For the sake of argument
Every 3rd Thursday of the month, I have to go to an appointment. I get dressed and walk downstairs from my apartment and stand on the street corner. Usually, a large people mover called a bus shows up. I get on and pay my fare.
Am I to assume that whenever I go to the corner, a bus shows up just because I am there?
That would be preposterous. The bus will show up if I am there or not.
Likewise, Katla erupts about every 47 years. Depending on how you work the average. Eyjafjallajökull, erupts about every 540 years or so. Odds are, that when Eyjafjallajökull erupts, Katla has either just finished an eruptive phase, or is well on its way to have one.
It has been said that there are lies, damned lies, and statistics. One of the most dangerous aspects of statistics is when you are not being able to tell when the data is lying to you, and what truth (as told by the data) is the real truth.
It is real easy for your own data and methods to convince you of something that isn’t real. Sometimes you have to take a step back in order to do a “sniff test” to see if it really makes sense.
Is there a connection between Eyjafjallajökull and Katla? Well, the jury is still out on that. I myself have seen what may be a connective region in the quake patterns, but that doesn’t make it real. Chemically, the two magmas are different. Each carries its own signature of constituent elements.
Now… about astronomical bodies
Vectors are mental mathematical constructs. They allow you to add two or more forces together to see what the result would be if they were to both act on an object at the same time. For example, if two pool balls, each traveling in its own direction strike each other, what direction would they go after a collision?
You can dig into it by representing each pool ball with a mass, and a speed… together with a direction. The mass and speed would give you a value of kinetic energy, and with the direction of travel, you get a vector.
The math can get hairy and tedious, so I will just point you at the law of cosines and the law of sines. All I wanted to point out is that you can add vectors to find out what the result will be.
The Sun is the most massive body in the Solar system. At about 1.99 x10^30 kg, it dwarfs the next most massive body (Jupiter) by factor of about 1048.
Newton’s law of universal gravitation shows that if you multiply the masses of the two bodies, then divide that by the distance between them squared, and then multiply that result by the Gravitational Constant, you can obtain the attractive force between the two objects.
So… lets do that for some of the more significant masses that affect the Earth.
This is a logarithmic scale, used only because the forces have such a wide range.
On average, the Sun exerts 175 times the force than the Moon
Mercury, 0.00004 times the force than the Moon
Venus, 0.00232 times the force than the Moon
Mars, 0.00005 times the force than the Moon
Jupiter, 0.00528 times the force than the Moon
Saturn, 0.00059 times the force than the Moon
So… Whenever you see someone spouting an astronomical theory about the influences of the planets, remember just how much significance that the planets have in relation to each other.
All of those forces are vectors. They have a level of force, and a direction. Those that pull along the same direction are additive, those that pull in opposite directions are subtractive.
There are also another set of forces that are at work that contribute to this whole she-bang… that of inertia. The Earth travels at a speed of about 29.3 to 30.3 km/s.
The mass of the Earth times the velocity would be the inertia that the Earth has. And that large value is mainly acted on by the 3.5711 x10^22 Newtons of force (towards the Sun) that bends the Earth into a mostly circular orbit.
Next, you have rotational inertia. In order to get really accurate with the effects you would have to account for that also.
And now the one caveat that most loons forget… all this is in real time with constantly changing angles.
That plot that I linked only shows the intensity of the various attractions over the next few months. Each one of those vectors pulls along a different axis.
Can it be calculated? Yeah, but I am not touching it, nor am I even going to try.
Once you realize that Jupiter and the rest have about 0.00528 the effect of the Moon… well, now you are into the noise floor… brutally.
Best-o-luck seeing how that shows up in your seismic listing or your volcano eruption.
In a nutshell… it ain’t there.