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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: The development of bubble sextants
From: Gary LaPook
Date: 2009 Aug 17, 00:59 +0200

```The problem with "frame-dependent" accelerations is that they are just
artifacts of the frame you chose to use to define the accelerations and
therefor the forces that must have caused the accelerations are also
arbitrary artifacts too. Since anybody can choose any gyrating,
spinning, hopping, twirling etc., accelerating frame of reference, any
measured motion of an object could have an infinite number of different
forces and accelerations. If I get to choose the right accelerating
frame I can prove that it was your nose that hit my fist. But for non
accelerating frames of reference, inertial frames, it doesn't matter
which frame you choose the observer will always calculate the same
forces for any observed object. I understand that there are some
computational advantages in some circumstances to create fictitious
forces when dealing with rotating frames such as the earth.  For
example, if I am demonstrating a loop to a flight student it is easy for
me to tell him that it is centrifugal force that presses his butt into
the seat at the top of the loop while we are upside down. This is easier
than the real explanation that pulling back on the stick while we are
upside increases the angle of attack of the wings causing the wings to
create a greater force. Since we are upside down this greater force from
the wings (lift) causes the aircraft to accelerate towards the earth at
a rate of acceleration greater than than the rate of acceleration caused
by gravity thereby leaving the pilot's behind behind. Even though this
is convenient, it that still doesn't make centrifugal force real since
it is just another fictitious force invented to allow a simple
explanation in the looping frame of the airplane.

gl

..

frankreed@HistoricalAtlas.com wrote:
> Quoting Gary:
> "Coriolis is a fictitious force use to explain the perceived curve of the
> flight path as observed by an observer on earth of other rotating frame
> of reference."
>
> Coriolis acceleration is a "frame-dependent" acceleration. That is, it
depends on the choice of coordinates that you use to define motion. The
expression "fictitious force" is a technical term intended to describe this
frame-dependence. Just so there's no misunderstanding, it DOES NOT mean that
the Coriolis acceleration is "fictional" in the ordinary sense of the English
word. Of course, Coriolis acceleration is "real" in the sense that in many
circumstances you find that the natural coordinates to describe the problem
are rotating coordinates. The weather on Earth or any other planet, for that
matter, is nearly impossible to understand in non-rotating coordinates but
quite easy to understand in coordinates which rotate.
>
> >From a modern perspective (modern = since the early part of the 20th
century, after the development of general relativity), even the common
acceleration of gravity near the surface of the Earth (at a single point) at
9.8 m/s^2 or 32 ft/sec^2 is a "fictitious force" since it can be eliminated
by going to a frame of reference which is accelerating toward the Earth's
center, in other words a freefall frame. And sure enough, if you place an
aircraft on a parabolic trajectory with that acceleration, gravity disappears
and passengers are rendered completely weightless exactly as if they are in
orbit (until the plane's acceleration trajectory is changed). It is not "as
if" there is no gravity; in that frame of reference, there really is "no
gravity" apart from local tidal accelerations.
>
> Many people are able to explain the origin of the Coriolis acceleration by
describing how it appears in an inertial, non-rotating frame of reference. In
such a frame, the object moves on a straight line "while the Earth turns
beneath it". This is very important information, of course, but it is a
derivation, like an "etymology". It tells us why this acceleration must exist
in non-inertial frames of reference, but it doesn't mean that it is fake or
"fictional". And you surely wouldn't want to revert to the derivation once
you understand why it works.
>
> In many ways, the expression "fictitious force" in physics has caused as
many problems as the expression "imaginary number" in mathematics. Neither of
these concepts are invalid or fictional or "un-real". For modern mathematics,
so-called imaginary numbers have no defects, no lack of reality to them. They
are what they are: solutions to algebraic equations. Likewise in physics,
so-called fictitious forces are not forces to be avoided or treated as
"un-real". They are what they are: forces arising from the choice of
coordinates.
>
> -FER
>
>
>
>
>
> >
>
>

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