Polaris Paradox – Update

I’ve been working on a new model based upon our conversation.  I found a bunch of errors in my original model that I missed the first time.

 

I was mingling FE with GE values which made the model not work properly.  Looking at it again, I built the model with the assumption of an FE.  There are only 2 assumptions:

 

1) Radius of FE a is 12,482 miles
2) The height of Polaris is 3959 miles (or radius of GE)

 

I fixed the graphs as well.  One of them didn’t provide any meaningful information so I removed it.

 

From this model I’ve developed FE latitudes which have nothing to do with GE values.  The latitude values are a function of radius and the height of polaris – [FE Radius]*COS((FE Latitude)/180*3.14159) = FE Radius @ latitude.

 

 

The viewing angle and perspective are an important concept in this model.  Here are some axioms that we can test:

 

– Viewing angle and latitude are not equal
– Objects at a distance increase in height at an unequal rate as the object approaches assuming a constant velocity.
– A viewing angle of 0-45 degrees is obscured from the bottom-up.
– A viewing angle of 45-90 degrees is obscured from the top-down.
– The obscured area subsequently obscures a proportional amount of viewing angle.
– At 45 degrees the obscured values are equal at the top and bottom

 

I’ve highlighted sections that have interesting or important values.  I have a hypothesis that the GE radius (3959 mi) was used since the distance to Polaris is 3959 miles.  They just rotated the model 90 degrees.

 

I’m added in some actual locations (Toronto, Vancouver, Quito, Monterey) and compared the model against real-world distances.  It fits quite well.  I think the Viewing Angle issue is resolved by the model since it shows how perspective obscures the top and bottom.
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