<p>It may be easier to visualize the formula by calculating the altitude based on the observer's latitude (lat) and the object's declination (<span class="math-container">$\delta$</span>), and then re-arranging the equation to find the observer's latitude. First, the equation is only true when the object is on the meridian. Here is a diagram through the meridian (for an observer at a northern latitude):
<a href="https://i.sstatic.net/J6Tbu.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/J6Tbu.png" alt="cross section through zenith" /></a></p>
<p>Since the declination at the zenith equals the latitude, the altitude of the celestial equator = 90-lat. Then the altitude of an object south of the zenith is
<span class="math-container">$$alt_s = (90-lat)+\delta_s$$</span>
<span class="math-container">$$lat=\delta_s+(90-alt_s)$$</span>
where <span class="math-container">$\delta_s$</span> is the declination of the object <strong>south of the zenith</strong> and <span class="math-container">$alt_s$</span> is the altitude measured from the southern horizon. Do not confuse <span class="math-container">$\delta_s$</span> to mean an object south of the equator!</p>
<p>For an object between the zenith and the celestial pole, the altitude is 180 minus the above formula, or
<span class="math-container">$$alt_n = 180-[(90-lat)+\delta_n]$$</span>
<span class="math-container">$$lat=\delta_n-90+alt_n$$</span>
<span class="math-container">$$lat=\delta_n-(90-alt_n)$$</span>
where <span class="math-container">$\delta_n$</span> is the declination of the object north of the zenith and <span class="math-container">$alt_n$</span> is the altitude measured from the northern horizon.</p>
<p>For an object between the celestial pole and the north horizon (that is, at lower culmination), another formula is required!</p>

CC BY-SA 4.0
2021-12-27T20:38:51.680Z
2021-12-27T20:38:51.680Z
JohnHoltz
<p>The <a href="https://en.wikipedia.org/wiki/Equatorial_coordinate_system" rel="nofollow noreferrer">celestial equator</a> is a projection of the terrestrial equator on the celestial sphere. So doesn't that mean the geographical latitude and the declination will be &quot;exactly&quot; equal, as they are measured from the same reference point (Celestial Equator = Geographical Equator)?</p>
<p><span class="math-container">$$\lambda = \delta \pm (90° - \rm{Altitude})$$</span></p>
<p>latitude = the star's declination ± its zenith distance
= the star's declination ± (90° - the star's altitude)
Source : <a href="https://cseligman.com/laboratory/navcalc.htm" rel="nofollow noreferrer">https://cseligman.com/laboratory/navcalc.htm</a></p>
<p>So what is the meaning of this formula as Latitude = Declination?
Also I'm unable to understand that plus-or-minus sign (north of zenith and south of zenith).</p>

CC BY-SA 4.0
2021-12-26T11:08:37.410Z
One more question In that equation we take the altitude of lower culmination or upper culmination. For example If a question is like this - " The altitudes of a circumpolar star at culminations are 70° and 10°, both culminations being north of zenith". And we have to find declination there will be two choices for altitude to put in that equation. Also I'm confused in south/north of zenith ( the plus minus sign) as mentioned above.
Particle king
CC BY-SA 4.0
2021-12-27T01:43:40.693Z
You should clarify what the equation is supposed to represent. I do not recognize the "random" formula.

Once we know what that formula is about, we can answer the other questions.
JohnHoltz
CC BY-SA 4.0
2021-12-27T04:06:31.330Z
@JohnHoltz https://cseligman.com/laboratory/navcalc.htm "latitude = the star's declination ± its zenith distance
= the star's declination ± (90° - the star's altitude)"
Particle king
CC BY-SA 4.0
2021-12-27T07:58:05.150Z
Yes, Studied them for Indian Astronomy Olympiad.
Particle king
CC BY-SA 4.0
2021-12-27T08:00:23.213Z
That plus - minus sign.
Particle king
CC BY-SA 4.0
2021-12-27T08:00:39.440Z
It says , south of zenith take +ve In north -ve but how will I know what is south of zenith what is north of zenith?
Particle king
CC BY-SA 4.0
2021-12-27T08:04:08.417Z
@Wanderer see this https://www.timeanddate.com/astronomy/horizontal-coordinate-system.html
Kavin Ishwaran
<coordinate><positional-astronomy>
What is the connection between declination and latitude?
Particle king
# What is the connection between declination and latitude?

(Asked by: username_0 on 2021-12-26)

The [celestial equator](https://en.wikipedia.org/wiki/Equatorial_coordinate_system) is a projection of the terrestrial equator on the celestial sphere. So doesn't that mean the geographical latitude and the declination will be "exactly" equal, as they are measured from the same reference point (Celestial Equator = Geographical Equator)?

$$\lambda = \delta \pm (90° - \rm{Altitude})$$

latitude = the star's declination ± its zenith distance
= the star's declination ± (90° - the star's altitude)
Source : <https://cseligman.com/laboratory/navcalc.htm>

So what is the meaning of this formula as Latitude = Declination?
Also I'm unable to understand that plus-or-minus sign (north of zenith and south of zenith).

**Tags:** coordinate, positional-astronomy

> **Comments:**
> **username_0**: One more question In that equation we take the altitude of lower culmination or upper culmination. For example If a question is like this - " The altitudes of a circumpolar star at culminations are 70° and 10°, both culminations being north of zenith". And we have to find declination there will be two choices for altitude to put in that equation. Also I'm confused in south/north of zenith ( the plus minus sign) as mentioned above.  
> **username_1**: You should clarify what the equation is supposed to represent. I do not recognize the "random" formula.  Once we know what that formula is about, we can answer the other questions.  
> **username_0**: @username_1 https://cseligman.com/laboratory/navcalc.htm "latitude = the star's declination ± its zenith distance = the star's declination ± (90° - the star's altitude)"  
> **username_0**: Yes, Studied them for Indian Astronomy Olympiad.  
> **username_0**: That plus - minus sign.  
> **username_0**: It says , south of zenith take +ve In north -ve but how will I know what is south of zenith what is north of zenith?  
> **username_2**: @Wanderer see this https://www.timeanddate.com/astronomy/horizontal-coordinate-system.html  

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## 1 answers

### Answer by username_1 on 2021-12-27. Score: 3 | Accepted answer

It may be easier to visualize the formula by calculating the altitude based on the observer's latitude (lat) and the object's declination ($\delta$), and then re-arranging the equation to find the observer's latitude. First, the equation is only true when the object is on the meridian. Here is a diagram through the meridian (for an observer at a northern latitude):
[![cross section through zenith](https://i.sstatic.net/J6Tbu.png)](https://i.sstatic.net/J6Tbu.png)

Since the declination at the zenith equals the latitude, the altitude of the celestial equator = 90-lat. Then the altitude of an object south of the zenith is
$$alt\_s = (90-lat)+\delta\_s$$
$$lat=\delta\_s+(90-alt\_s)$$
where $\delta\_s$ is the declination of the object **south of the zenith** and $alt\_s$ is the altitude measured from the southern horizon. Do not confuse $\delta\_s$ to mean an object south of the equator!

For an object between the zenith and the celestial pole, the altitude is 180 minus the above formula, or
$$alt\_n = 180-[(90-lat)+\delta\_n]$$
$$lat=\delta\_n-90+alt\_n$$
$$lat=\delta\_n-(90-alt\_n)$$
where $\delta\_n$ is the declination of the object north of the zenith and $alt\_n$ is the altitude measured from the northern horizon.

For an object between the celestial pole and the north horizon (that is, at lower culmination), another formula is required!


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