From: mcirvin@husc8.harvard.edu (Matt McIrvin)
Newsgroups: sci.physics
Subject: Re: satellite orbits
Date: 27 Jan 93 17:05:12 GMT

u108502@beta.lanl.gov (Andrew Poutiatine) writes:

>In article <1993Jan22.134213.6183@rhrk.uni-kl.de> kring@efes.physik.uni-kl.de (\) writes:
>>
>>Some people will tell you that centrifugal force is "not a real force" or
>>"pseudo force" but I think that's dubious.  The Theory of General Relativity
>>states that you can choose whatever system of reference you want, laws of
>>physics will be the same.  Using the standpoint of an observer on the
>>satellite is as reasonable as any other, only the forces you need are more
>>complex.  That is, you need more assumptions to explain the same observations.
>>Therefore, using Occam's razor ("Do not unnecessarily multiply entities" or,
>>as Einstein put it, "As simple as possible - but not simpler")
>>one normally chooses the frame of reference with less assumptions.
>>
>>BTW, that's the only reason why we say that the earth is rotating the sun and
>>  not the other way around: for simplicity.

>Some of what you say has merit, although the above is both wrong and 
>dangeroulsy misleading to those who wish to learn.

Perhaps if they're studying Newtonian mechanics-- but it is
not so incorrect or misleading if one is using GR.  In GR gravitational
forces are described as pseudoforces exactly like centrifugal force--
if you argue that the rotating frame in which centrifugal force exists
is the wrong one, you must treat gravity as equally fictional.  The most
natural frame in GR in which to discuss the motion of a satellite is
a frame in free fall, in which case there are no forces on the satellite
at all!

Yet, in the Newtonian limit, we find it convenient to use coordinates in
which there appears to be a gravitational force.  It is no less legitimate
to use a system in which centrifugal forces appear; the force could
even be called gravitational if your semantics respect the Principle
of Equivalence.  (I know that you can distinguish one from the other by
the presence of tides-- but in either case, the force really comes from
the choice of noninertial coordinates.)

>As far as what was said about Relativity, this in also not entirely true in 
>that Relativity _does_ distinguish between accelerating frames (i.e. non-
>inertial) and non-accelerating frames.  This is in my understanding the 
>basis for the resolution of the twin paradox.

In *special* relativity, this is the case.  General relativity, by
necessity, is expressed so that calculations may be done in any
coordinate system.  If the coordinates are locally freely falling,
falling objects' coordinates will be linear functions of proper time--
this is the only special frame, but it can generally only be defined
locally.  Another frame in which objects experience a gravitational
acceleration toward the earth is no more legitimate than one in which
they experience centrifugal and Coriolis forces.

>It is patently false to say that simplicity is the only reason why one 
>reference frame is chosen over another, and that that is the only reason
>why we say that the Earth rotates about the sun, and not visa versa. Conservat-
>ion of momentum distinguises between the inertial and non-inertial frames,
>which is why an inertial frame is called inertial.

Conservation of momentum in GR applies in the Newtonian limit; it becomes
far less clear in other situations.  In the Newtonian limit, an
"inertial" frame which leaves gravity as a force is simpler than
others, and this is the reason it is used.

In Newtonian mechanics, with gravity defined as an attractive force,
there is certainly a difference between gravity and something like a
centrifugal or Coriolis force.  In GR the distinction disappears;
*tides* have an existence independent of coordinate system, but the
gravitational *force* that pulls you toward the earth becomes
understood as something not fundamentally different from the
pseudoforces you feel in an accelerating car. 
-- 
Matt McIrvin