## How much can the location of sunset differ from due West? (Intermediate)

I am building a house in Costa Rica that is on a mountain that faces the ocean to the west. My goal is to orient the house in a way as to maximize the view of the sunset over the water, no matter the time of the year. (I am not sure it matters for this astronomy questions, but my property is at 9 degrees 17.54 minutes North latitude and 83 degrees 49.22 minutes West longitude.)

If I face the house toward the sunset on March 21st (or Sept 21st), how much "movement" can I expect the sunset to change to the "left" and to the "right" along the horizon from that center point? I THINK there is a 23.5 degree change through out the year. So my guess is that the sun would move 11.75 degrees to the "right" (north) in the summer, and 11.75 degrees to the "left" (south) in the winter.

Is this correct? If not, please let me know the correct answer.

Background: I consider myself a very knowledgeable amateur astronomer. (I took 4 college level Astronomy classes for my science credits in college, and did quite well.) I have always owned a very good telescope my adult life, and have enjoyed explaining astronomical concepts to others.

The size of the variation of the position of sunset to either side of due west is something which changes with latitude. The angle, 23.5 degrees that you remember is the tilt of the Earth's axis, and therefore the maximum deviation the Sun has above and below being directly over the Earth's equator. If you lived exactly at the equator, this angle would be the maximum azimuth the sunset moves from due West (ie. on Dec 21st, the sun sets 23.5 deg south of west at the equator, while on June 21st it sets 23.5 deg north of west), but north and south of the Equator the deviation is larger by a factor 1/cos(latitude).

Feb 2007 update: thanks to a Curious reader for pointing out that this is an approximate formula. The approximation breaks down at large latitudes - it does pretty much OK up to about 50 degrees North or South - so it's still fine for Costa Rica! The full calculation using spherical geometry (derivation) gives the angle from due west on the solstice as arcsin(sin(23.5)/cos(L)).

In Costa Rica, 9.3 deg North of the equator the deviation will be 23.5/cos(9) = 23.8 degrees.

You can see that at high northern and southern latitudes this movement of the location of sunset goes to very large angles, to the extreme that above the Arctic and Antarctic circles the Sun never sets/rises at times of the year.

Anyway that doesn't concern you. The point is that the sunset direction varies from 23.8 deg to the north of due west in the summer, to 23.8 deg to the south of due west in the winter, for a total angular shift of 47.6 deg over the year. If you point your house due west, you should always be able to see the sunset (with a wide enough field of view through the windows).

#### Karen Masters

Karen was a graduate student at Cornell from 2000-2005. She went on to work as a researcher in galaxy redshift surveys at Harvard University, and is now on the Faculty at the University of Portsmouth back in her home country of the UK. Her research lately has focused on using the morphology of galaxies to give clues to their formation and evolution. She is the Project Scientist for the Galaxy Zoo project.

Website:  http://icg.port.ac.uk/~mastersk/

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