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May 6th, 2012, 09:35 PM  #1 
Newbie Joined: May 2012 Posts: 2 Thanks: 0  Over the horizon distance question
Gents, New here, so hope am posting in right place...........................but an answer to the following would be much appreciated. Fact 1) If your eyeball is at 10 meters above waterline, horizon is at 11.3 kilometers away (could be rounded to 11 for this calc). Fact 2) If at 500m above waterline, horizon is 79.9km away. (could be rounded to 80kms for this calc). So, if 10m above waterline how far away would you be and see only the top 150m of a 650m high mountain (that is, 500m of mountain is out of sight below horizon)? TIA, Joey 
May 6th, 2012, 09:48 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: Over the horizon distance question
Here is a sketch (not to scale): [attachment=0:1rufvog4]lineofsight2.jpg[/attachment:1rufvog4] The red line is the line of sight. Do you see how to determine the distance of the mountain from the observer now? 
May 6th, 2012, 10:04 PM  #3 
Newbie Joined: May 2012 Posts: 2 Thanks: 0  Re: Over the horizon distance question
Thanks and yes I do, but.................... ……………I just didn’t think it was quite that simple, although seeing it drawn it does make sense. I couldn’t get quite my head around that from 10m you can see 11km, but from 500m you can only see 80km (a very different height to distance 'ratio' as it were). The old adage, a picture (or in this case a sketch) is worth a thousand words! Again, THANKS! 
May 6th, 2012, 10:42 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: Over the horizon distance question
Astute observation, indeed the horizon does not increase linearly with height. No matter how high you go, the horizon will never be farther that onequarter the circumference of the Earth.

May 7th, 2012, 10:04 AM  #5  
Member Joined: Feb 2008 Posts: 39 Thanks: 0  Re: Over the horizon distance question Quote:
 
May 7th, 2012, 10:18 AM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: Over the horizon distance question
Yes, the distance I was referring to is that from the point on the surface directly below the observer to the horizon. 

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