Re: Tides and tidal bulge

["Daniel L. MacIsaac" <danmac@physics.purdue.edu>]

Recently, Jim Green posted his annual claims about tidal bulges:

> And neither is the spring tide in coincidence with New/Full Moon.

....on 30 July (this month) the Moon is at perigee, and this coincides with a
full moon.  According to my astronomical almanacs that means the highest tides
of the year will occur on that date (with phase corrections for local
geometry and drag).  Pretty coincident for me.  Anyone living on the coasts
inclined to check local tide predictions and comment?
 
> Even though the force on the ocean due to the Moon exceeds by far the force
> on the ocean due to the Sun, the Moon's force need NOT predominate the
> tides.  Any periodic force can predominate as long as it is at the resonance
> frequency of the resonant body.  

Wrong.  Using Re-m as 3.80E+05km, Re-s as 1.50E+08km, Ms = 2.00E+30kg and
Mm = 7.40E+22kg, Fs-e is about 175X greater than Fm-e.  The sun pulls harder,
and your arguement is based on assumed bad numbers.  Get out a napkin and a 
calculator, figure the force ratio and see for yourself.
> Further if one wants to beleive in tidal bulges, the comparison force would
> be the NET force due to the Sun/Moon/(and maybe Jupiter) combination. THAT
> force will have no synchronization with the tides.
Sorry, too simplistic.  The Moon's predominant effect on the Earth's
oceanic tides is NOT due to simple net force.  The sun exerts more grav
force on the Earth's surface than the moon does (175X more by my numbers),
but it is about 400X farther away.  The moon's gravitational force is small,
but because it is so very close it has a large gradient across the diameter
of the earth.  This GRADIENT is responsible for the bulges (both of them).

In plain english, the Earth and Moon exert gravitational forces on one 
another as solid, semi-rigid bodies and fall (accelerate) towards one 
another.  The waters on the side of the Earth nearest the moon accelerates 
towards the moon at an above average rate, because they experience more 
gravitational force, 'cause they're closer by one Earth radius.  This causes
a bulge to be pulled up by the moon.  On the back side of the earth (away 
from the moon) the waters are two earth radii further away from the moon,
so the waters on the side away from the moon fall towards the moon with an 
acceleration less than that of the earth and are left behind, forming a 
second bulge.

While gravitational force goes as 1/r^2 , the variation in gravitational 
force goes as the cube.  This variation (gradient) is the key.  One earth 
diameter (1.2e4km) is about 1/32 of the distance to the moon (3.8e5km),
but is only about 1/12000 of the distance to the Sun.  The sun's gradient
is tiny compared to the Moon. The nearness of the moon causes the effect, 
and other near satellites in the solar system see the same tidal effects.  

Other effects: because the earth rotates faster than and in the same 
direction as the moon, the water bulges are dragged ahead of the moon, and are
not directly underneath the moon.  Because the moon transits 50 min later 
each day, high tides occur 50 min later each day.  The earth's crust 
experiences very little bulge due to this effect (Kaufmann, Universe 4th Ed 
says only 1 foot), but the moon's crust experiences significant bulges on 
both sides due to this effect.  These bulges in the moon's crust (Kaufman says
60 feet) have resulted in the moon becoming tidally locked to the earth.
Eventually, as the earth spins down losing energy by frictional heating of the 
moon, earth and ocean, the tidal bulges on the earth's oceans WILL occurr
directly under the moon and we will be tidally locked to the moon.  Similar
tidal interactions (greatly magnified) regularly turn Io inside-out as
it is squeezed like a tube of toothpaste in Jupiter's gravitational field
at a distance of only a little further than our moon, near a planet with 300X
the Earth's mass.

Yes, there are places on the Earth that experience only one, two or three 
tides a day.  Yes there are places resembling resonant chambers that see
unusual tidal phenomena.  Yes, local coastlines and enclosed lakes have
tides called Seiches that occur at resonant frequencies driven by the 
Earth-Moon system.  BUT the earth-moon tidal buldge system IS the paramount
driver of these phenomenon.  The Bay of Fundy system is awesome because it
is coupled closely (12.7 h) to the natural earth-moon system (12h25m) and
has that nice, high Q.  

Tidal bulges are real and deserve to be taught as such.  Didn't we have this
debate about a year ago?  I seem to have the refs on a nearby shelf with
printouts from that last round.  Do you, Jim?

Refs:  

Bishop, Roy L (1996).  The Observer's Handbook, RASC (p. 124, tides)
Arons, A. (1979) Basic Physics of the Semidiurnal Lunar Tides, AJP 47(11), 934
	(Nov 79).
Kaufmann, W,J, (1993) Universe, 4ed, p170 (Freeman).
E.P. Clancy, (1969).  The Tides.  Doubleday (Anchor) Out of print but 
	exceptional.

I got my numbers from Bill Arnett's THE NINE PLANETS at
http://www.seds.org/nineplanets/nineplanets/
and rounded lots.  Definitely check out this page if you are teaching about
the solar syste this page if you are teaching about
the solar system.
  
Dan M

Dan MacIsaac, Assistant Professor of Physics and Astronomy, Northern AZ Univ
Visiting Asst Prof, Purdue Univ;  Adjunct Faculty, Indiana Univ at Kokomo
NEW NET ADDRESSES:  danmac@nau.edu  http://www.phy.nau.edu/~danmac