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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 topo2 topo3 geo topo4

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    $\begingroup$ It's an interesting question, but I think the moon revolves around the Earth fast enough that there can be only one topographic conjunction per location per month, around the time of the New Moon. This video may or may not help: youtube.com/watch?v=qSbozfxAfDQ -- it shows the moon is always moving "forward" with respect to the Sun even when it's moving "backwards" with respect to the Earth. In other words, the moon is effectively also in orbit around the Sun. $\endgroup$
    – user21
    Commented Sep 20, 2019 at 18:38

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Let's double-check @barrycarter's conclusion:

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).

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 per lunar month.

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

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    $\begingroup$ Solar eclipse paths are consistent with this. Not sure inferior/superior distinction makes sense for other than Mercury, Venus. $\endgroup$
    – Mike G
    Commented Sep 21, 2019 at 18:09
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    $\begingroup$ @MikeG yep, that was a feeble attempt at humor; the Moon would have to leave Earth's orbit for that to happen. $\endgroup$
    – uhoh
    Commented Sep 22, 2019 at 0:21

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