Re: Mass was Re: Questions (Space)

On Fri, 14 Sep 2007 16:50:23 -0000, goodbyeblueskye@xxxxxxxx wrote:

On Sep 14, 6:10 pm, "Brian M. Scott" <b.sc...@xxxxxxxxxxx> wrote:
On Thu, 13 Sep 2007 21:15:14 -0000,
"goodbyeblues...@xxxxxxxx" <goodbyeblues...@xxxxxxxx> wrote
in rec.arts.sf.composition:

[...]

The notation doesn't matter, our two calculations are
exactly the same. [...]

Yes, they are. But Ric is correctly visualizing what's
happening, and his description of it is basically correct;

I appreciate your attempt to make some sense of things.

But I think that there is more to this than me (my name is Kristian,
by the way) and Ric talking past each other. I think Ric has some
serious misconceptions.

Remember that this whole discussion started off with this:

Is it constantly having kinetic energy added to it?
Yep. Of course it's always giving up kinetic energy at the same >time, so the total KE (which is a scalar, with no direction to it) >remains constant.

Is Ric now going to want to change this statement to the even more
nonsensical "it's always giving up kinetic energy, except at times t =
0, t = T/2 (T being the period), and all integer multiples thereof?"

Given how there is nothing special about the time t = 0 or the chosen
coordinate system, that would be quite an oddity.

your too narrow focus on the moment t = 0 is blinding you to
this.

The moment t = 0 is the moment Ric was looking at in his faulty
analysis, where he was claiming deceleration was happening.

(He's wrong, however, in objecting to your
calculation of v(t) and a(t): there's nothing wrong with
that, except that he was originally talking about a method
of *deriving* the equation of motion, while you *started*
with it.)

Uh, Ric's calculation-that-went-no-where started off with a drawing of
a circle. So how exactly was his a derivation from first principles,
while mine was not? Why was Ric talking about circular argumentation
on my part? In physics, one very often starts with the result, and
then shows that that result is in fact correct through calculations.
Note that the acceleration vector I arrive at points towards the
planet, has constant magnitude, and that the orbital radius is
unchanged. Considering how gravity works, those observations are
pretty much enough to prove that my starting-off point was correct. No
circular argumentation is involved at all.

1. My calculation began with a drawing of a circle as a construction
aid, to show where the tangents were. After that I did not refer to the
circle at all. You might as well say my argument is invalid because it
was posted on Usenet. Or would drawing it on a blackboard invalidate it,
because the chalk particles aren't /really/ in orbit?

2. You began your objection by saying flatly that deriving the equation
of motion was a useless exercise because we already knew what it was,
then wrote it out and started making inferences. I wanted to show that
you could get a circle from first principles; you assumed the circle,
then established that the equation of a circle proved it was a circle.
Well, d'oh.

3. Every tangent is like every other tangent. You can plug in t = some
value and calculate an acceleration at that moment; you can then redraw
the figure so that t = 0 and calculate an acceleration of zero. Both
can't be true at once. It's a sinusoid. The fact that it passes through
zero doesn't mean it isn't constantly there.

4. The error I pointed out was in the /very last step/, where you
(mistakenly) allowed your abbreviated notation to merge the X and Y
components of the motion, converting the analysis from one in Cartesian
coordinates to one in path coordinates along the satellite's motion.
That gives the speed of the satellite, correctly. It does /not/ describe
the components of the velocity and acceleration vectors ("state vector")
of the satellite.

5. Your depiction of the dynamic situation is at least somewhat valid,
but it leads either nowhere (you can't derive anything new and useful
from it) or to entirely mistaken concepts like "zero gravity". A
satellite in orbit is /not/ in "zero gravity". It is in free fall, so
that (according to the equivalence principle) the force of gravity is
not /felt/. The form of analysis I used demonstrates that or can be used
to do so, where yours ignores it (or, rather, denies it).

6. If you persist in modeling the situation that way, you will /never/
address the point I was trying to make, which is the difference between
unaccelerated ("constant") motion and accelerated motion; you will never
understand why movement in a curve is fundamentally different from
motion in a "straight line" or geodesic, and will be forever blocked
from an appreciation of the difference between Special and General
Relativity. You won't even be able to calculate a satellite orbit
correctly -- the phenomenon of "frame dragging", which is a consequence
of the accelerations acting on the satellite and General Relativity,
produces a large enough effect that, e.g., the maintainers of the GPS
satellite system have to take it into account for their ephemeris
calculations. Newtonian mechanics gives a marvelous first approximation,
but it /is/ a first approximation.

This whole thing reminds me of the lettercols of Fifties and Sixties SF
magazines, in which writers with partial (and often wrong) knowledge of
physics tried to find holes and exceptions to relativity that would
allow FTL -- I was particularly charmed by the liquid spaceship.

Regards,
Ric

--
Posted via a free Usenet account from http://www.teranews.com

.

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