Re: How can I tell if F is a string or if it is a number?

On Apr 28, 1:24 pm, tc...@xxxxxxxxxxxxx wrote:

You seem to have missed the point of the discussion of electrostatic forces..

I think this is true. I don't understand how electrostatic forces are
related to planetary orbits. Are there any observed orbits that are
held together by electrostatic forces? But I will go back and read the
whole thread, as suggested in your earlier post, and I might have a
more informed reply to this. I would also like to thank you and
everyone else who commented, this has been very helpful.

in both cases, F represents the numerical value of the force.  By
generalizing from observation, we are able to make two distinct statements
about F, namely F = ma and F = Gmm'/r^2.

I think this is at the heart of my confusion. You are saying that "by
generalizing from observation" we are able to write the two force
definitions. But I believe that observations of orbits do not support
this statement. Observed orbits are not dependent on F, m, m' or G
terms. Observations of orbits lead to the proportionality discovered
by Kepler that the period is proportional to the 1.5 power of the
radius of the orbit. "Generalizing from observations" leads to the
result that force does not enter the description of orbital motion.
Force in orbital motion exists only as a definition; observed orbits
are independent of force. Physicists start from Newton's definitions
of force (F=ma and F=GMm/R2) and fit observations to those
definitions. I start from observations and don't see force in the
observations. T = R^1.5 is the observation and it doesn't have a force
term in it.

The fact that we have two different equations for the same quantity is a
good thing,

I am not sure that the assumption that F_ma and F_GM are the same
quantity is justified. F_am is proportional to R, while F_GM is
proportional to 1/R2. I don't believe that the same quantity can
increase and decrease with R at the same time. If we were to equate a
force proportional to R and another force proportional to 1/R2, this
should lead to an absurd result. But it doesn't. Why? As far as I
understand, there is one possibility for this elimination to work: R/
T2 and 1/R2 must form a proportionality. In other words, physicists
put together the original proportionality that Newton split in two
parts by eliminating the placeholder F and recover the original rule,
R3/T2 to make computations. But this proves that force is not used in
orbit calculations, it's eliminated.

. . . because it means that we can use the mathematical technique
of eliminating variables (what you called "cancellation") to solve for
some of the quantities we're interested in.

Okay, thanks for clarifying this. I looked up the way we eliminate
variables in simultaneous linear equations. I assume that this is what
you were referring to. I would appreciate your comments on the
following.

For instance, let's say in a given set of simultaneous equations of x
and y, we eliminated y and obtained this expression for x: x = a + b.
Can you tell what y was? I don't think this is possible. The variable
y was eliminated, it doesn't exist in the formula anymore. In our
case, similarly, we eliminated F and we obtained R3/T2. When we use R3/
T2 the force term we eliminateed is no longer a factor in our
calculations of orbits.

But I don't think force is like the variable y in the above example.
For instance, if the given simultaneous equations are 2x + y = 8 and x
+ y = 6, let's write them as Equation1 = 2x + y – 8 and Equation2 = x
+ y – 6. To me, intuitively, the terms Equation1 and Equation2 are not
like the other variables x and y. Equation1 and Equation2 are names
that we assigned to the equations. We need to eliminate them to solve
the equations. Do you mind commenting on this? Is this intutition
correct? Force terms appear to me to be like Equation1 and Equation2.

Can we write R3/T2 as simultaneous equations? For instance, a/R2 = y
and bR/T2 = x. Are these now simultaneous equations? I think, in the
case of force, probably, we should write, a/x2 = A and bx/y2 = B. And
we must eliminate A and B by saying that they are equal. And indeed,
they must be equal since the ratios in an equality of ratios are equal
by definition. Thanks for helping to formulate the question this way.
.

Relevant Pages

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