Any Math Majors in the House? Help Wanted.

[waldronate]

Perhaps http://en.wikipedia.org/wiki/Space-o...tor_projection with the orbit angle of inclination and rotation periods selected to travel along the centerline of your archipelago?

[ender_wiggin]

I thought of this, but considered that if there are islands at both poles, those islands can "hold" the infinity of turns, and leave only one turn between them. Essentially, the rhumb line is being clipped at a latitude less than 90N/S.

That's a good point. I can start the rhumb line arbitrarily close to the actual pole. Although upon looking at the curve closely, I don't think a loxodrome is what I had in mind. I'm looking for a curve that hits every latitude and longitude exactly once. To do this I think the bearing changes.

Perhaps http://en.wikipedia.org/wiki/Space-o...tor_projection with the orbit angle of inclination and rotation periods selected to travel along the centerline of your archipelago?

That's an interesting find, thanks. Although the scanner satellite in that photo is a straight line, not a curve.

[waldronate]

the scanner satellite in that photo is a straight line, not a curve.

The earth turns under the satellite, making the the ground track a spiral. If the orbital inclination is polar (satellite scans pole to pole) and the rotation of the globe is faster than the orbital period of the satellite (say, exactly twice as fast), then the ground path should be a spiral that traces from one pole to another in the time that the globe rotates one full revolution. But math was never my strong suit, so take that estimate with a grain of salt.

I've attached the example image for this projection from Snyder's An Album of Map Projections (USGS Professional paper 1453).
DSC00978a.jpg

[ender_wiggin]

Wow, you're right. This looks very promising, thanks! Do you have a link to documentation explaining the projection and how to use his equations? The wikipedia article is a good intro but is a bit lacking for the inexperienced. I will look into this and post the results here. Thanks again.

Btw if anyone else also has insight into this problem, I'm all ears.

[gilgamec]

Wow, you're right. This looks very promising, thanks! Do you have a link to documentation explaining the projection and how to use his equations? The wikipedia article is a good intro but is a bit lacking for the inexperienced. I will look into this and post the results here. Thanks again.

As waldronate hasn't posted this, I'll mention that Snyder's "Album" can be downloaded from the USGS at http://pubs.usgs.gov/pp/1453/report.pdf. In addition, Snyder's "Map Projections - A Working Manual" goes into much greater detail about the equations, how they are derived, and how to use them; it's online at http://pubs.usgs.gov/pp/1395/report.pdf.

[ender_wiggin]

Ah, yes. Now there is the only issue of implementing this monster. Currently trying to brush up on my MATLAB..