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I'm creating a new setting for a novel. I'd like to build a world where the interaction between the planet and its satellite/satellites can generate a normal tide excursion around 6/8 metres. Furthermore I need that once every 500 years there occurs a low tide ten/twenty times that of the normal ones.

Can anyone suggest to me how to set up this relationship to be at least credible?

I'm thinking of a system with a central planet with 2 satellites, where the nearest is smaller and orbits faster, and a second one is bigger and farther away with a really slow orbit with a very elliptical path, but I don't know if this solution can work.

P.S.: Obviously the number is merely indicative only for give you an idea of how this thing should work.

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    $\begingroup$ Just for reference - Wikipedia's tidal range article states: "Coastal tidal ranges vary globally and can differ anywhere from near zero to over 38 feet (12 metres)" and "The world's largest tidal range of 16.3 metres (53.5 feet) occurs in Bay of Fundy, Canada, and the United Kingdom regularly experiences tidal ranges up to 15 metres (49 feet) between England and Wales in the Severn Estuary.". The map from that same article seems to indicate that most of Earth's oceans and coastal areas don't experience more than 0.60 meter (less than 2 feet) tides. $\endgroup$ – G0BLiN Feb 4 at 13:27
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    $\begingroup$ You may consider that not actually gravity, but possibly geographical structures are the determining factor for the average height of tidal waves. This way you can keep your moon similar to earth and only adapt your coast lines. $\endgroup$ – Alex2006 Feb 4 at 13:46
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    $\begingroup$ @Krokhmir if you put your satellite at 1/10th of the distance that the Moon is from the Earth, the tides will be a thousand times as big. Tidal force varies with the inverse cube of distance. $\endgroup$ – Mike Scott Feb 4 at 14:18
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    $\begingroup$ A low tide in one location requires a high tide elsewhere. This means your 500 year low 80-160m low tide will have a coastal-flooding-capable 80-160m high tide somewhere else. Are you OK with that? Also, please note that you can send a notification to a user that you're responding to their comment by placing a "@" before their username. So, to tell me you're responding to my comment you'd include @JBH somewhere in your comment. $\endgroup$ – JBH Feb 4 at 14:36
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    $\begingroup$ @JBH You can’t have a satellite of a habitable planet with a 500-year orbit; it will be way, way outside the planet’s Hill sphere. $\endgroup$ – Mike Scott Feb 4 at 16:57
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Tides are nothing but waves on the ocean, which are driven by the moon's and sun's gravitation. And, as with any wave, absolute hight depends heavily on resonances.

A commenter has already given the location on earth with the highest tides, which is a bay (https://en.wikipedia.org/wiki/Bay_of_Fundy). I.e. a half enclosed region of just the right size to produce such a strong resonance that you get 16m high tides. Most of the remaining water surfaces are not as highly resonant with the fixed frequency of gravity change, so you only get small tides that mostly don't exceed 1m.

So, you have two routes to go:

  1. You heavily increase the tidal forces. I.e. bigger moon that's closer by.

  2. You heavily increase the resonances. If you have a shoreline that's for some weird reason a sequence of bays like the Bay of Fundy, you get the high tides in each of those bays. You'll also get low tides at the coasts that are directly facing the open ocean.

    If you go this route, you can use bays of virtually any size, as long as you adjust the length of the day accordingly. The larger the bays, the longer the day needs to be.

In either case, be aware though that those large tides won't last for long (= long in the geographical sense): The higher the tides, the faster the energy transfer from the earth's rotation to the moon's orbit and water heat content. So, the higher the tides, the faster the earth's rotation looses speed. And as your days get longer (very gradually, but I'm speaking about geological timespans here), the bays will get out of resonance and loose their high-tide property.

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This has probably already happened to the Earth.

It is generally believed that the moon was formed from an impact event between a very young earth and a planet around the same size as Mars. In point of fact, it has been postulated that the young moon was responsible for the creation of life on earth, and that when it was newly formed from the debris ring around the earth, it was much closer to the earth, orbiting the earth every 6 hours or so and causing a massive tidal effect.

Ultimately, the closer you bring the moon to the Earth and the closer in relative size they are, the larger your tidal forces. The sun is also a factor though, so if you move the earth even slightly closer to the sun, and have a moon up close, you can end up with massive king tides as a result of alignment between sun and moon.

Mind you, the closer you put the Earth to the sun, the less time the earth will be in a habitable range (the sun is slowly heating up and in billions of years, Mars will actually be in the goldilocks zone, not earth) and having the moon closer, while potentially necessary for the establishment of life, may make the earth far less comfortable for the sustainment of life depending on what you're trying to achieve.

If the only thing you care about are tidal forces, then these configurations will help you. If you want this planet to harbour life to the point of intelligence, it may be a little more problematic. In any event, just move your moon closer to the earth and you get reasonable tidal variations quite quickly. You don't even have to move it much to have a great effect because of the squared effect of proximity on gravitational pull.

In other words, move it to half its current distance from the Earth, and your tidal forces quadruple. Move it to around a third of the current distance, and you have nearly 10 times the tidal forces in play. Of course, in both cases, your tides move much faster between high and low tides (unless you greatly slow down the rotation of the earth) so the impact on life is going to be greater than simple difference in tide height; you're generating a massive amount of momentum as well which brings its own problems that will have to be dealt with by life struggling to survive on the surface.

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Horseshoe Orbits

Yes, long term (geological timescales) stability will be an issue with this setup but it should be the setup that most closely matches your criteria.

Start with Earth's horseshoe orbit relationship with Cruithne, which is on about a 770 year cycle. This concept is easily modified to more closely match your 500 time requirement. From there, replace Cruithne with your tide "planet" and replace Earth with a large Gas Giant planet. When the Gas Giant approaches your tide planet, once every 500 years or so, the tides get huge for a significant time (probably several years, though I don't know how to do the math on it), before the tide planet and gas giant separate again for the next 500 years.

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