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November 20th, 2007, 12:23 PM  #1 
Member Joined: Oct 2007 Posts: 31 Thanks: 0  Finding the distance between two points on a sphere
I can't figure the following question out and need to know how it's done: Find the distance between the two cities. Assume the Earth is a sphere of radius 4000 miles and that the cities are on the same meridian. (one city is due north of the other) Dallas  32° 47' 9" N Omaha  41° 15' 42"N Thanks for any help given. 
November 20th, 2007, 12:30 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
So you have the two cities on a circle, with the arc connecting them being 8.5 or so degrees. So given the radius you can find the circumference, right? Then find the appropriate fraction of that circumference, given that there are 360 degrees in total.

November 20th, 2007, 12:37 PM  #3  
Member Joined: Oct 2007 Posts: 31 Thanks: 0  Quote:
 
November 20th, 2007, 01:24 PM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
 
November 7th, 2018, 10:10 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,375 Thanks: 2010 
41° 15' 42"  32° 47' 9" = 8° 28' 33" = 8.4758333° approximately. Hence required distance is 2ππ × 4000 miles × 8.475833333 / 360 = 591.7248 miles approximately. This assumes that the distance is measured along the meridian. 

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