Tides
Published on Jun 9, 2006 at 2:16 pm.
1 Comment.
Filed under Earth.
Anyone growing up near the coast, as I did, is well aware of tides. But, I find that most of my students, who grew up inland, know next to nothing about tides.
Basically tides are caused by a differential gravitational pull. In other words, gravity pulls harder on one part of an object than another, causing it to tend to deform along the direction of the gravitational gradient. The most common tidal effects are the ocean tides along the coast, but they are not the only ones. So, let’s look at ocean tides.
People living along the coast learn that there are two high tides, and two low tides each day. So, there is about six hours between high tide and low tide. What causes these tides. Most people know that the Moon is somehow involved. Simply, the Moon pulls on the Earth with its gravity. The side nearest the Moon is pulled hardest. The side farthest is pulled the least. And the middle of the Earth is pulled somewhere in between. It is clear, then, that there should be a high tide on the side of the Earth facing the Moon. In fact, there is! The high tide occurs when the Moon is high in the sky. But, here, people get confused. It would seem that the low tide should be on the opposite side of the Earth. However, opposite the Moon is another high tide. The low tides are at right angles to the line between the Earth and the Moon. That means that low tides occur about when the Moon is rising and setting. So, what gives?
The answer comes from Newton’s Laws of motion. As it turns out, the Earth actually moves as a result of the Moon’s gravity. Newton’s Third Law tells us that for every force there is an equal and opposite force. So, we know that Earth’s gravity pulls on the Moon to keep it in orbit, but the Moon’s gravity pulls equally hard on Earth. That means that Earth is also orbitting! As it turns out, the Moon doesn’t really orbit Earth. Rather both Earth and the Moon orbit the center of mass of the Earth-Moon system. The center of mass is sort of the average mass position. Since the Earth is much more massive than the Moon, the center of mass is much closer to the center of the Earth than to the Moon. In fact, the center of mass is below the Earth’s surface. So, both Earth and the Moon swing around this point. Since the center of mass is inside the Earth, it looks like the Moon orbits Earth and that Earth is wobbling as a result.
Now, there are two ways to think about what is happening with the tides. The easy way is to think of a bucket of water swinging around. Water will tend to slosh to the side of the bucket farthest out in the swing. So, you can think of the oceans doing likewise. That would explain the high tide opposite the Moon. The tug of the Moon explains the high tide nearest the Earth. This might be an easy way to visualize the situation, but it is not technically correct.
Rather, what keeps Earth orbiting the center of mass is the gravity from the Moon. The way that orbits work, the closer an orbit is, the faster it wants to move. The Moon is pulling on the Earth hard enough to keep Earth moving around in a nearly circular motion. This motion takes as long as it takes the Moon to make a complete orbit, too, about 27.3 days. The side of the Earth nearer the Moon, though, experiences more gravity. This means that it needs to orbit faster in order to have a stable orbit. Well, it can’t move faster because it is still part of Earth and Earth’s own gravity holds it in place. So, what happens is that the Moon’s extra gravitational pull simply pulls that part of the Earth somewhat towards it, creating the high tide. Now, the far side of Earth from the Moon experiences less lunar gravity. So, that means that its orbit should be slower. Again, Earth’s own gravity keeps it moving with Earth. Newton’s first law says that any moving body will tend to move in a straight line unless a force acts on it. The Moon’s gravitational force acts on Earth to keep it moving in a circular orbit. However, the Moon’s gravity is not sufficiently strong on the far side of the Earth to pull that portion of the Earth around into an orbit moving as quickly as the rest of the Earth. So, the far side of the Earth tends to try to move along a path outward from the motion of the rest of the Earth. However, Earth’s own gravity keeps it together, but even so, it moves outward a few feet — the anti-lunar high tide. With those two high tides, low tide will obvioiusly be in between. The high tides occur for a coastal dweller just about every twelve and a half hours.
So far we are talking about lunar tides. As it turns out, a similar effect happens due to the Sun’s gravitational field. The farther from the Sun, the weaker its gravitational pull. So, the side of the Earth nearest the Sun is pulled slightly harder than the side farther away. Now, the Moon is closer, so its tidal effects are more pronounced, but the Sun has a lot of mass, and thus a lot of gravity. Being so big, even at its great distance, there is enough differential in gravitational force to generate a tide. So, even if Earth had no moon, there would still be high and low tides, just based off of the Sun. The solar tides are a bit under half as extreme as the lunar tides.
But, this means that both the Sun and Moon are tugging on Earth to produce tides. When the two line up, then you get really high high tides and really low low tides. We call this spring tide. When the Sun’s tides and the Moon’s tides are at right angles, then the high tide of one is at the spot of the low tide of the other. Since the Moon’s tides are bigger, they dominate, but they are mitigated by the Sun’s tides. This means that low tides aren’t particularly low, and high tides aren’t particularly high. We call this condition neap tide.Â
So, how often do we get spring tides and neap tides? Well, spring tides occur every time the lunar tides line up with the Sun’s tides. Recall that the high tides are on the side nearest a body and on the opposite side. So, at New Moon, the Moon and Sun are both on the same side of the Earth, so we get spring tide. At Full Moon, the Moon and Sun are opposite each other as seen from Earth, so that means the side nearest the Moon is directly opposite the Sun, and the side opposite the Moon is nearest the Sun, so you again add high tide to high tide and get spring tide. Full Moons and New Moons are almost 15 days apart, so spring tides occur every two weeks. Neap tides will occur when the Moon and Sun are at right angles. This occurs at First Quarter and Last Quarter Moons, which occur midway between New and Full Moons. So, you get a spring tide followed by a neap tide a weak later and then another spring tide after that. If you are nearer a Full Moon or New Moon than you are to First or Last Quarter, you’ll have bigger than normal tides, and if you are closer to a Quarter Moon, than either to Full or New, you’ll have smaller than normal tides.
Now, all of this assumes circular orbits. As it turns out, neither the Moon’s orbit nor the Earth’s orbit is circular. When the Moon is closest to Earth, called perigee, you get bigger than normal tides, and when Earth is closest to the Sun, called perihelion, you get bigger than average tides. The worst case scenario for coastal dwellers is a New or Full Moon, while the Moon is at perigee, and the Earth is near perihelion. This happens about every 18 years, and on those days, the ocean appears to just keep coming inland, way past the normal high tide line, and often considerable damage is done.
Also, all of this discussion ignores local topography, which can affect how the water moves around, causing the high tide to be either a big bigger or later than it otherwise would have been.
This weekend is going to be Full Moon. So, that means that high tides will occur near the middle of the day and the middle of the night, with low tides near sunrise and sunset, and the tides will be a bit more extreme than normal. This statement will be most accurate nearest Sunday, when the Full Moon occurs, but it will be within a couple hours of correct a few days before or after. The Moon will be at about normal distance (neither near apogee nor perigee), and the Earth will be close to aphelion, so this won’t be a particularly strong spring tide, but if you live near the coast, you’ll certainly notice that the high tide is higher than normal.
-Astroprof
Astroprof on September 15, 2006 at 10:42 pm: 1
I have a later posting on tides here:
http://astroprofspage.com/archives/247