Wayne asked:

I have observed, with my aging eyes and an old protractor, that the apparent difference in the position of the sun, at sunrise or sunset, on June 21st is approximately 65 degrees north of its position, at sunrise or sunset, on Dec 21st. . . . I expected the distance to be 47 degrees. (Twice the angle of the earth's tilt.) Why wasn't it 47 degrees?

A hand-held plainisphere set to the time of sunset will help in visualizing path of the ecliptic and celestial equator discussed below. A small plainisphere can be bought at Clarke Planetarium for about $10. At the equinoxes, e.q. last March 21, the altitude of the Sun is equal to 90 degrees minus the latitude of Salt Lake City. Salt Lake City is at approximately 40 3/4 degrees north latitude. Directly over your head is at 90 degrees altitude above the horizon and is called the zenith. Your local zenith (altitude 90 degrees) and is equal to the geographical latitude of 40 3/4 degrees north latitude. Near noon on the equinox, the Sun travels directly over the Earth's equator. So, the Sun is 40 3/4 degrees south of your zenith. Thus, the altitude of the Sun on the equinox is 90 - 40 3/4 or about 50 1/4 degrees above your local southern horizon. On the equinoxes, think of the Sun as an over-the-horizon marker of the line of the Earth's equator. At the summer solstice, the apparent tilt of the Sun relative to the Earth's equator increases by 23 1/2 degrees. At Salt Lake City, the apparent altitude of the Sun also increases by 23 1/2 degrees relative to its equinox altitude of 50 1/4 degrees. So on recent summer solstice of June 21 last week, the Sun was at its maximum apparent local altitude of 23 1/2 degrees plus about 50 1/4 degrees or, the total of 73 3/4 degrees. This is about 18 1/4 degrees from the zenith directly above your head. At the last winter solstice on Dec. 22, 2006, the apparent tilt of the Sun decreased by 23 1/2 degrees relative to the equinox altitude of the Sun of about 50 1/4 degrees. In Salt Lake City on the last winter solstice near noon, the local altitude of the Sun above the southern horizon was 50 1/4 degrees minus 23 1/2 degrees, or the difference of 26 3/4 degrees. That altitude was about 63 1/4 degrees from above the zenith above your head. The difference between the Sun's apparent altitude above Salt Lake on the winter and summer solstice (73 3/4 minus 26 3/4) is 47 degrees, or twice 23 1/2 degrees. As the Sun sets around the solstice is a good time to gain a physical appreciation for the path of the ecliptic between the current summer solstice at the north western horizon and its position during the next winter solstice rising at the southeastern horizon. Your hand, held outstretched, provides a convenient means for measuring the angles described above. An outstretched hand, clenched as a fist, marks about 10 angular degrees. That same hand, with the fingers spread wide, marks about 18 angular degrees. Right 90 degrees angles can be measured using two arms outstretched marking the corner of a square. On the equinox, the Sun sets due east and due west. When the Sun sets on the summer solstice, it sets about 23 1/2 degrees north of due west. Facing due south, the celestial equator is traced from due east to about three outstretched spread hands above the due south (50 1/4 degrees altitude) and thence to due west. This point (due south and 50 1/4 degrees altitude) is in the constellation Virgo and is where the Sun will be at then next autumnal equinox during next September. This is about 90 degrees from the summer solstice setting Sun on the northwest horizon. The ecliptic can be traced from the western setting Sun to this point and thence to about 23 1/2 degrees south of due east. Currently at sunset, the bright planet Venus, which is also near the ecliptic, is brightest object in the western sky and can help tracing the ecliptic line from the point of the setting Sun to 50 1/4 degrees above due south. At the next winter solstice, the Sun will be in the constellation Sagittarius, near Scorpio, and is 180 degrees away from the setting summer solstice Sun (at the northwest horizon) along the ecliptic. At sunset Sagittarius and Scropio are rising in the southeast. Sagittarius is about 90 degrees from the position of the Sun at the autumnal equinox in the constellation Virgo. About an hour after sunset (around 10:30pm), the brightest object that you will see in the southeast is the planet Jupiter, now near Sagittarius and also near the ecliptic. Jupiter is near the second brightest object in the southeast sky, the star Antares in Scorpio. When Jupiter crosses due south (around 1 am), it will be about 26 degrees above the southern horizon, or 1 1/2 half outstretched hands. This about the altitude of the winter solstice Sun. Additionally, the distance from the North Pole Star to directly over your head - the zenith - is 90 minus your geographical latitude. This is 90 - 40 3/4 degrees or the difference of 50 1/4 degrees. The angular size of this span remains constant throughout the year. The altitude of the North Star about your north local horizon is equal to your geographical latitude - 40 3/4 degrees - and remains constant throughout the year. When you set up an equatorial mounted telescope at Salt Lake City, this is the angle between the telescope's central polar axis and northern horizon. If you build a sundial with a triangular style, this is included angle of the sundial's triangular style relative to the north horizon. Hope that helps. - Kurt My website on a local sundial that includes further discussion of the altitude of the Sun at the equinoxes and solstices: http://members.csolutions.net/fisherka/astronote/observed/ALSSundial/ALSPage... _______________________________________________ Sent via CSolutions - http://www.csolutions.net