Re: tides (again)

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

As has been noted on this list the "two bulge" model of the tides
is misleading at best:  There simply are not two bulges.
Nevertheless, the dominant tidal drive force *is* ~diurnal and
leads (at most positions) to ~diurnal tides.  The ~diurnal driving
force is a result of two simple facts:

1. The force of contact between an object and the surface of one
spherical body orbiting (or being orbited by) another is minimized
when it is located at either of the two surface points that lie
along the line from the center of one gravitating body to the
center of the other and is maximal when it is located near the
great circle that is equidistant from those two points.  (Draw a
picture!)

2. The Earth rotates with respect to its primary tidal partner,
the Moon, approximately once per day.

The relative rotation is critical because it causes the force of
contact at each location to vary, NOT because of any centrifugal
force that it produces.  If the Earth were not rotating at all, it
would still have tides.  The predominant period would simply be
be half a month rather than half a day and it would be modulated
by a half a year component due to the sun.

Thus, while I am a strong advocate of "centrifugal force" (used
judiciously and with due concern for one's audience), it is not
IMO relevant to the tides.

I have produced an Interactive Physics 5.0 simulation to
demonstrate all of this and put it on my Interactive Physics page.
For those who don't have IP, I shot a Quicktime movie of the
planet as it falls toward the Sun while rotating.  A meter
monitors the relative contact forces between the planet and four
people standing at 90 degree intervals around the circumference of
the planet as it rotates and falls.  These can be viewed at

 <http://www.csupomona.edu/~ajm/ip.html#tidalforces>

Justin Parke wrote:

> I was looking at an article the astronomy teacher was handing
> out to her class (9th grade earth science) which claimed that
> the second high tide in a day was caused by the fact that the
> earth does not rotate around its geometric center but that the
> earth and moon each revolve around their common center of
> mass.  The article said, basically, that it is a centrifugal
> effect.  I am suspicious of this explanation (as I am with
> most explanations in earth science texts).  My suspicion does
> not lie in how the earth-moon system rotates, but that this
> could cause a "tidal bulge" on the side of the earth opposite
> the moon.
>
> I have searched the archives of this list and found volumes on
> tides but none mentioned this effect (that I saw).  Any
> comments?

----------------------------------------------------------
 A. John Mallinckrodt        http://www.csupomona.edu/~ajm
 Professor of Physics      mailto:ajm@csupomona.edu
 Physics Department         voice:909-869-4054
 Cal Poly Pomona              fax:909-869-5090
 Pomona, CA 91768-4031     office:Building 8, Room 223