Oct 012018
 
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Tides are variable. They are affected by coastline, currents, and other factors we can usually ignore as world builders and writers. But the moon is the greatest cause of tides, followed by the sun. If we want moons different from ours in number, proximity, or orbit, we should understand the moon’s effect on tides. On Earth, tides can be so extreme that boats moored at high tide are sitting on the beach at low tide, which is one reason large vessels remain farther out and small boats are used to come ashore; such situations could be exaggerated with additional moons. Tidal forces are also causing our moon to get farther away, which would happen on any world we build (it if has oceans), but the rate is infinitesimal; still, a moon is unlikely to be getting nearer unless it’s already very close. Gravity will pull it in and rip it apart. This can be a very real doomsday scenario for a world because the moon’s debris will rain down on the planet’s surface and cause destruction; the planet’s tilt will also destabilize, affecting seasons and possibly causing dramatic and rapid-onset ice ages, for example (more on this in the next section).

Our moon causes high tide on the side of the Earth it faces because it is pulling the ocean away from the planet. The moon is also pulling the Earth that direction and away from the ocean on the opposite side, causing another high tide on the planet’s far side. The Earth’s other two sides experience low tide (see Figure 10 below).

Figure 10 Tides

Figure 10 Tides

This causes two high tides and two low tides per day. Those two high tides aren’t the same height, nor are the low. One reason is that the moon’s orbit is not perfectly circular. If we invent a moon with a more elliptical orbit, the tide will be less pronounced when the moon is farther away. Imagine your characters being aware that such a moon is coming close in a week and they must get to higher ground or be flooded where they are, and that many settlements have taken this monthly flooding into consideration.

Among high tides, the highest tides are when the moon, sun, and Earth form a straight line, such as Moon-Earth-Sun. But the very highest tides are when moon and sun are on the same side, such as Earth-Moon-Sun (See Figure 11 below), because the gravity of both moon and sun are most strongly affecting the same side of the Earth. This is called a “spring tide” but has nothing to do with the season—it occurs twice a month, as does the corresponding lowest tides, called “neap tides.” On a world of our invention, we might want to rename “spring tides” to avoid confusion.

Figure 11 Highest Tides

Figure 11 Highest Tides

A moon’s diameter (apparent size) isn’t particularly relevant for tides. Rather, mass and distance from the planet are the primary factors in tidal forces. Change either and we increase or decrease those forces and the resulting impact on a planet. More mass means more impact. More distance means less impact. Fortunately, our audience isn’t expecting us to tell them the mass of a moon or how far away it is, especially as compared to Earth’s, so we can usually ignore this, but we can at least know what we’re ignoring.

We’ll take a detailed look at how adding a second moon affects tides, as the observations can be expanded to additional moons and their impact. Using a clock face for orientation, with Earth at the center, what might the tides be like if the moons are:

  • the same mass
  • equidistant from the planet
  • at 12 and 3 (to start) and never get materially closer or farther from each other while orbiting?

Picture Moon One’s gravity pulling at the 12 and 6 positions (causing high tides there) while Moon Two’s equal gravity does the same to 3 and 9 (causing high tides there, too). Would they balance each other’s effect on the oceans, causing a constant water level (i.e., lack of tides)?

Unless we’re physicists, we can get ourselves into trouble with this kind of thinking, creating impossible situations. Is that’s why it’s called “science fiction?” Not really. SF is fiction which combines science that does not exist while hopefully getting right science that does (italics) exist. We have leeway to invent but should aim for believability.

Lack of tides isn’t particularly useful, interesting, or likely (without mutual tidal locking; see previous section). The theoretical scenario above is a starting point for making observations that can help us make informed decisions. Altering that example, if two moons are at 12 and 6 and stay that way (always on a planet’s opposite sides), we’d have more extreme tides. But if one moon had lower mass, it might have less impact on tides. This would also be true if one moon was farther away. Or had a more elliptical orbit.

Only distance, not mass, affects orbital speed. More distant satellites orbit slower, so two moons at different distances can’t stay on the planet’s opposite sides. Having two (or more) moons that are always in the night sky at fixed points to each other is unlikely. The nearer moon, moving faster, would appear to regularly catch and pass the farther moon. This will sometimes cause them to align in the sky. If they’re orbiting in the same plane (and most moons of a planet do), this will cause at least a partial eclipse of the farther moon by the nearer. The degree of eclipse is determined by the relative size, not mass, of the moons. For a total eclipse, the nearer one must be large enough (as seen from the planet) to completely block the farther one as seen from the planet.

An elliptical orbit would also mean that a moon’s effect on the world would ebb and flow depending on how far away it was; imagine it coming close once a month and causing a much stronger tide, and if this coincided with being on the same side as the other moon (and sun) every year, maybe we’d get a far stronger tide once a year.

If two moons are orbiting at different speeds (they do not stay at 12 and 6 in relation to each other), they can only do so at different distances from the planet. Otherwise they’d have crashed into each other, resulting in one merged moon and possibly a ring around the world from the impact’s debris. The falling remnants would wreak havoc on life. If the moons are at different planes (but the same distance), they could theoretically survive, but gravity would eventually draw them into a collision because orbits stabilize to the same plane in time. This is a potential doomsday event for inhabitants.

When the two orbiting moons form a straight line with the planet, the tide would be more extreme. Otherwise, tides would be weaker.

In the most likely case of two moons orbiting in the same direction but at different speeds, at different distances, we could decide how long it takes for each of them to orbit the planet. We can just pick a number. Keep in mind that a number less than Earth’s moon (which orbits in 27 days) means our invented moon is that much closer. A moon orbiting in 14 days is about half as close, when our moon is already very close. Anything that close will have a big effect on the planet, so unless we really want to emphasize the moon in some way, have the moon equidistant to or farther away than ours.

If our world has thirty days in a month, maybe we choose thirty days for one moon’s orbit. Then decide how fast the other moon orbits. With this decided, we can then figure out how often they’re on the same/opposite side of the planet. The formula is:

(P1 * P2) / (P2—P1) = C

P1 is the period that the closer moon takes to orbit the planet. P2 is the farther moon’s orbital period. C is the conjunction (when they’re together), though this could be any two relative positions. Assigning P1 to 15 days and P2 to 30 days, we get this:

(15 * 30) / (30—15) = 30

Breaking it down, 15 times 30 is 450. This is divided by the result of 30 minus 15, which is 15. So 450 divided by 15 is 30. Every 30 days, the moons will be in conjunction (or any other configuration).

If you’d rather not do these calculations manually, the “Moon Orbit Calculator” Excel spreadsheet included with the free templates allows you to type in the number of days for two moons and get the answer. If we’re after a certain result, we can keep changing the numbers until it produces an answer we like.

For example, on my world of Llurien, there are 28 days in every month (because there are 28 gods and each gets a day). I want the nearest moon to orbit in 28 days, heralding the start/end of each month. Three months is a season of 84 days. Each season, an arrangement of gods changes. I wanted a conjunction of moons to occur each time, adding increased significance to this seasonal event. That means a conjunction at 84-day intervals. So how long does it take for the second moon to orbit? I probably could’ve used math, but I just kept typing numbers into the spreadsheet until 42 for moon two’s orbital period caused the conjunction field to say 84, my goal.

Knowing when two moons coincide can help us determine how often eclipses happen. It also tells us when the highest tides are. Sailors and port townsfolk will be aware of this. A water-dwelling humanoid species might be, as would animals, both on land and sea, possibly taking advantage of this during birthing, hatching, or forays ashore.

This exercise can be imagined with more than two moons, though you’ll have figure out the formula for that. Effects on the planet start getting complicated unless we keep most of the moons farther away, give them less mass, and keep them in a mostly circular orbit. All of this reduces their impact so that we can include them, but concentrate on the influence of the one or two most influential moons have on tides.

What happens if there’s no moon? Probably very little tide; the sun would cause some tides.

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