Re: [asa] geocentricity

Yes, an observer in an accelerated frame like one in a braking car will feel
a "force" due to the acceleration. This is a fictitious force, simply part
of ma moved to the other side of the equation & labelled F in order to
maintain Newton's laws. That's the cost of pretending that an accelerated
frame is inertial in Classical physics. What Einstein realized is that such
fictitious forces have the same property of gravitation, that they're
exactly proportional to the inertial mass of a body they act on.
Gravitation itself is a fictitious force that's introduced so that we can
pretend that space-time is flat.

An accelerated observer will indeed "feel" fictitious forces. But the
equations of general relativity are indeed generally covariant and allow us
to use such a coordinate system if we wish, in spite of that. (& we don't
actually have to adopt that as our proper frame - just as we don't have to
ride through the lab in a rocket if we want to use the center of mass frame
to study a collision.) The generally covariant laws of physics are as true
in one system as in another. It's just a deeply held prejudice, related to
the notion of absolute space, that makes us think that a frame in which an
observer would feel no centrifugal, Coriolis &c forces is in some sense more
fundamental than another.

& when it comes to the solar system we have to be even more careful. First
we'd have to ask "With respect to what is the earth accelerated?" Of course
an observer on the sun will see the earth's velocity vector change. But the
earth itself is (in the usual coordinates) simply in free fall. An observer
moving with the earth feels no "gravitational force" due to the sun nor any
"centrigugal force" due to accelerated motion. In his/her proper frame -
which for many purposes is the most convenient for that observer - they
cancel out.

& in fact in the covariant formalism that observer has no acceleration in an
absolute sense: He/she follows a geodesic, & that means that the intrinsic
derivative (inner product of covariant derivative & four-velocity) of the
four-velocity with respect to proper time is zero.

In order to answer the question about a slingshot manuever in detail I'd
have to work out the math but I see no reason why there'd be a problem. The
necessary transformation (to sufficient accuracy) from heliocentric
coordinates (t', x', y', z') to geocentric ones (t,x,y,z) is x = x' -
acosWt', y = y' - asinWt', z = z', t = t' where a is the radius of the
earth's orbit & W is its angular velocity in the primed frame. (Note that
this is NOT a transformation to a rotating frame.)

Shalom
George
http://web.raex.com/~gmurphy/

----- Original Message -----
From: "Loren Haarsma" <lhaarsma@calvin.edu>
To: "_American Sci Affil" <asa@calvin.edu>
Sent: Thursday, July 05, 2007 1:56 PM
Subject: Re: [asa] geocentricity

>
>
> On Thu, 5 Jul 2007, George Murphy wrote:
>
>> I'm afraid that I may get to be known as a nutty advocate of geocentrism
>> (as distinguished from just nutty), but I have to point out again that
>> in the context of general relativity there is NO way to show that the
>> earth goes around the sun rather than the sun around the earth. A
>> coordinate system in which the earth is at rest is just as good as one
>> in which the sun is at rest & requires no superluminal speeds &c.
>
> I might be mistaken, but I don't think this is correct. Special
> relativity means that all inertial (non-accelerating) frames of reference
> stand on equal footing -- any one of them could equally be said to be the
> one "at rest." But earth is in an accelerating frame of reference.
> (Circular or eliptical orbits are accelerating frames of reference.) I
> believe that even under General Relativity, one can do experiments to tell
> the difference between being in an inertial reference frame (i.e. not
> moving) and an accelerating frame of reference. (Maybe you know about
> some alternative interpretation of GR of which I'm unaware.)
>
> Also, one might ask: If the earth isn't moving, how is it possible for
> satelites to acquire velocity when they make a "slingshot maneuver" around
> the earth?
>
>
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Received on Thu Jul 5 15:49:44 2007