Making doomsayers right - a moon(s), planet alignment that matters

I'm ~99% certain that the effects of a second celestial body on seismic activity on an Earth-like planet has been covered before (in that case, by a second Earth-like planet); if anyone can point me to it, that would be great. The conclusion - if I remember correctly, and I think I do - was that there wouldn't be any major effects in this area. I might have supported that conclusion, in which case I may have been wrong.

Scientific American has an interesting article on the subject. It turns out that a causal relationship between the moon and seismic activity was first postulated a long time ago. Scientific American itself published a minor story on the idea in 1855, based on the work of one Alexis Perrey. Apparently, Perrey showed three correlated relationships:

1. The frequency of earthquakes/tremors is increased during a syzygy - a time when the Earth, the Moon and the Sun are in a straight line.
2. The frequency increases during the Moon's closest approach (perigee), and decreases during the Moon's furthest approach (apogee).
3. The frequency increases when "the moon is near the meridian, than when 60° from it." I'm not entirely sure what Perrey means here, so I won't attempt an interpretation.

Perrey's work comes from "7,000 observations", which seems convincing, but it is entirely based on observations, it seems - there is no explicit theory as to why this is the case. I'm not saying that should remove credence from it, but note that no causal relationship was proven.

More recently, Straser (2010) and Vergos et al. (2015) (paywalled version; a difference version is available via ResearchGate)) investigated the problem. The former also summarized previous work on the problem, which had attempted to show a number of relationships between earthquakes and the Moon. Here are some of those works:

• Omori (1908): The rhythms of the tides can cause a rise in earthquake frequency.
• Bagby (1973): Syzygies increase earthquake frequency (this is the same as one of Perrey's conclusions).
• Kokus (2006): Changes in the Moon's motion can influence fault behavior.
• Kolvankar et al. (2010): Earthquake frequencies change according to the lunar cycle.
• Zhao (2008): The Earth can induce earthquakes on the Moon - "moonquakes".

The main point here is that tidal forces can apparently influence earthquake frequency. However, the author's conclusion was that - especially as regards his own research - links can be tenuous at times.

Vergos et al. studied an earthquake and related tremors in Greece, and established a relation between the phase angle of an earthquake ($\phi_i$) and the period of a relative tidal component ($T_d$): $$\phi_i=\left(\left[\frac{t_i-t_0}{T_d}\right]-\text{int}\left[\frac{t_i-t_0}{T_d}\right]\right)$$ Can we establish a causal relationship from all this data? Not necessarily. We have no theoretical model to explain it, either. The USGS has written some of the resultant phenomena off as coincidences (see this article). I think, however, that the evidence is compelling enough to show that some relationship might exist.

In your case, we can take advantage of syzgies. The more bodies - in this case, more moons - the greater the effects, in theory. The differential force experienced by Earth is proportional to $r^{-3}$, however, not $r^{-2}$ (see here; keep this in mind for calculations).

To answer your questions about mass and distance, I say only that it is up to you. We don't know enough to come up with accurate formulae for the effects - if they exist - so we can't know for sure what conditions are necessary to cause a given result. I can tell you that the alignment - for it is an alignment that you need, not an eclipse - would be periodic, because orbits (and therefore orbital alignments) are periodic.

I wrote more about stability in my answer here to your related question.

posted over 8 years ago

HDE 226868‭

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