<p>The declination (<span class="math-container">$\delta$</span>) of the celestial pole is 90°. Therefore the angle <span class="math-container">$\alpha=90-\delta$</span> and 2 times that value would be <span class="math-container">$180-2\delta$</span>. Two Alpha is not the declination.</p>
<p>The zenith distance is the angle measured from the zenith. I have added that angle (to the upper culmination) in this diagram:
<a href="https://i.sstatic.net/poxED.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/poxED.png" alt="zenith distance" /></a></p>
<p>The zenith distance at upper culmination would be <span class="math-container">$(90-\delta_z)-(90-\delta) = \delta-\delta_z$</span> where <span class="math-container">$\delta_z$</span> is the declination of the zenith. At lower culmination the zenith distance would be <span class="math-container">$(90-\delta_z)+(90-\delta) = 180 -\delta-\delta_z$</span></p>

CC BY-SA 4.0
2021-12-28T17:20:36.060Z
2021-12-28T17:20:36.060Z
JohnHoltz
<p>Is it true that angle subtended by the Zenith Distance at Upper and Lower culminations is equal to the declination of the star ?If It's true then why? Is the motion of Earth make the solid angle of the cone subtended at the centre by circumpolar stars equal to the declination of the star?.<a href="https://i.sstatic.net/be8YO.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/be8YO.jpg" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-12-26T12:48:53.340Z
What is the source of this task? (It's considered bad form to do somebody's homework form them)
James K
CC BY-SA 4.0
2021-12-26T13:07:59.300Z
@James K Do you think such a drawing could be homework question. It's my personal observation I don't even know this is correct or not . I just framed it like that ,apologies for that.
Particle king
CC BY-SA 4.0
2021-12-26T13:19:56.237Z
Yes, I do think the question is homework.  Have you been measuring the zenithal distance of various stars (at lower and higher culimnation) and noticed a pattern?  I think it far more likely that you have an assignment to "Prove that the angle subtended by the Zenith Distance at Upper and Lower culminations is equal to the declination of the star and justify the answer."  which you have copied directly into the question box.
James K
CC BY-SA 4.0
2021-12-26T13:20:40.733Z
Now that's not necessarly bad.  But it needs to be acknowledged.
James K
CC BY-SA 4.0
2021-12-26T13:30:01.603Z
Why should I acknowledge if that's not the case. First thing, Astronomy is not taught in my school so from where will I get the assignmemt to copy? As I said I don't even know that statement is correct or not. It may be wrong. I was solving an example from the book  by AE ROY and I saw this pattern in it.
Particle king
CC BY-SA 4.0
2021-12-27T21:43:40.057Z
@JamesK please review the community's feelings on going after "suspected homework question askers". In stack Exchange we simply can't pursue user's motives, intentions, situations, etc. We have to address the question at face value. "What have you tried?" type queries are helpful, but "I think you are cheating or asking in bad faith" is just not a good way as it's unverifiable.
uhoh
CC BY-SA 4.0
2021-12-27T21:44:16.083Z
@JamesK review:  [I can't find this site's "homework policy" or find out how "suspected homework question askers" should be treated](https://astronomy.meta.stackexchange.com/q/473/7982) and also [Stop the off-hand "this sounds like a homework question" comments that offer no guidance and raise false flags?](https://astronomy.meta.stackexchange.com/q/762/7982)
uhoh
CC BY-SA 4.0
2021-12-27T21:47:10.700Z
As for "But it needs to be acknowledged." the only rules the site has are the ones that are in the help center or established by the community in meta. Can you link to the place where it says "But it needs to be acknowledged."  *Thanks!*
uhoh
<star><observational-astronomy><positional-astronomy>
Angle of Declination and Culminations
Particle king
# Angle of Declination and Culminations

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

Is it true that angle subtended by the Zenith Distance at Upper and Lower culminations is equal to the declination of the star ?If It's true then why? Is the motion of Earth make the solid angle of the cone subtended at the centre by circumpolar stars equal to the declination of the star?.[![enter image description here](https://i.sstatic.net/be8YO.jpg)](https://i.sstatic.net/be8YO.jpg)

**Tags:** star, observational-astronomy, positional-astronomy

> **Comments:**
> **username_1**: What is the source of this task? (It's considered bad form to do somebody's homework form them)  
> **username_0**: @username_1 Do you think such a drawing could be homework question. It's my personal observation I don't even know this is correct or not . I just framed it like that ,apologies for that.  
> **username_1**: Yes, I do think the question is homework.  Have you been measuring the zenithal distance of various stars (at lower and higher culimnation) and noticed a pattern?  I think it far more likely that you have an assignment to "Prove that the angle subtended by the Zenith Distance at Upper and Lower culminations is equal to the declination of the star and justify the answer."  which you have copied directly into the question box.  
> **username_1**: Now that's not necessarly bad.  But it needs to be acknowledged.  
> **username_0**: Why should I acknowledge if that's not the case. First thing, Astronomy is not taught in my school so from where will I get the assignmemt to copy? As I said I don't even know that statement is correct or not. It may be wrong. I was solving an example from the book  by AE ROY and I saw this pattern in it.  
> **username_2**: @JamesK please review the community's feelings on going after "suspected homework question askers". In stack Exchange we simply can't pursue user's motives, intentions, situations, etc. We have to address the question at face value. "What have you tried?" type queries are helpful, but "I think you are cheating or asking in bad faith" is just not a good way as it's unverifiable.  
> **username_2**: @JamesK review:  [I can't find this site's "homework policy" or find out how "suspected homework question askers" should be treated](https://astronomy.meta.stackexchange.com/q/473/7982) and also [Stop the off-hand "this sounds like a homework question" comments that offer no guidance and raise false flags?](https://astronomy.meta.stackexchange.com/q/762/7982)  
> **username_2**: As for "But it needs to be acknowledged." the only rules the site has are the ones that are in the help center or established by the community in meta. Can you link to the place where it says "But it needs to be acknowledged."  *Thanks!*  

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## 1 answers

### Answer by username_3 on 2021-12-28. Score: 1 | Accepted answer

The declination ($\delta$) of the celestial pole is 90°. Therefore the angle $\alpha=90-\delta$ and 2 times that value would be $180-2\delta$. Two Alpha is not the declination.

The zenith distance is the angle measured from the zenith. I have added that angle (to the upper culmination) in this diagram:
[![zenith distance](https://i.sstatic.net/poxED.png)](https://i.sstatic.net/poxED.png)

The zenith distance at upper culmination would be $(90-\delta\_z)-(90-\delta) = \delta-\delta\_z$ where $\delta\_z$ is the declination of the zenith. At lower culmination the zenith distance would be $(90-\delta\_z)+(90-\delta) = 180 -\delta-\delta\_z$


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