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

In article <bf526a8e-5cc9-4db7-bc45-cd47084ac699@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Pioneer1 <1pioneer1@xxxxxxxxx> wrote:
But perturbations are additive. As Newton did, I can compute
perturbations between three bodies by computing perturbations between
each pair and add. If force does not enter two-body problem what is
the justification that it will enter three-body problem?

The justification for introducing forces into the three-body problem is that
there isn't any other good way to solve the three-body problem.

Three-body motion isn't necessarily periodic. So there aren't any "orbits."
If there are no orbits, how are you going to apply Kepler's laws?

But this is about the absence of force in Newton's equations of motion.

Newton's equation of motion has force in it. F = ma. F is force.

When you solve certain simple problems, you can eliminate F. That does not
mean that F is not present. This is a simple matter of clear thinking and
clear speaking, not physics. The meaning of the word "eliminate" is to get
rid of something that is there. If something is not there, then you cannot
"eliminate" it, or "cancel" it. It has to be there in the first place
before it makes sense to talk about getting rid of it. Force is there in
the equation. To say otherwise is doubletalk. Don't use doubletalk. Speak
precisely, or you will confuse yourself.

Not about the precision of Kepler's rule. Without force and
mass Newton's equations of motion reduce to Kepler's rule.

Not true, except in the extremely special case of two bodies.

Again, you're avoiding doing the hard work of actually solving the
three-body problem, in favor of handwaving. Write down the positions,
velocities, and masses of three approximately equal bodies in space. Now
tell me what the positions and velocities of these bodies are, say, one
year later. Don't tell me in vague terms how you would go about doing this,
applying Kepler's laws---actually do it. Pick specific numbers for the
positions and velocities and masses, and then tell me what the positions
and velocities are one year later. When you have finished your calculation,
post the numbers here. Then we can talk.
--
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
.