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why do they take λ₁ = 1 295 977 422.834 29ʺ from subsection 5.8.3.¹ (mean elements referred to the mean dynamical ecliptic and equinox J2000), and not λ₁ = 1 296 027 711.034 29ʺ from subsection 5.9.3.¹ (mean elements referred to the mean dynamical ecliptic and equinox of date), when they obtain the sidereal year of the Earth from its mean longitude at t = 0?

  1. Numerical Expressions for Precession Formulae And Mean Elements for the Moon And the Planets (Simon et al., 1994)
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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Feb 19, 2022 at 6:54
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    $\begingroup$ The difference is between referring to the rate of change of $\lambda$ with respect to the J2000 ecliptic and equinox, or with respect to the moving ecliptic and equinox of time t. It isn't clear to me which value has been used but the reason for the choice can probably be best confirmed by Christian Bizouard christian.bizouard[at]obspm.fr (I'd speculate that it is because the J2000 ecliptic is fixed wrt distant objects, which is required for a calculation of the sidereal year) $\endgroup$
    – James K
    Feb 19, 2022 at 9:52
  • $\begingroup$ thank you, James. now i see. i don't know why you wrote it as a comment and not an answer. i'd accept it. i can't add a plus to the comment because i've got too little reputation in the community as of now. $\endgroup$
    – theorist
    Feb 19, 2022 at 10:59

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Adding to what James K already helpfully posted:

The second figure quoted in the question, 1 296 027 711.034 29 (arc"/julian millennium wrt (moving) equinox of date), gives the mean tropical year (close to 365.24219 days).

The first figure quoted, 1 295 977 422.834 29( arcʺ/julian millennium wrt fixed equinox of J2000), is the real motion with respect to the stars, and gives therefore the mean sidereal year (close to 365.25636 days).

I hope that helps a bit.

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    $\begingroup$ @theorist In Stack Exchange we generally post follow-up questions as new questions, and within them include links back to the previous question and/or answer from which it flows. Questions in comments are not easily found in searches and the whole idea behind Stack Exchange is to generate answers that are as useful to future readers as they are to the asker. You can ask as many on-topic questions as you like; the sky's the limit! $\endgroup$
    – uhoh
    Feb 20, 2022 at 6:02

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