Circular orbits, and other stuff

[LUDWIK KOWALSKI <KOWALSKIL@alpha.montclair.edu>]

I have another question for those who teach astronomy. The first question
(how is solar spinning angular momentum transferred to the revolving planets
via magnetic forces?) was not answered. I assume it is not a simple topic.

This question has to do with the fact that planetary orbits are often
nearly circular. The same is true for numerous moons and rings. Kepler's 
laws would not be violated if eccentricities of planetary orbits were 
very large. Why are most orbits nearly circular? 

Except for Mercury (e=0.206) and Pluto (e=0.253) the values of e for planets
are smaller than 0.1. For example, 0.007 for Venus, 0.017 for Earth, etc.

How do elipticities change when the spin of our Sun is being transferred to
planets?
.......................................................................
Yesterday, A. R. Marlow, responded (in the apparent weight thread) to this:

> > In my opinion, no harm can result from explaining certain things in terms 
> > of *centrifugal* forces, magnetic *poles*, light *rays*, etc. Yes, I am 
> > sticking out my neck again. Later courses, if any, may elaborate on 
> > limited utility of simple explanations and deal with hidden nuances.

He wrote:
> I must have missed the posts where these examples were presented, but 
> they are perfect examples to illustrate the pedagogical advantages of 
> doing away with fictitious forces.  We miss a powerful teaching 
> opportunity if we do not use them to illustrate how the inertia of the 
> component particles in both cases (rather than any imagined outward 
> force) completely explains both phenomena.

The message that you did not read (it was in the same thread to which you
made many interesting contributions) clearly stated that the most desirable
way of attacking a problem is to avoid non-inertial frames. But that does
not mean that a student, or teacher, should be forbidden other alternatives.
In some cases alternative approaches can lead to shorter explanations or
to faster predictions. Two examples were given. We need more examples to 
convince ourselves that the concept of *centrifugal force* is worth keeping 
because it can be as useful as other concepts of limited utility (*light 
rays*, *magnetic poles* and even *caloric*, as in calorimetry).

Let me try to consider a very massive star and a single small planet. We 
know that an orbit is circular if the initial v=0.5*m*r^2  (in a typical 
problem) has no radial component. The same planet is at rest in the frame 
of reference whose one axis is always directed from the star to the planet.
How this be explained?  By saying that a centrifugal force 0.5*m*v^2, "due 
to rotation"  happens to be equal to the centripetal force G*M*m/r^2 "due 
to gravity". The net force is zero and that is why the planet is at rest.

I am not saying the second explanation is better. I am saying it is not
heretical. One way of deciding which model is better, in the long run, is
to compare efforts needed to calculate ellipticities, for example, when
the initial condition is changed by doubling the speed. But that is not
the issue.

Here is a quote from my earlier message:

> > I know, you will say "why teach them something they must unlearn in 
> > more advanced physics courses?". And you know what my answer would be, 
> > "most of these students ...". In my opinion, no harm can result from 
> > explaining certain things in terms of *centrifugal* forces, magnetic 
> > *poles*, light *rays*, etc. [Concepts students often already have are
> > not always misconceptions.].
> >
> > Yes, I am sticking out my neck again. Later courses, if any, may 
> > elaborate on limited utility of simple explanations and deal with 
> > hidden nuances. What is wrong with this attitude. Explain why you 
> > think this attitude must be rejected. 
> >
> > How can the constructivist way of teaching (students rediscover the 
> > laws of physics through guided activities) be implemented if we say 
> > "according to authorities you are not allowed" to use this term or 
> > concept. The "less is more" principle also calls for some changes 
> > of attitude.
> >
> > What is heretical about stating a rule according to which "any particle 
> > in a rotating frame of reference is subjected to a centrifugal force 
> > F=0.5*m*v^2"? The particle would accelerate (at a=F/m) if other forces, 
> > (due to springs, friction, viscosity, etc.) were not present.


                                                 Ludwik Kowalski