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

In article <fd7c8fdd-c85e-4ea9-8969-1d26f317ff0b@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Pioneer1 <1pioneer1@xxxxxxxxx> wrote:
On Apr 24, 9:46 am, Patricia Shanahan <p...@xxxxxxx> wrote:
Pioneer1 wrote:

I think you are making a mistake in even trying to understand one
equation in isolation from the theory of which it is part. The "F" in
"F=ma" carries meaning from static mechanics.

Okay, I understand but the meaning from statics does not carry to
orbital motion. In statics force is communicated by pulleys and
strings. In orbital motion there are no strings, force acts
instantaneously from a distance.

The force that is "communicated by pulleys and strings" still acts at a
distance---it's just that the distances are at the molecular level. You
seem to have missed the point of the discussion of electrostatic forces.

And the F term cancels out of the formulas used to compute orbits.

I explained elsewhere what cancellation means. Did you see my explanation?

I am just looking at formulas for orbits and those are not the formulas
of static mechanics. Is this observation wrong?

If you're asking whether F = ma and F = Gmm'/r^2 are distinct formulas,
then the answer is yes. They represent different physical laws. But
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.

The fact that we have two different equations for the same quantity is a
good thing, 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.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.