Re: Reduced mass problem

[Leigh Palmer <palmer@sfu.ca>]

> Concerning where Bob Carlson wrote:
> > ...
> > To test for an ellipse of the form x^2/a^2 +y^2/b^2 = 1, you can try this:
> > ...
>
> I don't think that Tom had made it clear that the center of the possible
> ellipse to be fitted to the (x,y) data was supposed to be at the origin,
> nor that its principal axes were necessarily oriented along the x & y
> coordinate axes.  We may need more information here.

We must also know what the axes represent, and what the
relative uncertainties are in the two directions. A best
fit criterion should also be specified.

David's concerns are just those that confront an astronomer
in fitting the observations of a visual binary over time to
an apparent orbit. The orbit will always be elliptical. A
best fit must involve adjusting *five* parameters: the two
coordinates of the center, the length of the semimajor axis,
the orientation of the axis, and the eccentricity. Contrary
to Onsager's famous claim one could not fit an elephant with
variation of those parameters. (If one is dealing with
relative rather than absolute coordinates then only three
free parameters remain to be fit. That is the more common
case.)

Leigh