# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: A simple three-body fix puzzle**

**From:**Tom Sult

**Date:**2010 Dec 10, 21:06 -0600

Thomas,

You could not be further from the truth with both your assumptions.

On 2010-12-10 21:16, Tom Sult wrote:It seems to me the point of this is that the best probability of location is a "donut" that roughly follows the lop's around the hat.

Not at all. It's always an ellipse, centered on the MPP. In fact, the closer you get to the MPP the bigger the chance that you are actually there. To leave a hole out like in a donut is totally pervers.

We have learned that we have perhaps a 25% +/- the details chance of being close to any "center" of the hat. And we can calculate the probability distribution of our location along any one of our LOP's. If the gausien distribution is centered on the LOP then we have a "fuzzy donut" probability and not a Position.

The gaussian distribution is not centered on the LOP, it's centered on the MPP derived from the LOPs.

So the answer to "whitch point is it is correct?" is... There is no point.

You are a medical doctor? Let me ask you a medical question.

A patient who suffers from Prinz's disease comes to see you. WonderDrug offers an FDA approved cure. After much statistical research they decided that one shot of 30mg per day is optimal, much less is ineffective, much more is counterproductive. Will you deny your patient the treatment because you don't really know how much to give him? Or will you start him off with 30mg and see what happens?

Herbert Prinz

Thomas A. Sult, MDSent from iPhoneHerbert,

Could you inspect and comment on the linked diagrams.

The first linked diagram shows a 30°/60°/90° triangle plot with bisected vertex, internal circle tangents, vertex to tangent intersections (symmedian or Gergonne point), and the d/2 circle around point P.

(very busy plot)The Gergonne point (Gp) seems to be dependent on the bisected angle point (Bp). Point Bp weighs each LOP equally and point Gp shifts away from the smallest angle and toward the largest angle. The d/2 circle intersects at three points along the bisection and tangent lines.

The question now is which point is correct ? Gp or one of the three d/2 intersections ? If I had to guess then I would select the intersection of the d/2 circle, P perpendicular, and 60° vertex to inner circle tangent (see second linked diagram)

Greg Rudzinski

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