Foreward

I started writing ‘Jason’s Tale’ (1) in 2015 or -16, soon after I ran across the “Damsels in Distress” (2) shared story-universe. The originator of the series, Lazlo Zalezac, says the planet Chaos has no moon. Several authors have followed that. Several other authors say, yes it does, but they are all heretics who should be stoned in the village square. While ‘Jason’ was getting proofread, Old Man With a Pen published a story ‘Stuck on Chaos’ that mentions two moons!

Who cares? Well, moons mean a lot of light at night, sometimes, while other nights will be moonless and dark. That can be factored in to a good story. A moon also means tides, and that’s important to anyone who deals with the sea or the coast. Since this was a naval adventure story, I had to get that right. I chose to follow LZ’s version. No moon, no tides.

Then Ernest Edwards/Bywater posted a couple of short stories that said there was a tide. I sent him a private note that said no moon - no tide, and he replied that the sun provides a tide, too.

When you’re right, you’re right. Perhaps I’ve started to enter my second childhood, since I have spent most of my life on or near the water and am exhaustively familiar with the tides. Of COURSE the sun provides a tide! It’s nowhere near as strong as Earth’s Moon’s tides, but it is a measurable effect. Chaos does have tides. I changed the story to fit THAT, but then I had to come up with a defendable explanation of how large the tides were.

To readers looking forward to another great story with lots of sex and gore, you’re in the wrong place. This is merely an essay on tides.

I - Theory and Overview

To start with, tides are a ‘gravitational phenomenon’. That’s it, pure and simple. Tides come from gravity. Only, Earth’s tides don’t come from Earth’s gravity. Tides come from another body like the Moon, and its mass pulling on the Earth’s mass.

Imagine that you are an astrophysicist. Or, maybe you actually are, in which case you probably won’t learn anything from THIS essay. I should have you write it for me...

Anyway, it’s hard to run an experiment or calculate the expected results when your experiment has millions of random factors. Billions? It’s easy, though, when you can simplify everything and get rid of all those side-effects. That’s why we do thought-experiments. No real-world equipment, just your mind, a pencil and paper, and maybe a calculator.

Imagine a universe with only two bodies in it, the Earth and the Moon. Okay, ignore for a moment the fact that if there was no Sun then both the Earth and the Moon would be frozen solid. Pretend that the universe only has the Earth and the Moon, but somehow both are at their normal everyday temperatures.

Each body has mass, and each body’s mass has a gravitational effect on the other. Of course there is the gross overall effect of attraction, that’s why the Moon orbits the Earth. You can look at the Earth as a single body and the Moon as another single body, and it’s fairly easy to calculate the total force from each on the other.

You can also, if you’re good enough with calculus, calculate the effect that each body has on each and every individual atom of the other. If your math is right, once you add them up all together you should come up with the overall effect, right? So no one bothers with doing it the hard way.

Except ... The Earth is a rough sphere around 12,740 Km across (3). The Moon is VERY roughly 385,000 Km away (4). That number is somewhat of an average, since the Moon’s orbit is nowhere near round. The important takeaway here is that, regardless of where the Moon happens to be at any particular time, one edge of Earth is ~12,740 Km closer to the Moon than the opposite edge.

Using that ‘average’ distance, the nearest edge of the Earth is only 385,000 - 6370 = 378,630 Km away from the Moon while the farthest edge is 385,000 + 6370 = 391,370 Km away. That difference of 12,740 Km is enough that the gravitational pull is noticeably different. The near side of Earth is pulled toward the Moon more than the far side is.

How much more? Well, it’s only a little bit. The accepted lunar pull is ~1 x10^-7 g, and the difference between near and far is much smaller yet. Do you really need all the numbers? This is a high-school level essay. You need more numbers you can figure them out.

If the Earth was solid, we’d never notice that small force, but it’s ALWAYS pulling. For millions and billions of years, it’s been pulling.

And the Earth is not solid. The rock itself isn’t solid, and much of the rock is covered by a liquid, and the whole thing is covered with several kilometers of a gas mixture. The gas mixture -our atmosphere- is constantly moving anyway so we don’t notice any tidal effects. That flow is lost in the much greater winds. On the other hand, the liquid covering -our oceans- is pretty much held in place so since us humans live on the edge between the land and the sea we DO notice when the sea moves.

II - Earth’s Tides

So, the Earth has tides (5). If it was just the Moon, the tides would be pretty big. That’s a very small force, but adding up over millions and billions of years, the tides would be HUGE. However, it’s time to drop the thought-experiment and let the real world in.

We don’t live in a two-body experiment. We live in the real universe and Earth has noticeable tides from two different sources. Sure, the Moon is closest and gives us the biggest tides, but the Sun has been there even longer than the Moon, it’s been there since before the Earth was there, and it also gives us tides.

The Sun’s pull is roughly half of the Moon’s pull. Since the Earth spins once per day (that’s the definition of day, right?), the Sun’s tidal pull is spread out all over the world. The Moon’s pull should be the same way, but since the Moon slowly orbits the Earth (Roughly once a month, right? That was the original definition of ‘month’, after all.), the Moon’s effect isn’t on a 24-hour period like the Sun. It is a ‘day’ due to the Earth’s rotation, plus however much farther the Moon has moved during that day. It comes out to about 24 hours and 50 minutes.

If the Moon’s gravity was just a simple static pull, the tide would only be something like two feet difference. However, it’s a cycle. When the Moon is overhead, it pulls the most. When it is off to the side, it pulls somewhere else the most. When it is on the other side of the Earth, it pulls the least.

The pull is resonant, like a guitar string or a swingset. When you pluck a guitar string, it doesn’t simply return to where it was and stop. Instead, it continues on away from you and then returns, over and over and over again, the vibration slowly dying out as the energy is lost to the air, friction, and heat.

The same way, you don’t have to push your child very hard to get the swing moving. If you stop there, the swing will go back and forth and slowly come to a stop. However, your child is screaming “More, daddy, more!” When it comes back, you push it again. Over time, the little pushes will add up and your child will start to really move. Okay, it’s time to stop. You don’t want him to fall out!

What would the tides be like if there were no continents, island chains, or underwater mountain ranges to interfere with the tides? Think of that swingset again. With a resonant push, the swing will go farther and farther each time until some other limit is reached, and it never ends well. For me as a ‘tweener on a swingset intended for smaller children, the whole swingset decided to follow me over. That ended with a visit to the emergency room. For most smaller kids, though, the swingset stays where it is supposed to be, you lose momentum halfway up, fall, come out of the seat, and still go to the emergency room.

Here on Earth, however, the tides are constrained by the land. There are enough land masses to keep the tides from flowing around the globe and following the Moon. And, because the water takes so long to flow from one place to another, how far a place is from the open ocean affects both the time and size of the tides. In some places, there is effectively no tide. There is a tide in the Atlantic Ocean, and a smaller one in the western Mediterranean. The central Mediterranean has an even smaller tide, and there is basically none at all in the Black Sea.

On the other hand, there are places where the tides are amplified. The tides are extreme along western Europe and the British Isles, at Newfoundland (50 feet difference or more between high and low tide is common!), and on the western coasts of Panama, New Zealand, and Australia. Oddly enough, the eastern coasts of Panama, New Zealand, and Australia have very mild tides. Clearly, it’s a complex subject! (6)

One other thing that keeps our tides so chaotic is the simple fact that the solar and lunar tides are constantly interfering with each other. The solar tide is on a 24-hour schedule. The lunar tide is almost on a daily schedule. These two schedules return to their start every 28 days. And, as the Moon moves in its orbit, it gets closer at times and has a greater pull, then gets farther away and has a weaker pull.

All this means that explaining and predicting the tides is not a task for the faint of heart. People have been trying to explain the tides since we first started living along the shore, and the best we can do is record what it does and use those observations to predict the tides in the future.

Note that, due to the way the ocean flows around various land masses, a tidal chart for one place is completely useless anywhere else. Each location needs its own tidal chart.

Also, note that the tide affects water levels in rivers far inland. Rivers flow downhill, right? They flow because the water level up there is higher than the water level down here. Again, there are several factors, but mostly the flow rate depends upon the height difference.

Assume a slow-flowing river with a drop of three feet over a distance of twenty miles, where the river ends at the ocean. Just for some detail, lets say that the final two miles are mostly river delta and mudflats, and the river only drops half a foot in those two miles. The other two and a half foot drop in river level is evenly distributed over the higher eighteen miles.

If the tidal difference at the mouth is two feet, that will make a major change in the river flow. Just to keep things simple, we will say that all our measurements were taken at low tide. That means that at high tide, mudflats of the delta aren’t half a foot above sealevel, they are one and a half feet BELOW sea level where they can’t be easily seen but they can cause trouble for ships.

The higher part of the river no longer drops two and a half feet to the beginning of the delta. At high tide, there’s only half a foot difference between the top of that eighteen-mile run and the bottom. The river will flow a lot slower at high tide than it will at low tide.

Water is still running into the river, though, from the upstream parts. It’s flowing in, and it isn’t flowing out. The river will rise. Naturally, the river rising will give it some more height difference and it will start to flow faster again, but people who live on the river will see the rise.

Last, all these effects will be delayed, because it takes time for water to flow and once it starts flowing it has momentum and it takes more time for it to stop flowing. Down at the delta, the water level will rise and fall with the tides. The farther upstream you go, though, the later and later this effect will be seen. Ten or fifteen miles up, this rise and fall could be a couple of hours after high and low tides at the delta.

III - Meanwhile on Chaos...

Let’s get back to that two-body system of our thought experiment. What if there was a Sun keeping the Earth warm, but there was no Moon? The Sun’s pull is roughly half of the Moon’s pull. Yes, it’s almost infinitely more massive than the Moon, but it’s also much further away and gravity falls off as the square of the distance.

On the one hand, solar tides are only half as strong as the lunar tides. On the other hand, with no lunar tides to confuse the issue resonance would allow the solar tide to grow as large as it could. Over millions of years, the solar tides would grow until the energy input from the sun would be countered by the energy lost by friction. We can consider the tides to be a permanent world-circling wave that has a period of exactly 12 hours.

Yes, but give us some numbers! Sure, as soon as we find a planet like that and we can make some measurements, I’ll get right back to you on that. Until then, this is all guesswork. Even with the largest variable removed, there are still too many variables to make any predictions.

In my story “Jason’s Tale” -set on the planet ‘Chaos’ in Lazlo Zalezac’s ‘Damsels in Distress’ universe- I claimed that, just like on Earth, the tides would depend upon where you were. Further, I made some assumptions that Lazlo may or may not agree with, but I couldn’t get him to cough up his opinion so I went with this:

1) First, of course, I assumed that all the physics is the same. Chaos is the same size and mass as Earth, has roughly the same land/sea ratio, has the same sun at the same distance, the speed of light is the same, the universal gravitational constant is the same, the Planck Constant is the same. After all, none of the other authors mentioned the sun being different or the gravity being different.

2) Chaos has no moon. We aren’t going to get into how this would affect the circadian rhythm of all the plants and animals on the planet, okay? We just aren’t.