Talk:Haversine formula: Difference between revisions

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Different results

I find it interesting that there are two 'clusters' of results around 2886.4 and 2887.26 with very few 'significantly' differing ones- Now: who is 'correct' here ??? and why are so many others 'wrong'??? --Walterpachl 19:08, 16 August 2012 (UTC)

2886 km (1793 miles)                  
2886.326609413624                     
2886.327                              
2886.4 km                             
2886.44                               
2886.44 kilometers  (or 1793.55 miles)
2886.44444099822                      
2886.444442837984                     
2886.44444                            
2886.4                                
2887 km.                              
2887.2599 km                          
2887.2599506071097                    
2887.25995060711                      
2887.2599506071106                    
2887.2599506071106                    
2887.2599506071106                    
2887.259950607113                     
2887.25995060711                      
2887.26 km.                           
2887.26 km.                           
2887.260 km.                          
2887.2600 km                          
2887.26                               
2887.3 km (1794.1 mi.)                
2887.3 km                             
2889.68

This might be due to the different values given for the rough radius of the Earth, in kilometers, for different examples. --Paddy3118 19:22, 16 August 2012 (UTC)

Some reasons probably are:

using a different (mean) radius of the earth
using a derived radius from the earth's circumference
use of difference precisions
use of different formulas for trigonometric functions
use of smaller numbers via radian (or degree) reduction/normalization.

-- Gerard Schildberger 19:25, 16 August 2012 (UTC)

Apparently it's the two different values used for the eartH's radius: 6372.8 and 6371.0, respectively- --Walterpachl 20:14, 16 August 2012 (UTC)

Right, “6371.0” is the authalic radius based on/extracted from surface area, while “6372.8” is an approximation of the radius of the average circumference (i.e., the average “great-elliptic” or “great-circle radius”), where the boundaries are the meridian (≈ 6367.45 km) and the equator (≈ 6378.14 km).

See Ellipsoidal quadratic mean radius. ~Kaimbridge~ 17:44, 19 August 2012 (UTC)

@@ Line 48: / Line 48: @@
 Apparently it's the two different values used for the eartH's radius: 6372.8 and 6371.0, respectively-
 --[[User:Walterpachl|Walterpachl]] 20:14, 16 August 2012 (UTC)
+:Right, “6371.0” is the authalic radius based on/extracted from surface area, while “6372.8” is an approximation of the radius of the average circumference (i.e., the average “great-elliptic” or “great-circle radius”), where the boundaries are the meridian (≈ 6367.45 km) and the equator (≈ 6378.14 km).
+:See ''[http://math.wikia.com/wiki/Ellipsoidal_quadratic_mean_radius Ellipsoidal quadratic mean radius]''. [[User:Kaimbridge|<span style="border:1px solid green;color:#e55b3c; padding:2px;background:#fde0bc">~<font face="courier new bold" class="title" title="Kaimbridge M. GoldChild">Kaimbridge</font>~</span>]] 17:44, 19 August 2012 (UTC)