John! An excellent question that gave me pause to ponder.
The fact that the sun happens to pass through an observers zenith does not of itself add length to the day. What does add length to the day is sunrise earlier than 6am local apparent time and sunset later than 6pm local apparent time. The earlier and later sunrise/sunset times are a function of the observers latitude. For an observer located somewhere between the equator and the tropic of cancer, the earliest sunrise and latest sunset will occur when the sun is in the tropic of cancer (its northernmost position on the celestial sphere.) Let me see if I can describe a picture that may help you visualize this: First case: Imagine you are standing on the equator facing due east, looking at a flat horizon. If it were painted on the sky, you would see the celestial equator rising perpendicularly from the horizon due east of you. The celestial tropic of cancer would appear to rise perpendicularly from the horizon at a point 23.43 degrees north of east. The celestial tropic of capricorn would appear to rise perpendicularly from the horizon at a point 23.43 degrees south of east. Imagine a line, perpendicular to these three circles that cuts all three and is centered at the point where the celestial equator intersects the horizon. The hour angle where each of these lines touch the horizon would be 6 hours. Therefore, at the equator only, sunrise would occur at 6am L.A.T. every day of the year. Second case: Image you are standing at 15 degrees north latitude facing due east looking at a flat horizon. The three circles mentioned in the first case above would make an angle with the horizon of 15 degrees and they would be leaning to the right (south). The line mentioned above that intersects all three circles and is perpendicular to all three is still centered on the intersection of the celestial equator and the horizon. This line also is inclined 15 degrees. It still cuts all three circles at the hour angle of 6 hours BUT now the tropic of cancer has a little bit more visible between hour angle 6 and the horizon. The tropic of capricorn's 6 hour point is now below the horizon. Because you are north of the equator, earliest sunrise and latest sunset (and therefore the longest day) will occur when the sun is in the tropic of cancer. The reverse would be true if you were south of the equator. Oh, by the way, in the second case above, the points where the tropical circles intersect the horizon will be further north and south of east than in the first example. In fact, as you move further north, the tropical intersection points will move further from the equator and closer to the poles. When you reach 66.57 degrees north latitude (arctic circle) the sunrise point will just touch true north and the entire celestial tropic of cancer will be above the horizon. At the same time the last bit of the tropic of capricorn will have just vanished below the horizon at a point due south of you location. See, my logic is much more tangled than yours. If anyone on the list cares to correct any errors I have made, please do so, so I can learn something too! Charles At 08:23 PM 3/2/98 GMT, you wrote: > >This may seem a very silly question but here goes.. > >What is the behaviour of the sun path through the year in the tropics? > >The following description of the problem may be so shot with misconceptions >that the question itself may be the problem, but.... > >As I understand it, taking an Earth-centred view from northern latitudes, the >Sun's path steadily rises in the sky till the summer solstice at which point >the sun is straight overhead at the tropic of Cancer. It then sinks in the >sky until the winter solstice at which point it is directly overhead on the >tropic of Capricorn. > >If that is true, then between say the equator and the tropic of Cancer the >sun is directly overhead twice in the year, once as it 'heads north' to the >tropic of Cancer and again as it 'heads south' past the equator. On this basis, >any point between the tropics has two longest days in the year and at a point >infinitessimally close to the equator the (marginally) longest days are at the >equinoxes. > >Is this true or am I tangled in my own logic?... > >... and thanks to "Sundials on the Internet" for pointing me at this list .. > >John Butler email: [EMAIL PROTECTED] > ___ >Department of Computer Science WWW: http://www.dcs.ed.ac.uk/home/jhb (ovo) >University of Edinburgh phone: (+44) (0)131-650-5181 ((`-')) >Edinburgh EH9 3JZ, UK. fax: (+44) (0)131-667-7209 -"-"- > >
