My Math Forum Over the horizon distance question

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 May 6th, 2012, 10:35 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, 10:48 PM   #2
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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?
Attached Images
 lineofsight2.jpg (9.3 KB, 98 views)

 May 6th, 2012, 11:04 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, 11:42 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 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 one-quarter the circumference of the Earth.
May 7th, 2012, 11:04 AM   #5
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Re: Over the horizon distance question

Quote:
 Originally Posted by MarkFL Astute observation, indeed the horizon does not increase linearly with height. No matter how high you go, the horizon will never be farther that one-quarter the circumference of the Earth.
...not accounting for the distance to the face of the earth; if you climb to a height of a light-year, the horizon will be pretty close to a light-year away...

 May 7th, 2012, 11:18 AM #6 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 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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