THE SOUTHWORTH PLANETARIUM
207-780-4249 www.usm.maine.edu/planet
70 Falmouth Street Portland, Maine 04103
43.6667° N 70.2667° W
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
____________________
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.