THE SOUTHWORTH PLANETARIUM
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Founded January 1970
Julian date: 2457688.16
"We'll leave the night on for you."
THE DAILY ASTRONOMER
Tuesday, October 25, 2016
Poseidon's Tide
___________________
To LW,
who gave me the idea
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It is traditionally called a "King Tide," but, since we're Americans descended from a noble people who railed against the British monarchy and all its nefarious works, we opted for the moniker Poseidon's Tide. (Yes, actually, it is national fertilizer day.) Actually, being mythology geeks, we couldn't resist this alternate title. Scientifically, we should refer to it as the "perihelic perigean spring tide," a term that skips off the tongue like it was just kicked out of flop house. We are referring to an extremely high tide that occurs when either the new or full moon is at perigee around the same time Earth is close to perihelion. As we'll experience such a high tide in November, it is high time we discuss Poseidon's Tide.
However, before we can explain Poseidon's Tide, we have to contend with explanations of tides, themselves. And, yes, we understand that tide talk is the astronomical equivalent of visiting a Medieval dentist who secretly relishes others' pain. Nevertheless, despite the torment, we proceed. Earth generally experiences two high tides and two low tides a day,* The tides result from a differential gravitational force (pay no attention to that drilling sound.) We know that all massive objects exert a gravitational force on all other massive objects, in accordance with Isaac Newton's Universal Gravitation Law. Moreover, the magnitude of the gravitational force between all massive objects diminishes with the square of the distance. (If you double the distance between two objects, the force is reduced to a quarter; triple the distance, the force is one ninth of the original value.) Now, if all massive objects were point masses, as described in elementary physics texts, then the matter would be simple: the forces would be equal along each mass and the math would treat us sweetly. Of course, the physical world doesn't have point masses. Instead all massive objects occupy a specific volume, whether they're volleyballs or planets. Differential gravity arises from this inconvenient breadth.
Regard Earth and the Moon. Both bodies exert a force on one another. However, the magnitude of the force varies within each body because different regions experience a different gravitational force. The portion of Earth closest to the Moon feels a greater tug than the planet's center because gravity falls off with the square of the distance, which is 6,371 km (3,959 miles).
Regard Earth and the Sun. Yet, again, both bodies exert a force on each other. And, likewise, the gravitational force the Sun exerts on Earth varies along its volume. The part of Earth closest to the Sun (noon) experiences less gravity than the part farthest away (midnight.) However, the Sun is much farther away from us than the Moon. The Sun's mean distance is 93 million miles; the Moon's is 240,000 miles, so the 'tidal force' the Sun causes will be less than the Moon (44% as great, actually.) This is because the force difference between the near and far sides of Earth relative to the Sun is not as profound as the difference the Moon induces.
Both the Sun and Moon contribute to the high tides, although, as mentioned previously, the latter is more influential than the former. Each day, as Earth rotates beneath the Moon, the planet 'bulges' along the Earth-moon line.** This bulge region has a high tide. Yet, so, too does the point on Earth that is diametrically opposite of the first bulge. Here, our intuition fails us. Though it might be easier to understand why the area just under the Moon has a high tide because of the differential gravity, one is at a loss to know why the most distant region also experiences one.
Spring and neap tides Both the moon and the Sun exert tidal forces on Earth. The Sun's tidal force influence is 44% that of the moon's. When the moon and Sun are aligned,as they are during a full or new moon, the tides will be at their highest. We refer to these higher tides as "spring tides." When the moon is at the quarter phase, the Sun and moon will be working in opposite directions and the tides will be lower. We call these lower tides "neap tides." When the moon is new or full around the same time it is near or at perigee, we'll have perigean spring tides,which will be higher than other spring tides. Finally, when Earth is at or near perihelion around the same time as the full or new moon it at or near perigee,we'll experience a perihelic perigean spring tide.
Think of this: the pull of the Moon, and to a lesser extent, the Sun, exerts a "bulging effect" on Earth, similar, in principle, to the effect of squeezing the planet into an oblong shape. When we regard this issue physically, we can think of Earth's center as being stationary, with the two opposite points along the Moon-Earth line pulled away. The water is drawn toward both these bulges, while the two areas perpendicular to it experience low tides. The water amount is constant, so an excess in one region must create a deficiency in another.
To add a little more complexity, we remind the reader (yes, we know you haven't forgotten) that the angle between the Sun, Moon and Earth is always changing. During New Moon, the Moon is between the Sun and Earth, so both Moon and Sun are puling in the same direction and their gravitational influence is combined. At full moon, Earth is between the Moon and Sun. They're pulling in different directions, of course, but they're both operating along the bulges. The tides occurring around new and full moon are known as "spring tides." The lowest high tides happen during first and last quarter (quadrature), when the Moon and Sun are operating perpendicularly and therefore diminishing the tidal effect.
Now, to make life even more interesting, the Moon's distance from Earth and Earth's distance from the Sun are both constantly changing. This continuous change happens because both Earth and the Moon travel along elliptical orbits, which we can envision as 'ovals.' If the orbits were perfect circles, the distance would be constant. Of course, it isn't. During every orbit the Moon reaches a point of least distance, called "perigee." Just as Earth, itself, also has a closest point, called "perihelion." When the Moon reaches perigee, the tidal forces are enhanced because the differential gravitational force varies with the cube of the distance. The same effect occurs, to a lesser extent, when Earth reaches perihelion because at that time the Sun is closest to us,
Here is where we watch the gears turning: Every so often, the Moon will reach perigee around the time it is either at full moon or new moon. This coincidence is called 'astronomical high tide,' a term also applied merely to the tides corresponding to the full and new moon. (Although the term 'spring tide' is more apt.) Perigee doesn't generally correspond to the full or new moon because the period between successive perigees, called an 'anomalistic month,' is about 27.5 days, whereas the phase cycle, called a 'synodic month,' is 29.5 days. However, when they correspond, the tides will be quite high.
On November 14, the Moon will be full about 2.4 hours before it reaches perigee. Moreover, Earth is approaching perihelion, which it will reach on January 4, 2017. The full perigee moon occurring around the time of perihelion (within less than two months) and the tides should be high enough to even sweep austere, embittered people off their feet.
Poseidon's Tide is a term that was born -and most likely will perish- in this very article. But, like the double rainbow fading above a remote and unpeopled glacial plain, it existed, if only for a moment.
*Sometimes, a high tide will occur just after midnight, so a certain day might have just one high tide and two low. Or, vice versa.
**The Moon is not exactly aligned with this bulge, to be more accurate, but let's not extract too many molars.