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Perikles
2011-Feb-03, 04:02 PM
Not strictly astronomy, but a question in (almost) spherical geometry. A friend intends to climb the peak of the mountain on Tenerife, overnight, to view the sunrise. (This involves a 6-hour slog up a 45 degree slope on 17th May, which he claims will be assisted by a full moon.)

Given that the peak is 3,700 metres above sea level, and the sun will rise over the sea or very low land (African coast) how much earlier will sunrise be compared with sunrise times on the coast?

NEOWatcher
2011-Feb-03, 04:13 PM
Not strictly astronomy, but a question in (almost) spherical geometry.
Actually; it's a simple triangle with Earth radius as one leg of a right triangle, Earth's radius plus elevation as the hypotonuse, and the other leg of the triangle being the approximate distance of the sunrise. Then it's a matter of dividing 24K miles by this to get the time difference.

Perikles
2011-Feb-03, 07:03 PM
Thanks for that - thinking about it, it is much easier than I first thought. I get an answer of around 7 to 8 minutes.

plphy
2011-Feb-03, 10:14 PM
The relevant technical term is "dip of the horizon (http://mintaka.sdsu.edu/GF/explain/atmos_refr/dip.html)".

Bye,
Thomas

tony873004
2011-Feb-06, 06:44 PM
Thanks for that - thinking about it, it is much easier than I first thought. I get an answer of around 7 to 8 minutes.
Distance to horizon in miles can be approximated by sqrt(height in feet)*1.17
Speed of terminator is 1000 miles per hour cos(latitude)
time=distance/velocity = 8 minutes 46 seconds

The neat thing about watching sunrise from elevation is to see the shadows of mountains beyond your horizon. Check out the African coast for peaks.
The sun should rise at 7:15:25 or 7:06:40 adjusted for elevation, Daylight Savings time (UTC +1). It will rise at an azimuth of 67.5 (not adjusted for elevation).
The moon sets at an azimuth of 245.75 at 6:59:47 not adjusted for elevation.

Perikles
2011-Feb-06, 07:11 PM