<p>The most precise and quite intuitive formula I could find online is here: <a href="https://www.celestialprogramming.com/snippets/angleBetweenEclipticAndHorizon.html" rel="nofollow noreferrer">https://www.celestialprogramming.com/snippets/angleBetweenEclipticAndHorizon.html</a></p>
<blockquote>
<p><span class="math-container">$$\cos I = \cos ϵ \sin ϕ − \sin ϵ \cos ϕ \sin θ$$</span></p>
<p>ϵ is the obliquity of the ecliptic (e.g. 23.4°), ϕ is latitude, θ is the Local Sidereal Time.</p>
</blockquote>
<p>Even though it makes sense that it depends on the sidereal time, latitude and inclination angle, I can't find a demonstration for this formula, so I'm wondering how can I demonstrate this formula?</p>

CC BY-SA 4.0
2023-06-24T01:54:41.393Z
@astridlovespie *Welcome to Stack Exchange!* By "demonstrate" do you mean to plot it, or explain it, or derive it, or... We don't normally say "demonstrate a formula". *Thanks!*
uhoh
CC BY-SA 4.0
2023-06-24T04:54:47.813Z
See https://en.wikipedia.org/wiki/Spherical_law_of_cosines
PM 2Ring
CC BY-SA 4.0
2023-06-24T22:24:29.600Z
Local sidereal time is an angle. 0 radians is when the plane of your local meridian passes the vernal equinox pi radians is 12 hours later.
stretch
CC BY-SA 4.0
2023-07-01T23:52:01.477Z
@ Greg Miller he may just be looking for the derivation. No one seems to know what he means by demonstration. His question is about your formula on a different site,
stretch
<the-sun><coordinate><ecliptic><horizon><spherical-astronomy>
Demonstration- formula for angle between horizon and ecliptic
astrid lovespie
# Demonstration- formula for angle between horizon and ecliptic

(Asked by: username_0 on 2023-06-23)

The most precise and quite intuitive formula I could find online is here: <https://www.celestialprogramming.com/snippets/angleBetweenEclipticAndHorizon.html>

> $$\cos I = \cos ϵ \sin ϕ − \sin ϵ \cos ϕ \sin θ$$
>
> ϵ is the obliquity of the ecliptic (e.g. 23.4°), ϕ is latitude, θ is the Local Sidereal Time.

Even though it makes sense that it depends on the sidereal time, latitude and inclination angle, I can't find a demonstration for this formula, so I'm wondering how can I demonstrate this formula?

**Tags:** the-sun, coordinate, ecliptic, horizon, spherical-astronomy

> **Comments:**
> **username_1**: @username_0 *Welcome to Stack Exchange!* By "demonstrate" do you mean to plot it, or explain it, or derive it, or... We don't normally say "demonstrate a formula". *Thanks!*  
> **username_2**: See https://en.wikipedia.org/wiki/Spherical_law_of_cosines  
> **username_3**: Local sidereal time is an angle. 0 radians is when the plane of your local meridian passes the vernal equinox pi radians is 12 hours later.  
> **username_3**: @ Greg Miller he may just be looking for the derivation. No one seems to know what he means by demonstration. His question is about your formula on a different site,  

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## 0 answers

