<p>Actually, you can do this with the setting first quarter moon, which is a special case. The following was noted in the answer given to a similar question, recently -</p>
<blockquote>
<p>The angle between the lunar line of demarcation and horizon at, or near, the time the first-quarter moon sets, can be easily determined on any date when the moon is in its first quarter, as the sum of the solar declination on that date and latitude of the observer.</p>
</blockquote>
<p>The answer is in regard to a similar aspect given <a href="https://astronomy.stackexchange.com/questions/41789/why-can-i-see-sometimes-a-horizontal-half-moon-instead-of-a-vertical-one/41895#41895">here</a>.  However, a line connecting the tips of the crescent will only be parallel to the north-south line at two specific times of the year.</p>

CC BY-SA 4.0
2022-01-01T19:37:20.497Z
2022-01-01T19:37:20.497Z
Thomas Perry
<p>They don't.  In this image (from 28th Dec 2021) the blue grid represents lines on an equatorial grid. The lines that run from top right to bottom left are North-South lines. The tips of the crescent very clearly don't point to the North.</p>
<p><a href="https://i.sstatic.net/njmt2.png" rel="noreferrer"><img src="https://i.sstatic.net/njmt2.png" alt="enter image description here" /></a></p>
<p>The moon is lit by the sun and both the sun and the moon are in the plane of the ecliptic (to within a few degrees). So, as the &quot;bulge&quot; of the crescent points towards the sun, and along the ecliptic,  The tips of the crescent will point towards the ecliptic pole which is about 23 degrees away from North.</p>
<p>However since the moon is not exactly on the ecliptic even this is not exactly correct, and close to new moon the tips of the moon could point almost anywhere (think how the invisibly thin cresent will rotate as the moon passes the sun on a new moon at which there is no eclipse.)</p>

CC BY-SA 4.0
2022-01-01T10:55:03.017Z
https://olympiads.hbcse.tifr.res.in/wp-content/uploads/ino20/INAO2020-Solutions-20200204.pdf   please check problem 7
Particle king
CC BY-SA 4.0
2022-01-01T10:57:10.030Z
https://www.naturalnavigator.com/find-your-way-using/moon/
Particle king
CC BY-SA 4.0
2022-01-01T11:05:23.163Z
@Particleking: Yes, it’s *basically* N–S, but it not always is *exactly* N–S. Meeus 1998 provides a formula for calculating the tilt of the Moon’s axis with respect to the celestial N–S line.
Pierre Paquette
CC BY-SA 4.0
2022-01-01T12:07:27.367Z
Whay about latitude?
Particle king
CC BY-SA 4.0
2022-01-01T12:16:05.907Z
Also could you please specify the chapter number where it is mentioned in Meenus 1998?
Particle king
CC BY-SA 4.0
2022-01-01T10:42:17.483Z
2022-01-01T10:42:17.483Z
James K
<p><a href="https://i.sstatic.net/znavv.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/znavv.jpg" alt="." /></a></p>
<p>Can it be shown mathematically that the line connecting tips of crescent is parallel to the North-South line and the line gives latitude of the plane ( When the Moon is sufficiently close to the horizon, we can approximate the surface of sky as a simple plane.)</p>
<p>Sources :</p>
<p><a href="https://olympiads.hbcse.tifr.res.in/wp-content/uploads/ino20/INAO2020-Solutions-20200204.pdf" rel="nofollow noreferrer">https://olympiads.hbcse.tifr.res.in/wp-content/uploads/ino20/INAO2020-Solutions-20200204.pdf</a></p>
<p><a href="https://www.naturalnavigator.com/find-your-way-using/moon/" rel="nofollow noreferrer">https://www.naturalnavigator.com/find-your-way-using/moon/</a></p>

CC BY-SA 4.0
2022-01-01T09:11:13.350Z
I think yes it can, perhaps faster in [Math SE](https://math.stackexchange.com/) than here if you need a proper mayhematical proof.
uhoh
CC BY-SA 4.0
2022-01-01T09:30:11.757Z
They said it's off topic there https://math.stackexchange.com/questions/4346311/tips-of-crescent
Particle king
CC BY-SA 4.0
2022-01-01T09:38:37.630Z
Here's a related question on our sister site: https://physics.stackexchange.com/q/6969/123208
PM 2Ring
CC BY-SA 4.0
2022-01-01T10:39:44.940Z
@Particleking ya it seems two long-time users mentioned that. Okay let's see what we can do here!
uhoh
<the-moon><positional-astronomy>
Tips of Crescent
Particle king
# Tips of Crescent

(Asked by: username_0 on 2022-01-01)

[![.](https://i.sstatic.net/znavv.jpg)](https://i.sstatic.net/znavv.jpg)

Can it be shown mathematically that the line connecting tips of crescent is parallel to the North-South line and the line gives latitude of the plane ( When the Moon is sufficiently close to the horizon, we can approximate the surface of sky as a simple plane.)

Sources :

<https://olympiads.hbcse.tifr.res.in/wp-content/uploads/ino20/INAO2020-Solutions-20200204.pdf>

<https://www.naturalnavigator.com/find-your-way-using/moon/>

**Tags:** the-moon, positional-astronomy

> **Comments:**
> **username_1**: I think yes it can, perhaps faster in [Math SE](https://math.stackexchange.com/) than here if you need a proper mayhematical proof.  
> **username_0**: They said it's off topic there https://math.stackexchange.com/questions/4346311/tips-of-crescent  
> **username_2**: Here's a related question on our sister site: https://physics.stackexchange.com/q/6969/123208  
> **username_1**: @Particleking ya it seems two long-time users mentioned that. Okay let's see what we can do here!  

---

## 2 answers

### Answer by username_4 on 2022-01-01. Score: 9 | Accepted answer

They don't. In this image (from 28th Dec 2021) the blue grid represents lines on an equatorial grid. The lines that run from top right to bottom left are North-South lines. The tips of the crescent very clearly don't point to the North.

[![enter image description here](https://i.sstatic.net/njmt2.png)](https://i.sstatic.net/njmt2.png)

The moon is lit by the sun and both the sun and the moon are in the plane of the ecliptic (to within a few degrees). So, as the "bulge" of the crescent points towards the sun, and along the ecliptic, The tips of the crescent will point towards the ecliptic pole which is about 23 degrees away from North.

However since the moon is not exactly on the ecliptic even this is not exactly correct, and close to new moon the tips of the moon could point almost anywhere (think how the invisibly thin cresent will rotate as the moon passes the sun on a new moon at which there is no eclipse.)

> **Comments:**
> **username_0**: https://olympiads.hbcse.tifr.res.in/wp-content/uploads/ino20/INAO2020-Solutions-20200204.pdf   please check problem 7  
> **username_0**: https://www.naturalnavigator.com/find-your-way-using/moon/  
> **username_5**: @Particleking: Yes, it’s *basically* N–S, but it not always is *exactly* N–S. Meeus 1998 provides a formula for calculating the tilt of the Moon’s axis with respect to the celestial N–S line.  
> **username_0**: Whay about latitude?  
> **username_0**: Also could you please specify the chapter number where it is mentioned in Meenus 1998?  

---

### Answer by username_3 on 2022-01-01. Score: 4

Actually, you can do this with the setting first quarter moon, which is a special case. The following was noted in the answer given to a similar question, recently -

> The angle between the lunar line of demarcation and horizon at, or near, the time the first-quarter moon sets, can be easily determined on any date when the moon is in its first quarter, as the sum of the solar declination on that date and latitude of the observer.

The answer is in regard to a similar aspect given [here](https://astronomy.stackexchange.com/questions/41789/why-can-i-see-sometimes-a-horizontal-half-moon-instead-of-a-vertical-one/41895#41895). However, a line connecting the tips of the crescent will only be parallel to the north-south line at two specific times of the year.


---

