Re: Rocket action

["John S. Denker" <jsd@MONMOUTH.COM>]

At 05:36 PM 12/9/99 -0600, brian whatcott wrote:

> I have written up my objection to the list two or three
> times by now.    Is the objection not intelligible?

The objection is groundless.

--------------------------

The correct analysis has been posted two or three times.  The interesting
question is why the correct analysis is not universally intelligible.

Here are a couple of hypotheses.

1) At the very least, understanding the answer (and indeed understanding
the question) involves a change of reference frames.  Not everyone is
comfortable with Galileo's principle of relativity.

2) In particular, in most of our experience with moving vehicles such as
cars or airplanes, there is a preferred reference frame.  For airplanes, it
is simply not true that continued thrust results in continued
acceleration.  Drag intervenes.  Drag involves the air, thereby locking
down a preferred reference frame.  This is a fine example of a situation
where intuition and terrestrial experience predict one thing, and the laws
of physics predict something wonderfully different.

3) The usual analysis involves not one but many changes of reference
frame.  For people who had only a shaky grasp of Galileo's principle of
relativity to begin with, this leaves them in the dust.  I personally am
perfectly happy handling the physics of an accelerated object using a
succession of instantaneously comoving frames, but that's something that
most people don't see until they get to a graduate-level general-relativity
course.

=======

Constructive suggestions:

a) Make sure we state the problem carefully.  In particular, it may help to
specify that the experiment is done in interstellar space so that
gravitation and friction are negligible.

b) Consider the following discrete approximation to the analysis:  Consider
a rocket initially at rest in the lab frame.   Suppose it discretely ejects
exactly half its mass in one big impulse.  The situation is easy to analyze
by symmetry.  Call the resulting velocity V0. Now change into the reference
frame of the left portion.  Eject half of what's left, and iterate.  After
N iterations, the velocity (relative to the *lab* frame) is N*V0, and the
mass has gone down by a factor of 2**N.

If the student can follow the discrete argument, it may be the better part
of valor to stop there.  One can tantalize the better students by saying
that continuous thrust (as opposed to bang bang thrust) replaces 2**N by
e**N and changes the constant out front, but the qualitative point
remains:  the rocket speed can exceed the discharge speed by a factor that
is logarithmic in the ratio of initial mass to final mass.