Tides and earthquakes

 Orbits are ellipses.  Is there any evidence connecting earthquakes with times when the Earth is closest to the Sun or the Moon is closest to the Earth?

Yes—but with an important qualification. There is fairly good evidence that the gravitational tides raised by the Moon and Sun can slightly influence the timing of some earthquakes, but much weaker evidence that simply being at lunar perigee or solar perihelion produces a recognizable increase in earthquakes.

The distinction matters because the relevant quantity isn't really distance by itself. It's the tidal stress on a particular fault.

The Moon and Sun deform the solid Earth by measurable amounts. As the Moon moves around its elliptical orbit, that tidal stress varies, and when the Moon is near perigee the lunar tidal effect is stronger. Likewise, the Earth's elliptical orbit means the solar tide is somewhat stronger near perihelion. If a fault is already extremely close to failure, a tiny additional stress might be enough to make it rupture.

There have been several statistical studies finding just that. For example, a study of 442,412 earthquakes found a small but statistically detectable preference for earthquakes to occur at certain phases of the solid-Earth tidal cycle, particularly among small, shallow earthquakes. Another large study found no overall correlation for earthquakes ≥5.5, but did find significant correlations when earthquakes were separated according to fault type, especially shallow reverse-fault earthquakes.

And there is an especially interesting result from a 2016 Nature Geoscience study: the researchers found that the largest earthquakes tended to occur when tidal stress was relatively high, and that the proportion of large earthquakes increased as tidal shear stress increased. The effect was not apparent in the small-earthquake population.

But this is quite different from saying:

    "Earthquakes happen more often when the Moon is closest."

That's a much cruder hypothesis. The Moon's perigee occurs roughly once a month, but the maximum stress on a particular fault depends on the geometry of the Sun, Moon, Earth and the fault itself. A full moon or new moon can produce strong tides, for example, but even that isn't a universal earthquake trigger.

In fact, studies looking specifically at lunar phase have produced mixed results. One Taiwan study found about a 30% increase in smaller earthquakes around full moon, while finding essentially no relationship for larger earthquakes. Other global analyses have found no significant overall lunar correlation.

So I'd put it this way:

The Moon and Sun probably don't cause earthquakes. They can, however, sometimes provide the last tiny shove to a fault that was going to break anyway.

And the magnitude of that shove is remarkably small compared with the stresses involved in tectonic deformation. One study estimated the tidal stress changes at roughly 103 pascals, while the stress changes associated with an earthquake are vastly larger. That's why the effect is most plausible for a fault already sitting essentially on the edge.

There's also a nice analogy here: the tide doesn't load the gun; it may occasionally pull the trigger.

If you're interested, there is an even more intriguing question: whether the 18.6-year lunar nodal cycle or the Earth's annual orbit produces a detectable cycle in major earthquakes. That's much closer to the perihelion/aphelion question you started with.

So a slight but measurable effect on smaller quakes, it might be that a smilar effect exists for the larger ones but they are too rare for the statistics.

Yes. That's a very reasonable interpretation, with one qualification: the evidence for large earthquakes isn't simply "too weak to see." There are studies that do find a tidal correlation for larger events, but the effect is small and inconsistent across datasets.

The underlying logic is exactly what you suggest. Suppose tidal stress adds, say, a tiny amount to the stress on a fault. There will be enormous numbers of faults that are nowhere near failure, so nothing happens. But among the population that is already very close to failure, that tiny perturbation can determine when the rupture occurs.

That produces an interesting statistical prediction:

The closer an earthquake population is to its failure threshold, the easier the tidal signal should be to detect.

Small earthquakes are extremely numerous, so you can accumulate hundreds of thousands of observations and detect a tiny preference in their timing. Large earthquakes are much rarer, and there are many other variables obscuring the signal, so detecting the same effect becomes much harder.

There's another subtlety: if tides really do act as a clock rather than an engine, they shouldn't substantially increase the long-term number of earthquakes. They should mainly redistribute their timing—pulling a few earthquakes forward by hours, days, or perhaps longer, while others that would have happened slightly earlier or later disappear from the corresponding tidal phase.

So if you found that there were, say, 5% more earthquakes during a particular tidal configuration, that wouldn't necessarily mean the tides created 5% more earthquakes. It could mean they advanced the timing of earthquakes that were already going to happen.

And that is why I think your intuition is basically the right one: a very small physical effect can be real even when it has almost no predictive value for an individual earthquake. It can emerge clearly in a huge population while being practically useless for predicting the next big one.