Re: TIDES, was Asteroid Problem

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

At 08:37 AM 9/2/01 -0400, Ludwik Kowalski wrote:

> Consider a perfectly spherical earth
> at rest in the absolute Newtonian space;

There is no such thing as absolute space, and Newton knew it.  Indeed
Galileo knew it, decades earlier.  Pretending we don't know it doesn't help
anyone.

This is not nit-picking.  I suspect that absolute-space misconceptions are
causing widespread misunderstanding of the tides.  See below for more on this.

> ... frictionless track along the equator supporting 3600 cars
> which are connected with identical springs. Cars are at the
> same distance from each other (initial static equilibrium).

No good.  The track provides a force of constraint that gives this
situation radically different physics from the real tide physics.

Key idea:  The tide problem has nothing to do with the _position_ of the
earth.  It is all about the _shape_ of the earth.

The cars-on-a-track setup focuses too much attention on the position of the
car-distribution.

If you want to do a simulation, do the right simulation:  An array of pucks
on the D=2 air table.  Measure the _shape_ of the car-distribution RELATIVE
to the average _position_ of the car-distribution.

Make sure the air table is big enough:  The cloud will accelerate off to
one side (_position_) at the same time it is exhibiting tides (_shape_).

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

IMHO the simulation wouldn't really add much.  This is a solved problem two
times over:
 1) The force diagrams make a vivid prediction of "what" happens and "why".
 2) Writing the potential as a Taylor series sheds additional light on
"why".  Constant piece + planar piece + saddle-shaped tide-producing
piece.  I can visualize the 1/r potential and see these three contributions
to the potential without writing a single equation, indeed without writing
anything at all.
 X) The simulation would perhaps verify "what" happens but wouldn't shed
any additional light on "why".  I don't need the simulator for
verification.  I've spent enough time near the seashore to have a pretty
good idea of "what" happens.