<p>I'm not absolutely sure if it is correct, but I use information from this site: <a href="http://star-www.st-and.ac.uk/~fv/webnotes/chapt9a.htm" rel="nofollow">http://star-www.st-and.ac.uk/~fv/webnotes/chapt9a.htm</a></p>

<p>And I convert equatorial coordinates (RA = α, Dec = δ) to ecliptic coordinates (λ, β)  using this formula.</p>

<blockquote>
  <p>sin(β) = sin(δ) cos(ε) - cos(δ) sin(ε) sin(α)</p>
  
  <p>cos(λ) cos(β) = cos(α) cos(δ)</p>
  
  <p>ε = Axial tilt (23,5°)</p>
</blockquote>

<p>I know that due to precession only λ changes (β remains same for ecliptic coordinates). So I add the angle of precession to the λ. Then I convert the new λ and β back to the equatorial coordinates.</p>

<blockquote>
  <p>sin(δ) = sin(β) cos(ε) + cos(β) sin(ε) sin(λ) </p>
  
  <p>cos(λ) cos(β) = cos(α) cos(δ)</p>
</blockquote>

CC BY-SA 3.0
2016-03-21T21:15:30.403Z
I guess this might work, but not very well over 3000 years because the ecliptic pole isn't fixed, but moves at 0.5 arcsec/yr.
ProfRob
CC BY-SA 3.0
2016-03-21T15:51:07.617Z
2016-03-21T15:51:07.617Z
Brob
<p>I have this problem: I want to calculate the declination of the star in the year 5000. And I know <strong>RA</strong> (right ascension) and <strong>Dec</strong> (declination) of the star right now.</p>

<p>How can I calculate it using spherical trigonometry.</p>

<blockquote>
  <p>I know that the declination changes over time due to the precession
  and somewhere I read that I should use spherical triangle, but I am not
  really sure how to use it.</p>
</blockquote>

<p>Thank you for your ideas.</p>

<coordinate><declination>
Declination change due to precession
Brob
# Declination change due to precession

(Asked by: username_0 on 2016-03-18)

I have this problem: I want to calculate the declination of the star in the year 5000. And I know **RA** (right ascension) and **Dec** (declination) of the star right now.

How can I calculate it using spherical trigonometry.

> I know that the declination changes over time due to the precession
> and somewhere I read that I should use spherical triangle, but I am not
> really sure how to use it.

Thank you for your ideas.

**Tags:** coordinate, declination

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## 1 answers

### Answer by username_0 on 2016-03-21. Score: 0 | Accepted answer

I'm not absolutely sure if it is correct, but I use information from this site: <http://star-www.st-and.ac.uk/~fv/webnotes/chapt9a.htm>

And I convert equatorial coordinates (RA = α, Dec = δ) to ecliptic coordinates (λ, β) using this formula.

> sin(β) = sin(δ) cos(ε) - cos(δ) sin(ε) sin(α)
>
> cos(λ) cos(β) = cos(α) cos(δ)
>
> ε = Axial tilt (23,5°)

I know that due to precession only λ changes (β remains same for ecliptic coordinates). So I add the angle of precession to the λ. Then I convert the new λ and β back to the equatorial coordinates.

> sin(δ) = sin(β) cos(ε) + cos(β) sin(ε) sin(λ)
>
> cos(λ) cos(β) = cos(α) cos(δ)

> **Comments:**
> **username_1**: I guess this might work, but not very well over 3000 years because the ecliptic pole isn't fixed, but moves at 0.5 arcsec/yr.  

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