By Alex Jackson

Tide goes in, tide goes out. Never a miscommunication. You can’t explain that.

— Bill O'Reilly on “The O'Reilly Factor”

Fortunately it is possible to explain the tides, otherwise we’d have a bit of a problem when it came to the Geography exam. The tides are the periodic variation in sea level that occur primarily because of the Moon’s and the Sun’s gravity. Understanding how the Moon & the Sun causes the tides isn’t too complicated but it does involve just a little Physics.

A Primer on Gravity

N.B. What follows is a super basic introduction to gravity. It’s not essential for understanding the Geography but it’s interesting and certainly helps. If you hate Physics then shame on you but here’s a link to skip this section.

Let’s start off with the basics. Gravity is an attractive force and it is always attractive. You’re never going to find repulsive gravity1. Sorry to ruin your Sci-Fi dreams. Any object that has mass (that is to say, any object) has gravity. The object produces a gravitational field that is sort of like a magnetic field but it always points towards the centre of mass of the object and doesn’t have any poles. The gravitational field of an object extends to infinity but it weakens as you get further away from the object following what is known as an inverse square law. Sounds scary but it’s quite simple. If I double my distance from the object, the field strength is reduced by a factor of four. If I quadruple my distance, it’s reduced by a factor of sixteen. What this effectively means is that moving a small distance in a gravitational field produces a comparatively large change in its strength.

The inverse square law describes how the strength of the gravitational field changes with distance but what controls the strength to begin with? The object’s mass. This rule is even simpler than the inverse square law. If I increase my object’s mass, the gravitational field strength increases proportionally. Double the mass, double the field strength. Triple the mass, triple the field strength. You get the picture.

Let’s take these two rules and put them in action. Consider Jupiter, the Earth and you. All three of these objects have a gravitational field and all three of these objects have a vastly different mass. Let’s say your mass is 60kg, the Earth’s is roughly 6×1024 kg and Jupiter’s is somewhere around 1.9×1027 kg or 310 times the Earth’s. In the current universe (universe 2 according to a friend of mine), you are 6,400km from the centre of the Earth (for simplicity’s sake, imagine the mass of the Earth and Jupiter is concentrated in an infinitesimally small ball in the centre of each planet). Jupiter is, at the time of writing, around 917 million kilometres away from the Earth and you. Despite being quite a bit more massive than the Earth, you do not feel attracted to Jupiter (gravitationally2) because it’s so far away from you that the gravitational field strength is almost imperceptible on the Earth.

Now let’s move to another universe (universe 3). In this universe the laws of Physics were very different during the formation of the solar system so Jupiter was able to form where the Moon is in our universe. What this means is that the distance between the surface of Jupiter3 and the surface of the Earth (and you) is around 380,000km. What do you think the effects of this will be? Will you float away from the surface of the Earth towards Jupiter? Nope. Make no mistake, the effects of Jupiter being this close to the Earth would be catastrophic but you wouldn’t float away from the Earth4. Even at this distance, Jupiter’s gravitational field is still weaker than the Earth’s at the Earth’s surface because of the inverse square law. The point I’m trying to make here is that the inverse square law plays a huge role in the strength of a gravitational field at different points. Beyond a fairly short distance, it plays a much bigger role than the object’s mass.

Tidal Forces & The Tides

This bit’s important.

With a basic understanding of gravity under your belt, let’s take a look at how gravity is responsible for the tides. In particular, we want to look at how the Moon’s gravity produces the tides. Although it’s much less massive than the Earth, the Moon is still quite massive. As a result, the strength of the Moon’s gravitational field at its surface is about 17% the strength of the Earth’s field at its surface. Compared to the moons of some other planets (I’m looking at you Mars) that’s quite significant.

On average, the Moon is 385,000km from the Earth so, thanks to the inverse square law, the Moon’s gravity is very weak at the surface of the Earth. It gets even weaker though when we move to the side of the Earth facing away from the Moon. On this side of the Earth, there’s another 12,800km between the Moon and the surface and so the Moon’s gravitational field at the Earth’s surface is ~90% of what it is on the side facing the Moon.

This difference in the Moon’s gravitational field across the Earth gives rise to tidal forces that, as the name suggests, are responsible for the tides. On the side of the Earth facing the Moon, the Moon’s gravitational field is strong enough to attract the water on this side towards it, creating an ever so slight tidal bulge. This tidal bulge is what we associate with a high tide.

At the same time we get another high tide on the opposite side of the Earth. Initially this seems a bit counterintuitive. After all, won’t the Moon’s gravitational field pull the water on the other side of the Earth and produce a low tide? The thing we have to consider is how the Moon’s gravitational field affects the solid Earth. The solid earth is also subject to tidal forces which distort it and create a small tidal bulge in the solid earth. The centre of the Earth is effectively pulled towards the Moon and because it is 6,400km closer to the Moon than the far side of the Earth, it is more strongly attracted to the Moon than the water on the far side of the Earth. The net effect of this is to produce a second high tide on the far side of the Earth because the Earth is moved more than the water.

These two high tides “thin” the oceans at points on the Earth’s surface between them, producing two low tides.

If you’re still a bit confused, these diagrams might help clear things up. The first shows the attraction of different points on the Earth towards the Moon. The length of the arrows indicates the relative strength of the attraction. Bigger arrows mean a stronger attraction:

An image showing the relative strength of the gravitational attraction towards the Moon of different points on and inside the Earth.
The relative strength of the attraction of different points on the Earth towards the Moon. The longer the arrow, the stronger the attractive force. The different colours are just for legibility.

The diagram shows that the near side of the Earth is more strongly attracted towards the Moon, the centre less so and the far side even less so. When you account for5 the attraction of the centre of the solid Earth towards the Moon, you end up with a diagram which looks like this:

An image showing the tidal forces acting on the Earth from the Moon when the acceleration of the Earth's centre of mass is taken into consideration
The tidal bulge that forms as a result of the Moon when the attraction of the Earth is taken into account. The (exaggerated) blue outline shows where high and low tides would appear.

Tide Times

Because the Moon orbits around the Earth in the same direction the Earth is rotating, high tides occur once every 12 hours and 25 minutes rather than once every 12 hours. You get one high tide when you’re facing the Moon and then 12 hours and 25 minutes later you get another one when you’re facing away from the Moon. Just like clockwork. Isn’t it nice when something in nature is simple?

Unfortunately it isn’t that simple. Logic would suggest that you get a high tide when the Moon is directly overhead and another one when it is directly underneath you. The thing is you don’t. You also don’t get a high tide once every 12 hours and 25 minutes. In some places you get two high tides each day, in some you only get one and in some you get two high tides that have different heights.

This is because there are several other things which affect the tides besides the Moon. These include the varying depths of the oceans, the continents, the shape of coastlines, the interaction of the surface of the oceans with the atmosphere and a few other things. They all create complications in how water moves meaning that the Earth’s water doesn’t immediately form a bulge when the Moon is overhead. In reality, it takes a bit of time for the water to react to the Moon’s passage.

Tidal Range

The tidal range is the difference in height between successive high and low tides. In most parts of the world, the tidal range varies every couple of weeks because of another massive body in the Solar System. The Sun, being a star and all, is even more massive than the Moon or the Earth (about 330,000× the Earth’s mass). Despite this its gravitational field is fairly weak here on Earth because it’s 150 million kilometres from us. The Sun’s gravitational field actually ends up being about half as strong as the Moon’s gravitational field at the Earth’s surface. When combined with the Moon’s gravitational field though, the Sun can help produce two special types of tides known as spring tides and neap tides.

Spring tides occur when the Sun, the Earth and the Moon are aligned—an event known as syzygy. When this happens, the tidal forces of the Moon are reinforced by the Sun’s producing higher than average high tides and lower than average low tides. The net effect of this is to increase the tidal range.

Note that spring tides have absolutely nothing to do with the season of spring. Spring tides occur once every two weeks6 whereas the season occurs once a year.

A diagram showing the alignment of the Sun, Earth and Moon to produce a spring tide
A spring tide, produced when the Sun, Earth and Moon are aligned. The blue halo shows the exaggerated tidal bulge. Please note we don’t actually have two Moons, this diagram is showing the possible positions of the Moon.

When the Sun and the Moon are perpendicular to one another, the Moon’s tidal forces are partially cancelled out by the Sun’s producing a neap tide. During a neap tide, the height of the high tides is lowered and the tidal range is reduced. Like spring tides, neap tides occur once every two weeks.

A diagram showing the misalignment of the Sun, Earth and Moon to produce a neap tide.
A neap tide, produced when the Sun and the Moon are at 90° to each other. The blue halo shows the exaggerated tidal bulge that is produced.

  1. I’m going to regret writing this in a few years when someone writes a paper about antigravity.

  2. I’m sorry, I had to make some joke about the attractiveness of Jupiter.

  3. In this universe Jupiter has a solid surface. It also has no moons to mess with this thought experiment.

  4. In order for Jupiter to even start to pull you off of the Earth, the distance between the surface of the Earth and the surface of Jupiter would need to be ~44,500km. Of course, even at this distance you wouldn’t be pulled off of the surface of the Earth because the Earth, and by extension the surface, wouldn’t exist anymore thanks to tidal forces.

  5. For the more mathematically inclined, the arrows in the previous diagram are vectors showing the acceleration of a 1kg test mass in the Moon’s gravitational field. We want to find the tidal acceleration of this mass relative to the Earth’s centre of mass so we simply subtract the acceleration of the Earth’s centre of mass from the other two vectors to obtain it. This gives us a smaller acceleration on the near side of the Earth and a negative acceleration on the far side—our tidal bulge.

  6. Why every two weeks? Because that’s half of a lunar month (the time it takes the Moon to orbit the Earth once) which is 28 days.