From: Ronald Wong (ronwong@inreach.com)
Date: Thu Nov 28 2002 - 16:35:14 PST
Message-Id: <l03102800ba03423d1bce@[209.209.18.213]> Date: Thu, 28 Nov 2002 16:35:14 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: re: Gravity
Not too long ago, Jennie Brotman raised a few questions regarding the
concept of gravity. I responded with a suggestion and some ideas/opinions
as well.
Initially she said:
>Today i introduced the concept of gravity as a force of attraction between
>all objects and the reason why objects fall towards the center of the earth
>on our planet. my students were perplexed by the abstract concept that
>there is this invisible pulling on things (by the earth/planet) to make them
>fall. am i right in saying that we don't REALLY know exactly what gravity
>is- what we know is how planets, objects, etc. behave and so have tried to
>formulate theories to explain that behavior, one of which is that there is
>this force of attraction called gravity attracting things to each other? are
>there further theories about where this force comes from or what it is more
>precisely? any info on the "why?" ...
My suggestion was that she should expose her students to an idea regarding
falling bodies that was so simple and appealing that it, and the science it
was associated with, was considered to be quite sufficient for explaining
the way nature behaved for 2000+ years.
In it's simplest form, objects that fell to the ground were said to be
returning to their natural place. It was something that they did by nature.
Their motion under these circumstances was referred to as natural motion
and, since this was something the objects did by nature, no force was
required.
When students jump off their stools, chairs, desks, or tables, this is
exactly what they experience.
I then went on to say:
>If your students are elementary/middle school students and you have
>successfully brought them to the point where they understand that
>scientists explain how nature works by using models based on observations
>and assumptions, you can tell them that at a later time a different set of
>observations were made which, on the basis of a different set of assumptions,
>led to the perplexing idea that one could explain certain events in nature
>by means of an "invisible pulling on things".
>
>When you students ask you, "What observations are we talking about?", "What
>assumptions were being made?", and "How did the two come together to form
>an idea that contradicts our common sense experience of things?", tell them
>that they will find all the answers to their questions when they enroll in
>their high school physics class.
So, here are all the answers:
_______________________________________________________
1. The Observations:
A. Terrestrial - Newton's observations
The first observation (which can be done at any grade level):
Using logic - possibly that used by Galileo - and/or some well
chosen demonstrations (a book sliding to rest on a table, an
inclined plane), a teacher can show that objects seem to want to
remain at rest, when initially at rest, or move with uniform velocity
when no unbalanced forces act on them (A final demonstration with an
air track/table clinches this conclusion and frequently puts the students
in a state of awe as well).
Another observation (which can also be done at any grade level):
A simple lab/activity involving spring balances, some weights, a paper
clip, etc. quickly lead students to a second observation that forces
always appear in pairs which act on different bodies and are equal in
magnitude and opposite in direction.
A third observation:
The classic high school physics lab involving a cart, some string,
weight(s), pulleys, and some means of measuring time will lead to the
idea that unbalanced forces acting on a mass produces an acceleration
that is proportional to the ratio of the force to the mass.
These three observations are nothing more than Newton's Three Laws. The
laws, whether stated mathematically or in words, are nothing more than a
description of how nature appears to behave.
The first steps in a *fundamental* science is to describe, as accurately as
we can, what we see nature doing. For this reason, these three laws are
called "empirical" laws. There's nothing here that has been arrived at by
means of the "Scientific Method" that is so often discussed in science
textbooks. There is no place for "Testable hypotheses" here. It's too basic.
B. Celestial - Kepler's observations (another example of empirical laws)
Using the same mathematical devices used by Copernicus and Ptolemy, Kepler
struggled for a couple of years trying to create a model for the motion of
Mars that would predict it's position with the same precision as the
instruments he had on hand (an assumption if there ever was one). In the
end, Kepler gave up and stated that neither Copernicus nor Ptolemy got it
right.
Working strictly from the data gathered by Tycho Brahe at Uraniborg he came
up with the most precise model of his day for heavenly motion. The model is
described in terms of his three observations/laws:
The first observation:
A line connecting the sun and a planet sweeps out equal areas in
equal intervals of time.
Another observation:
The orbit of a planet is an ellipse with the sun at one of the focal
points.
A third observation:
The period of a planet when squared is proportional to the cube of it's
mean distance from the sun.
These three laws, like Newton's, can be expressed mathematically. Like
Newton's laws they are nothing more than descriptions of what we see when
we look at heavenly motion.
_______________________________________________________
The assumptions:
Newton understood quite well that ALL investigations have inherent
assumptions built into them and he took great pains to point out the ones
that were important in his analysis. He referred to them as the "Rules of
Reasoning"
1. Nature is essentially simple. Thus a simple explanation is to be
preferred over a more convoluted one.
Based on this idea...
2. To the same effects, we must apply, as much as is possible, the same
causes.
And...
3. Properties common to objects within our sphere of experience shall
apply to all objects in general (unless proven to be otherwise).
4. Laws/Principles arrived at through our investigations shall be
considered accurate and true - despite opposing viewpoints - until
further investigations prove them false or lacking in accuracy.
It is worth your while to point out to your students a number of examples
of how these assumptions pop up in their daily lives. Since most of them
have never given these assumptions any thought, they are usually surprised
how much of their lives are governed by them.
_______________________________________________________
Applying the assumptions to the observations:
With these assumptions in mind, Newton did what none of his peers or
predecessors had considered doing.
He applied his three laws that were based on his observations of the ever
changing terrestrial world to the laws Kepler arrived at from his
observations of the unchanging, eternal cycles of the heavens.
In light of his Law of Inertia, Kepler's Law of Ellipses (wherein the
planets didn't move in straight lines) meant that an unbalanced force
must be acting on the planets.
Newton then went on to show that Kepler's Law of Areas meant that the
unbalanced force was always directed towards the sun.
And finally, he was able to show that Kepler's Law of Periods meant
that the magnitude of the unbalanced force was inversely proportional
to the square of the distance between the planet and the sun.
In fact, using his new mathematical tool (known today as calculus), we can
work backwards and, by invoking the existence of a central force acting on
a planet whose magnitude depended on the inverse square of the distance
between it and the sun, derive all three of Kepler's laws. Of course, this
should not be surprising since Kepler's laws were the starting point from
which he developed his law of universal gravitation.
The important point to notice here is that the force, with it's attendant
properties, exists only because, when Newton applied his set of
observations to Kepler's, based on a set of assumptions that allowed him to
do so, it was forced upon him. It was a mathematical consequence of
bringing together heaven and earth - as he makes clear in his work,
"Principia Mathematica...".
If this sounds like the concept of universal gravitation can be arrived at
by a simple, straight-forward process, rest assured that this is not the
case (just sit down and spend a little time reading the "Principia").
Newton deserves all the credit and honor that he is given for his
development of this new idea.
_______________________________________________________
Now I can address some of the questions that Jennie brought up.
Notice that whether it's Aristotle with his natural order, Kepler with his
three laws of celestial motion (based on Tycho Brahe's observations), or
Newton with his three laws of terrestrial motion, they all begin with a set
of basic observations. Nothing in this process addresses the question of
why there is natural order, or why planets move the way they do, or why
objects move with uniform motion when the forces are balanced, etc.
The assumptions, whether it's "seeking one's natural place", having a model
as precise as one's instrumentation, or the "Rules of Reasoning", preclude
a "why".
And so does the steps pursued by Newton in his development of the Theory of
Universal Gravitation precludes. The resultant theory is a mathematical
consequence of applying terrestrial laws to celestial motion based on the
assumption that you can.
Taken together, it should be clear that the way in which science pursues
it's study of nature precludes any attempt to address "why" something is
and "why" it has the properties that it possesses.
You can ask such questions but they are not scientific in nature and can't
be answered by either a scientist or a science teacher. That is why, as
science teachers, we shouldn't be raising such questions in our classes
unless it's to point out the fact that such questions don't belong there.
The fact that "we don't REALLY know exactly what gravity is" - as Jennie
put it - is not a problem in science. If it is a problem, then it is a
problem in some other discipline.
Although it has not prevented others from trying, Newton made it very clear
to everyone that his observations and analysis offered no answer to the
question of "why?".
_______________________________________________________
Some personal observations:
When we apply Newton's laws of dynamics to circular motion, we end up with
the well known formula, F=m(v^2)/r. When we apply the same laws to heavenly
motion, we end up with another well known formula, F=GmM/(r^2). Both
mathematical expressions account for the motions observed and, in that
sense, explains the two motions (one of Jennie's points). From this
standpoint, it should be clear that Newton's Theory of Universal
Gravitation is "just" another physics problem (but see comment above
regarding the "Principia"). In some of today's university level physics
classes it is treated just that way.
The successful prediction of the appearance of what we now call Halley's
comet and the discovery of Neptune from predictions based on the motions of
the planet Uranus are frequently offered as evidence that the Theory of
Universal Gravitation is valid.
But the Theory of Universal Gravitation was NEVER an hypothesis. It's a
mathematical consequence of applying the terrestrial observations of Newton
to the celestial observations of Kepler. Since it's not an hypothesis it
doesn't need to be validated.
What WAS proven by these events was that you CAN apply terrestrial laws to
celestial motion. Newton's Rules of Reasoning - basically, educated guesses
- are apparently valid because the actions predicated on these guesses
leads to a statement which when tested has been found to be true.
So, thanks to science, we now can say that there is evidence that nature is
simple, that similar effects have similar causes, that .... - that the
underlying assumptions behind much of what we do in our lives are valid.
_______________________________________________________
Many people may have agreed with John Lahr when, in defense of the
"mysterious force of gravity", he said:
>As I sit here I do feel a force pulling me down. Only my chair prevents
>my movement. When I hold my arm out horizontally I feel a force trying
>to pull it down. My muscles get tired keeping it in position....
Or Eric of mcelover@yahoo.com when he said:
>i think what's at issue here with the mysterious gravity force is that
>we as humans are quite ill-adapted to feeling things. ...
But such sentiments went by the boards almost a 100 years ago and I hope to
make this clear in my final - I promise - comment to Jennie's questions.
ron
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