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Re: non-inertial: ad infinatum

On Tue, 30 Apr 1996, Rauber, Joel Phys wrote:
...

Instead, simply get rid of the rather strange idea that every acceleration
relative to any arbitrarily accelerated reference frame must have a force
associated with it.

Its not a strange notion. In fact one uses it everytime they use a spring
balance to measure a force. You balance the spring force against the force
you are trying to measure. The idea being you set the acceleration equal to
zero and use the notion that that implies zero net force: and voila, the
spring balance reading then equals the magnitude of the force you trying to
measure and the direction of the force you were trying to measure is in the
opposite direction of the spring force on the object.

That is you used this strange notion of associating acceleration with a
force!
...

If this is what goes on every time you use a simple spring scale, than we
are indeed in a very strange world. Acceleration should enter into the
process in no way whatsoever.


...
This is not what Newton's second law says -- Newton's
second law only says accelerations correspond to forces in inertial
reference frames -- and then when you come to need to compute accurate
values of dynamical quantities, you will not have to sort out fiction from
fact.


Again, Newton's laws expressed in a non-inertial frame, with kinematic and
interaction force terms present are formally the same as Newton's laws in
inertial frames; therefore any idea derived from them in inertial frames
have their equivalent in the non-inertial frame; even the dynamical ones.
...

EXCEPT, you must remember not to let the energy company bill you for the
terms that are purely (mass x acceleration relative to noninertial frame).

Al Clark wrote:

I think the point is that some people find it easier to handle problems
of motion in a rotating reference frame with the use of the apparent
centrifugal and coriolis "forces", and there is no reason to deny them
the freedom to do that as long as they know what they are doing, and that
the apparent kinetic energy may be just that, apparent only.

I basically agree with this statement. However, I would ask , are we being
told that when I compute 1/2 m v^2 for a baseball thrown to the batter that
we start calling that "apparent kinetic energy" rather than "kinetic
energy". I vote no. because it has all the properties of kinetic energy,
namely the ability to do work. It will drive a nail as far into a plank of
wood as the same quantity(experiment) would if calculated (performed) in an
inertial frame...

Of course you must take that into account if you want a very accurate
computation of kinetic energy. The amount of Coriolis and centrifugal
acceleration because the Earth's surface is accelerating relative to an
inertial frame only makes a small correction necessary in the horizontal
plane (direction of motion of baseball) over the small time the baseball
is in flight, but if you want an accurate account of kinetic energy,
accurate, say, to the fifth decimal place and beyond, you must compute it
relative to a nonaccelerating frame (i. e., inertial frame -- but you
can use the stars as a guide), and so you must incorporate both the Coriolis
and centrifugal accelerations explicitly, as Coriolis showed. The effect
on energy computations is MUCH more serious on ballistic missile
calculations and their fuel consumption.

...
I'll give it a shot, but I would like some clarifications. All I have to do
is compute the mass of the sun by working in a non-inertial frame of
reference? I'll interpret this to mean solve for "mass of sun".

Correct.

Now explain
what you meant in the other post about the correction "m+M". I wasn't privy
to original statements...

There wasn't any original statement about M+m. I simply point out that
the only accurate computation I am aware of calculates mass of sun + mass
of Earth (M+m) and cannot calculate M (Sun) alone. I would be interested
however in an accurate method of calculating EITHER M or M+m by applying
Newton's laws in a reference frame in which Earth and Sun are at rest,
using any pseudoforces necessary to make this come about.


Also, is it sufficient for purposes of this problem to assume the center of
mass of the system is for all practical purposes at the center of sun and
that the earth orbits about that center of mass in a circle?

The condition of the problem specifically says "by applying Newton's laws
in a frame in which Earth and Sun are at rest," so there is no orbiting
going on in that frame at all; however, you may introduce any pseudoforces
necessary to balance the real interaction between Earth & Sun (Newtonian
action-at-a-distance inverse square approximation fully acceptable! No GR
considerations needed.) But no, you cannot make any false assumptions
about the center of mass -- that's a well defined quantity involving
only masses and positions, with no reference at all to velocity or
acceleration.

Your claim has been that Newton's three laws are equally true relative to
either noninertial frames or inertial frames, as long as you can introduce
pseudoforces in the noninertial frames to balance the real forces.
Prove it.
In other words, if you are going to state Newton's laws without referring
to inertial frames, than you ought to be able to apply the laws without
using such a frame. I don't see it, but you claim to.

... More precisely, I want to know the ground rules of what it is I'm
supposed to calculate...

Ground rules as stated; derive an astronomically accurate formula for
either M or M+m by applying Newton's laws relative to a frame of reference
in which Earth and Sun are at rest, using Newtonian formula for
gravitational interaction between Earth and Sun, and any pseudoforces
you need.

A. R. Marlow E-MAIL: marlow@beta.loyno.edu
Department of Physics PHONE: (504) 865 3647 (Office)
Loyola University 865 2245 (Home)
New Orleans, LA 70118 FAX: (504) 865 2453