NavList:

Alan,

As Brad Morris and others have noted, this amounts to a confusion of the Sun's azimuth and the Sun's hour angle. This is not a bad approximation at latitudes of 60 and above, and even in Scotland, it's not far off (see below). Also as Brad suggested, it's very useful to consider a couple of special cases. What is the Sun's motion in the sky like near the north pole, south pole, and equator... on the equinoxes and on the solstices? Everyone trying to understand celestial navigation should be able to picture these cases. It's also important to be able to visualize the Sun's motion in the sky around sunrise and sunset and at meridian passage for these special locations and dates and also more generally. For example, if you see observe the Sun at some time shortly after sunrise and then observe it again exactly one hour later, where will it be? The angular distance from its first position to its second will have changed by just about 15 degrees (there's a small declination correction). This motion will be partly in altitude and partly in azimuth. As long as the Sun is within about 30 degrees of due east (neither too high nor too far from it in azimuth), the motion will be mostly in altitude --rising vertically-- in low latitudes near the equator or mostly in azimuth --nearly horizontal motion-- for high latitudes near the pole. If we do the math (or just make an educated guess), the change in altitude will be approximately 15*cos(latitude) and the change in azimuth will be 15*sin(latitude). The angle that the Sun's path in the sky makes with the local vertical is approximately equal to the latitude. Again this applies when the Sun's position in the sky is relatively close to (not more than about 30 degrees from) due east or due west. For a typical "mid-northern" US latitude of 37 degrees, the Sun near sunrise climbs at a rate of about 12 degrees per hour and shifts its azimuth at a rate of about 9 degrees per hour. If you work out the hypotenuse for that triangle, you'll get 15 degrees per hour. By comparison, if you go to northern Scotland at latitude 58, the Sun (near sunrise) rises at about 8 degrees per hour and changes its azimuth at about 13 degrees per hour (so it's not a bad estimate way up there to say that the Sun's azimuth chnages at 15 degrees per hour. You can work out exact numbers for all of these with proper spherical trigonometry, but you should be able to get "ballpark" numbers with a quick sketch and plane trig. Just remember that the Sun's motion, when rising or setting and not too far from east/west makes an angle with the vertical that is nearly equal to your latitude.

-FER

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