<p>I am learning astronavigation. I arrived to formulas for height and azimuth of heavenly bodies.</p>
<p>I can easily find equations I and II from screenshot (the book is &quot;The American Practical Navigator - An Epitome Of Navigation by Nathaniel Bowdith):</p>
<p><a href="https://i.sstatic.net/idwpn.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/idwpn.png" alt="Formulas" /></a></p>
<p>These two come from navigational triangle which can be solved using spherical cosine law.</p>
<p>However, I can't derive or find any clue where does the III formula comes from? It allows to calculate azimuth (Z) independently of heavenly body height (using Local Hour Angle instead).</p>
<p>Will be very grateful for every aid!</p>
<p>Thanks</p>

CC BY-SA 4.0
2023-09-12T21:48:31.550Z
“Heavenly body height” is indeed in the formula: d is the object’s declination, so its “height” in the sky…
Pierre Paquette
CC BY-SA 4.0
2023-09-13T02:13:02.390Z
This link's "atan2 method" explains that your eq III is derived from two other equations for Az.  https://www.celestialprogramming.com/convert_ra_dec_to_alt_az.html
Greg Miller
CC BY-SA 4.0
2023-09-14T18:09:50.980Z
@PierrePaquette Is heavenly used to indicate height in the sky?
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<navigation><azimuth>
Azimuth formula (independent of height of body)
3igen3ggy
# Azimuth formula (independent of height of body)

(Asked by: username_0 on 2023-09-12)

I am learning astronavigation. I arrived to formulas for height and azimuth of heavenly bodies.

I can easily find equations I and II from screenshot (the book is "The American Practical Navigator - An Epitome Of Navigation by Nathaniel Bowdith):

[![Formulas](https://i.sstatic.net/idwpn.png)](https://i.sstatic.net/idwpn.png)

These two come from navigational triangle which can be solved using spherical cosine law.

However, I can't derive or find any clue where does the III formula comes from? It allows to calculate azimuth (Z) independently of heavenly body height (using Local Hour Angle instead).

Will be very grateful for every aid!

Thanks

**Tags:** navigation, azimuth
> **Comments:**
> **username_1**: “Heavenly body height” is indeed in the formula: d is the object’s declination, so its “height” in the sky…  
> **username_2**: This link's "atan2 method" explains that your eq III is derived from two other equations for Az.  https://www.celestialprogramming.com/convert_ra_dec_to_alt_az.html  
> **username_3**: @PierrePaquette Is heavenly used to indicate height in the sky?  

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## 0 answers

