:52
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First we need to decide what you mean by "year"

The first time period you mention "365.256" is the Orbital period of the Earth. It is equal 365 days, 6 hours, 8 minutes, 38 seconds.

The second period is the tropical year, the time between two equinoxes. They are not equal because this period depends on the tilt of the Earth. As the tilt changes (called precession) the tropical year is about 20 minutes shorter than the orbital period of the Earh. Since this is the time between seasons, this is the length of the year that is more important practically, and is the basis of most calendars.

These periods do change over time. This is due to solar system dynamics. The Tropical year can change because the rate of precession is not constant.

The Orbital period also changes due to perturbations from other planets (mostly Venus and Jupiter) The Earth can gain some orbital Energy from other planets, causing it to move slightly further from the sun and increase the length of the year. It could also lose some energy, causing it to approach the sun and shorten the length of the year.

This rate of change is not constant. And over the long term the Earth sometimes gains energy and sometimes loses. Currently, the Earth is gaining energy (mostly from Jupiter) and the distance to the sun is increasing by 0.0005% each year

However if you look at the average changes over a period of 6000 years, there is almost no change in the length of the orbital period. In fact, on average over a period from 3000BCE to 3000CE the Earth has actually lost energy and the distance to the sun has dropped by 0.000003% per year. (Figures from https://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf)

Your value of 5.5 seconds relates to the tropical year and so includes second-order precessional effects.

While these can be usefully modeled by a linear formula over 1000 years, this is just an approximation and over the longer term the actual orbit of the Earth is pretty stable.

Over the very long term (billions of years) other factors, such as loss of mass by the sun need to be considered, but that is not the cause of the short term variation in year length.

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  • $\begingroup$ Thank you for your answer. I added some references above. Anyway, I think I understood from your answer that it's not really changing over the years, while according to the sources mentioned above by me it's changing ever year for real (see here in clause 4: aa.quae.nl/en/antwoorden/kalenders.html#v578 $\endgroup$ Apr 15 '20 at 10:57
  • $\begingroup$ It is changing for real. And over a thousand years, that change can be modelled as a linear function. But over the longer term it is not linear and can get both longer and shorter. $\endgroup$
    – James K
    Apr 15 '20 at 12:43
  • $\begingroup$ Does it mean it isn't predictable? $\endgroup$ Apr 15 '20 at 14:18
  • $\begingroup$ Not in the long term. The solar system is technically "chaotic" which means that the long term behaviour isn't predictable $\endgroup$
    – James K
    Apr 15 '20 at 17:01

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