Circle of 3D Coordinates

Oh boy do I have a sweet math problem for you.

I have a list of 43 3d coordinates (x,y,z)

I want to find the best coordinates that form a circle of approximate diameter of 140 to 150 and then place them in order, clockwise or counter-clockwise. I'm not picky as to how many coordinates can be in the circle.

How would I go about this?

I have taken the first step and made a table with the distances between each coordinate.

data:
see attached

any ideas?

Does this webpage offer any help?:

http://www.mapleprimes.com/maplesoft...ata--An-Update

Hi Stockgoblin,

I think the problem is really this:

Find the center of a sphere and its radius that comes as close as possible to the given points. Is that the problem? You have some (x,y,z) coordinates listed. Are those the points?
Do you want us to use the least squares method for the minimum distance? Do you mean sphere instead of circle in the problem?

Is this what you are asking?

MarvinP I thought this was a sphere problem too but I think it might now actually be a circle in a 2d plane in a 3d space.

StockGoblin are the x, y and z corodintae in the yellow highlight all supposed to be in the same circle (orbit)?

Yes, it is a circle problem in 3d space. In fact, it's a trade route in outerspace with maximum profitability being at 150 Ly away. So, I thought the best way to route would be in a circle with 150 light years as a diameter, buying and selling at opposite points on the circle. I understand the circle will be jagged but I'm looking for the best fit. I'm currently thinking this problem would easily be solved visually so I'm looking for a 3d graphing program but I was wondering how to go about it mathematically as well.

3d plot of points in space.xlsm
Stockgoblin,

I wanted to get a feel for what your points looked like in 3d to see if there was a visual solution. I don't think there is but the attached is pretty cool to play with. I set it up to show the 3d points in a 2d space and by rotating (pressing the up and down buttons) you get a feel for where the points are relative to each other. I'm only rotating in one dimension (ie yaw only but no pitch or roll).

I'll let the mathematicials work out the least squared solution for your circle.

As an aside, if you're travelling through space you wouldn't travel directly from one to teh other anyway would you because by the time you arrived your destation would have moved due to it's natural orbit!.

Wow, that's cool. I didn't know you could set up a 3d graph in excel. Nice Job. Yes, I don't see a visual solution either.

As an aside to your aside. The coordinates are for the main star of the system.

I reckon the 3d graphs in excel are useless so this one is all macro driven using lines and circles from the shapes menu

Yeah that one's cool too.