<p>Let's double-check <a href="https://astronomy.stackexchange.com/questions/33425/how-many-moons-topocentric-conjunction-occurs-per-lunar-month#comment63247_33425">@barrycarter's conclusion</a>:</p>

<p>Ignoring the rest of the solar system and even the Moon's non-negligible mass, the velocity of the Moon's motion around the Earth is on average roughly <strong>1 km/sec</strong> per <span class="math-container">$v=\sqrt{GM_E/a_M}$</span> (the <a href="https://en.wikipedia.org/wiki/Vis-viva_equation" rel="nofollow noreferrer">vis-viva equation</a>).</p>

<p>The Earth is about 12760 km in diameter, so the Moon traverses the Earth's projection in about <strong>3.5 hours</strong>.</p>

<p>A topographic point traverses the Earth's projection in <strong>12 hours</strong> with a <em>tangential velocity</em> that's <strong>never more than 0.47 km/sec</strong>. </p>

<p>That means that the moon's projected position always "moves" faster than a topographic location, so <strong>there can never be more than one topocentric <a href="https://en.wikipedia.org/wiki/Conjunction_(astronomy)#Superior_and_inferior" rel="nofollow noreferrer">superior conjunction</a> per</strong> <strong><em>lunar month.</em></strong> </p>

<p>Hopefully there will never be any inferior topocentric conjunctions for this Earth at least.</p>

CC BY-SA 4.0
2019-09-21T18:09:41.070Z
Solar eclipse paths are consistent with this. Not sure inferior/superior distinction makes sense for other than Mercury, Venus.
Mike G
CC BY-SA 4.0
2019-09-22T00:21:21.910Z
@MikeG yep, that was a feeble attempt at humor; the Moon would have to leave Earth's orbit for that to happen.
uhoh
CC BY-SA 4.0
2019-09-21T05:03:36.837Z
2019-09-21T05:03:36.837Z
uhoh
<p>It is clear that only one Moon's Geocentric Conjunction occurs per lunar month, what about the Topocentric Conjunction for a given location?</p>

<p>without scale I can imagine <strong>many</strong> Topocentric Conjunctions as shown in the pictures below:</p>

<pre><code>yellow disk : Sun
gray disk   : Moon
blue disk   : Earth
yellow box  : Observer's Location
red line    : Conjunction's Line
</code></pre>

<p><a href="https://i.sstatic.net/m6PFx.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/m6PFx.png" alt="topo1"></a>
<a href="https://i.sstatic.net/1cda8.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1cda8.png" alt="topo2"></a>
<a href="https://i.sstatic.net/rO2V5.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/rO2V5.png" alt="topo3"></a>
<a href="https://i.sstatic.net/67NgQ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/67NgQ.png" alt="geo"></a>
<a href="https://i.sstatic.net/UFgen.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/UFgen.png" alt="topo4"></a></p>

<the-moon><moon-phases>
How many Moon's Topocentric Conjunction occurs per lunar month?
geek
# How many Moon's Topocentric Conjunction occurs per lunar month?

(Asked by: username_0 on 2019-09-18)

It is clear that only one Moon's Geocentric Conjunction occurs per lunar month, what about the Topocentric Conjunction for a given location?

without scale I can imagine **many** Topocentric Conjunctions as shown in the pictures below:

```
yellow disk : Sun
gray disk   : Moon
blue disk   : Earth
yellow box  : Observer's Location
red line    : Conjunction's Line

```

[![topo1](https://i.sstatic.net/m6PFx.png)](https://i.sstatic.net/m6PFx.png)
[![topo2](https://i.sstatic.net/1cda8.png)](https://i.sstatic.net/1cda8.png)
[![topo3](https://i.sstatic.net/rO2V5.png)](https://i.sstatic.net/rO2V5.png)
[![geo](https://i.sstatic.net/67NgQ.png)](https://i.sstatic.net/67NgQ.png)
[![topo4](https://i.sstatic.net/UFgen.png)](https://i.sstatic.net/UFgen.png)

**Tags:** the-moon, moon-phases


---

## 1 answers

### Answer by username_1 on 2019-09-21. Score: 3 | Accepted answer

Let's double-check [@barrycarter's conclusion](https://astronomy.stackexchange.com/questions/33425/how-many-moons-topocentric-conjunction-occurs-per-lunar-month#comment63247_33425):

Ignoring the rest of the solar system and even the Moon's non-negligible mass, the velocity of the Moon's motion around the Earth is on average roughly **1 km/sec** per $v=\sqrt{GM\_E/a\_M}$ (the [vis-viva equation](https://en.wikipedia.org/wiki/Vis-viva_equation)).

The Earth is about 12760 km in diameter, so the Moon traverses the Earth's projection in about **3.5 hours**.

A topographic point traverses the Earth's projection in **12 hours** with a *tangential velocity* that's **never more than 0.47 km/sec**.

That means that the moon's projected position always "moves" faster than a topographic location, so **there can never be more than one topocentric [superior conjunction](https://en.wikipedia.org/wiki/Conjunction_(astronomy)#Superior_and_inferior) per** ***lunar month.***

Hopefully there will never be any inferior topocentric conjunctions for this Earth at least.

> **Comments:**
> **username_2**: Solar eclipse paths are consistent with this. Not sure inferior/superior distinction makes sense for other than Mercury, Venus.  
> **username_1**: @username_2 yep, that was a feeble attempt at humor; the Moon would have to leave Earth's orbit for that to happen.  

---

