Tides with 3 Largish Moons

Question

I would like to have an Earth-like planet (~Earth gravity, ~Earth day, ~Earth year, and liquid water oceans) with extreme variance in its tides. I want the lowest tide to reveal about 30 miles of floodplain, and I want there to be occasional massive tidal waves. I understand that, in theory, this might be achieved by giving the planet several relatively large moons with different orbital periods, such that sometimes they are spaced out, so they balance out the tides (a kind of medium tide), and sometimes they are all together on one side of the planet so that they create a highest / lowest tide.

The star and other solar system features can be placed under whatever side conditions to improve stability, if they can improve stability.

I am building animal life cycles so that they correspond to different tidal conditions. As such, knowing the approximate frequency of high/low tides and tidal waves would be really handy.

Is there a way to set up the orbits of the moons in a stable way such that tidal waves occur predictably and that high/low tides are relatively rare? (Of the order of every 30-40 days.)

Added bonus, if you can provide any spitballed numbers for viable orbital periods and tidal patterns.

Answer 1

Using the comment "The tides are the story-significant feature. The rest can be adjusted." I recommend a single massive moon (relatively massive compared to most natural moons that we know of) on a highly elliptical orbit, making a close approach to the planet every 30 - 40 days. When it gets close, you have the awesome tides you want. The rest of the time, the lesser tides are caused by the star.

Using the Earth and Moon as examples, because the influence (using loose terms here, not specific scientific ones) of gravity increases exponentially as distance decreases, if the Moon were to change to an orbit where it was only half as far away from Earth, its gravitational influence wouldn't be doubled, but quadrupled. This wouldn't necessarily mean that tides would be 4 times as dramatic as they are now, because there are many other factors, besides simple gravity (such as coastline shapes and arrangements, wave frequencies and resonance, etc) but it's a good starting example to explain it.

If you decrease the average distance by half like that, but without changing the shape of the orbit (which is currently pretty close to circular), you get a much faster orbit, maybe a complete orbit every 10 days, instead of the current 28 or so. But if you then stretch the orbit to a long thin oval, increasing the average distance again, so that it goes back to a 30 or 40 day orbit, you can have a close approach MUCH closer than it currently comes (massive tides for a few days or so), and then it will retreat much farther than it currently does as well (diminishing tides while it retreats, increasing when it starts approaching again).

Answer 2

You can't achieve what you want with reality

I should have explained this clearly when I first wrote the answer. I apologize for not having done so. I do not believe it is possible to achieve the effects you describe with reality. Moons large enough to create the tidal waves and the tidal shifts you're describing would make life on the planet miserable (volcanism, for one thing) and tidal waves would occur all the time. There is no coincidence of smaller moons that can bring them about, either.

This leaves you only two options: walk away from what you want for your story, or happily live with suspension of disbelief.

For the purpose of suspension-of-disbelief, yes you can

"Suspension-of-disbelief" describes the balance between detailed reality and fiction such that your reader enjoys the story without being distracted by the "unreality" of what you're describing. To be honest, you really want to simply use whatever schedule you want for your story. If you want that rare event to occur only once a month or so, then do so. You need a believable solution — not necessarily a scientifically accurate solution.

Having said that, don't let our science fans on this site get too out of control. Every once in a while they get so wound up in saying "you can't do that!" that they forget that you're writing a story and not a textbook about lunar orbital mechanics.

So, what can I do?

You can create a believable condition for nearly any kind of tide structure you want with three moons.

Moon #1 is a bit smaller than our Luna and about at the same distance. It orbits the world in roughly 30 days and the world rotates in one day, which is what's creating the daily tides. It's a good starting point.

Moon #2 is a larger moon. How much larger depends on how much greater tidal difference you need. You don't need to go wild here. We're not talking anything more than 1.5X the size of Luna. It's a bit further out in orbit and it orbits more slowly than Moon #1 such that the two moons line up only about every 30-40 days. Now, your planet is turning once a day and that means that the water directly beneath either moon is getting pulled toward said moon as the planet rotates it beneath said moon. Your tides are pretty complex now. The larger moon is further away, so its overall effect is more-or-less the same as the closer, smaller moon. Basically, you now have two tides per day. But when those two moons line up, you get HUGE tides. You do need to remember that as the two moons get closer to each other (and, subsequently, further away from one another), the effect gets slowly worse. So, while the worst day is when they're lined up, you do have the week ahead and the week behind of ugly tides.

Thanks to @Eth for pointing out that my original comment about M2 moving a hair more slowly isn't believable. When considering how fast each moon is moving, think about it this way: Moon M1 orbits once every 30 days and we want them to cross every 40 days or so. M2 will travel some amount of its orbit in the same M1 travels up to 133% of its orbit. The lower the number (which must be less than 100%), the more believable the scenario.

Moon #3 Those first two moons are on the same orbital plane. This moon is not. It's tilted like Pluto. This has a bunch of complex effects, but to simplify them: (a) the tides for this moon are pulled away from the tidal pulls of the other moons. The tides will be complicated, but they'll also be "smoothed out" a bit. (b) Remember that tides are due to the pull of water toward the moon, and this pull is closer to the Tropics of Capricorn and Cancer where Moons #1 and #2 are pulled at the equator. But here's the fun part: (c) Now you have a condition where all three moons can line up. Due to the orbital inclination, that line up has a dramatic effect. You can now get your tidal waves via suspension-of-disbelief (the three moons in reality can't do this. No moon or combination of moons can. But you're looking to tell a good story, not write a textbook.)

Using any combination of these three moons, their size, and their orbital speed allows you to basically create any believable tidal system you want. Don't worry about being mathematically correct. If you want a larger tidal wave, make Moon #2 or Moon #3 a little bigger. If you want them to line up more rarely, make Moon #2's or Moon #3's orbital speeds a little faster. Tweak it just enough that people can believe what you're telling them and focus on the story you really want to tell.

Answer 3

I commented on another answer by Brythan & Dalila. They pointed out that an elliptical orbit will produce massive tides only at the close approach.

Orbital period depends only on the major axis of the orbital ellipse. So you lower the perigee by say 150,000 km, and raise the apogee by the same amount, the period will remaint the same 28 days we have now. There's a square root of axis cube in there. So if you double the length of the axis, the period goes up by the square root of 2^3 or about 3 -- ballpark 90 days.

However this has some side issues:

A: Really massive tides are going to have a huge erosion component. You put 50 feet of water over and over again, and the currents that move that water to and from the ocean are going so scour the land. You will not have mud flats. You will have bare rock. If 30 miles of flats are exposed during an 11 hour tide cycle then you have average tide speeds of 60/11 -- about 5 miles an hour. First approximation they are sinusoidal, so the peak speed would be roughly 7.5 miles per hour. That would mean tides come in at a speed most people can't run at for extended distances. That's better than a 4 hour marathon.

Look up tides in the English Channel. Look up tidal currents too. Multiply by 8. Getting on/off shore is going to be a challenge.

Tides are affected by the shape of land. The Bay of Fundy funnels the tides and so instead of 4-6 feet it has places with tides of up to 40 feet. The Pacific Coast near Kitimat has 15-25 foot tides now.

B: It's not just the seas that have tides. The air does too. Google lunar fluctuation air pressure. (4 mb?) Pretty small right now. Same factor will apply to those changes. Even now there is a slightly greater chance of storms at new and full moons, in part to the larger air tide. You can use this to make a few more disasters.

C: The air tides will skim off the atmosphere. You need to have a natural process that regenerates the atmosphere. Look up atmosphere origins.

D: The earth's crust will also be deformed by tides. This flexing generates heat. You are going to have a lot more earthquakes and a lot more vulcanism. Vulcanism generates lots of CO2. Several of the Earth's extinctions are blamed on major volcanic events either as principle or triggering events. This solves your air problem, but you will run out of Nitrogen. This also will help rebuild the eroded coasts.

E: Because of the greater distance variation, tide tables are going to be a lot more complicated.

F: Choose your distance right, and the moon at peragee will slow and stop. The moon will be orbiting at the same speed as the earth turns. This will lengthen the period of high tide. To do justice to this you need to invest in decent orbital simulator.

G: Right now the moon's orbit is thirty and change degrees tilted to the Earth's rotation. This has a stabilizing influence on the the earth's tilt. Putting at an even steeper angle would make the tidal wave pattern not repeat as often.

H: Earth at one point had a 6 hour day. The tugs of the tides have slowed down the earth, with the energy increasing the diameter of the Moon's orbit. This would happen faster with the elliptical orbit. The process tends to make the orbit more circular since more of the energy transfer occurs at perigee. You need to explain why it's not rounder. (You can leave it as an unsolved mystery. Then in a sequel, posit some Engines of God that power the station keeping. Niven had to do this when MIT students found that the Ringworld wasn't stable.)

Answer 4

The simplest way to model wave propagation and dispersion is through a sine wave. Let's start by modeling the effect by an individual moon in 1 constant position using the following equation:

WaterSurfaceElevation = Amplitude × sin(( Frequency × T ) + Phase)

For our purposes:
Amplitude = The strength of the moon during its peak
Frequency = How many times the moon completes an orbit in a unit of time
T = Time since the start of the Moon's cycle
Phase = Phase at T(0) with 360 equating to one 1 full cycle

Moon red has: an amplitude of 1.5, frenquency of 1.2, and Phase of 0 Moon blue has: an amplitude of 1, frenquency of 0.7, and Phase of 90

The green line represents the net effect of both moons. This process can be used for any number of moons.

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On the possibility of 3 moons orbiting 1 planet, this is very possible. First we arrange the orbits in such a way that satisfies the 3 Body Problem. While this is very complex task, The Institute of Physics Belgrade has compiled a demonstration of the various "families" of solutions. Any of these solutions can be modified to solve this problem. To counteract gravitational pull from a central object the initial velocities could be proportionally scaled. While extremely unlikely, the physics do check out.

Answer 5

Reality check:

I have asked on this forum, physics.SE and several other science based forums if multiple significant moons are possible.

Criteria:

• Had to have a visual diameter of at least 1/2 degree (same as Luna)
• Roughly same density.

All of the existing examples of multibody systems in the solar system the primary is MUCH more massive than the satellites.

So far all of the answers have either been, "No" or didn't get an answer at all.

I've played with a simulator, trying one moon the size of luna, and one 1/2 the diameter (= 1/8 the mass) at 1/4 the distance. This gives the same sized tides as Luna, is visually larger than the moon.

I spent some time tweaking the orbits either trying to hit or avoid resonances. Most either threw the smaller moon out of the system, or crashed it into the earth.

As a counter example, we have Mars with two moons in fairly close orbit, but with small masses -- small enough that even if Mars had oceans, the tides would be insignificant.