Re: double tide cause

["John S. Denker" <jsd@MONMOUTH.COM>]

At 10:36 AM 9/1/01 -0400, Herbert H Gottlieb wrote:

> When the sun and the moon are on the same side of the earth there is a
> very very high tide at that point (Spring Tide).

Right.

> However, an equally high tide occurs on the opposite side of the earth.

Right.

> Shouldn't the indirect high tide on the side of the earth opposite the sun
> and the moon be a bit lower than that on the side closest to the sun  and moon?

No.

Try this:

People often miss the following distinction:  You need to distinguish
 a) the plain old gravitational pull, versus
 b) the tidal stress.

This distinction can be explained in a number of ways.  Let's start with
the pictorial approach:

                                downward
                                 force
                                  \ /
                                   .

                                  eee
                               eeeeeeeee
                             eeeeeeeeeeeee
        (moon)    <====      eeeeeeeeeeeee     <==
                  large      eeeeeeeeeeeee     small
                 leftward      eeeeeeeee      leftward
                  force           eee          force

                                   .
                                  / \
                                upward
                                 force


.   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .
And, ~1/2 month later:


                                downward
                                 force
                                  \ /
                                   .

                                  eee
                               eeeeeeeee
                             eeeeeeeeeeeee
                   ==>       eeeeeeeeeeeee     ====>         (moon)
                  small      eeeeeeeeeeeee     large
                rightward      eeeeeeeee     rightward
                  force           eee          force

                                   .
                                  / \
                                upward
                                 force


Key idea:  A planet subjected to a truly uniform pull would feel no tidal
effects whatsoever.

The AVERAGE pull toward the moon is balanced by the earth's orbital
motion.  That's a solved problem, and is of no further interest when
calculating the tides.  The only thing that matters for the tides is the
DEVIATION from the average.  It turns out
 -- we have an OUTWARD deviation on the moon-facing side, and
 -- we have an OUTWARD deviation on the opposite side.

Larger-than-average to the right is the same as lower-than-average to the left.

This explains why we have twice-a-day (not once-a-day) tides.

If you superpose the lunar double tide with the solar double tide, it's
clear that they reinforce each other ~2 times a month (specifically, at new
moon and full moon).

==================

Again, the key idea is that is dimensionally incorrect to speak of the tide
as a "force".  It is a stress.  An object subjected to a uniform
gravitational force would feel no tidal effects whatsoever.

Imagine a group of positively-charged particles held together by massless
springs.  If we suddenly apply a uniform electric field, the whole group
will accelerate _together_.  This acceleration will _not_ induce any stress
in the springs.  (The analogy to gravitation is obvious;  I mention
electrical fields only because it might be hard to visualize suddenly
applying a uniform gravitational field.)

Bottom line:  I changed the subject of this thread from "Indirect high tide
cause" to "double tide cause" because there is no such thing as an indirect
tide.  Every tide is a double tide.  Every tide has quadrupole
symmetry:  outward at a pair of antipodal points, and inward on the ring of
points 90 degrees away from that pair.

(Actually if you want to get fancy, the quadrupole term is just the lowest
term in a series, but the higher-order terms are quite tiny in comparison.)

So we see that this quadrupole term doesn't even have the same symmetry as
the plain old gravitational-pull term.  Different symmetry, different
dimensions -- how different can you get?