Hi Rui, I like the interactive projects that you are proposing. The best way to learn is to do. I am amazed at what this interest in sundials has taught me. Books and computers do not teach as well as an activity. Observations, measurements and calculations are the best way to learn a subject. My old trig teacher often said that "All knowledge comes up through a pencil."
Again I recommend a proper armillary sphere and its projection, an analemmatic sundial, as excellent teaching tools to demonstrate these concepts. Every student in Portugal should know why the armillary sphere is the Royal Symbol on the flag of Portugal. The armillary sphere shows the apparent path of the sun on the ecliptic ring. This allows you to determine the solar declination on any date. If you know the declination and measure the altitude of the sun at noon at its maximum, you can easily calculate your latitude. It is child's play. Shadow sticks, string and a protractor could be used to determine the maximum altitude of the sun. Altitude = 90- Latitude + Declination or Latitude = 90 - Altitude + Declination With an armillary sphere you can show why this so. This was the technology secret that allowed the Portuguese explorers to embark on the Voyages of Discovery and find their way home again. An armillary sphere can also be used for the moon. Have a close look at the ecliptic ring. Notice that it is wider than the other rings. On a proper armillary sphere the ecliptic ring is 12 degrees wide. This extra width is to include the plane of the moons orbit which is tilted at =/-6 degrees to the ecliptic. The moons orbit is not often shown on this ring as the position of the nodes keeps changing, but you can add a ring to show this. Make a clear plastic ring out of recycled garbage, 12 degrees wide and equal to the circumference of the ecliptic ring. Place it to cover the ecliptic ring. Mark the plane of the moons orbit on that plastic ring. Position it to read correctly at some time that you know the declination of the moon. Then use it to show through the month and year the position of the moon in the sky. You may even be able to use it as an eclipse predictor using the logic in John Carmichael's recent note. We will have to try this experiment. The path of the shadow from a stick is also a great way to learn about the position of the sun and astronomy in general. The curves are hyperbolas. In the fall and winter when the declination of the sun is negative, they curve away from you. On the equinox they make a straight line from west to east. In the spring and summer when the declination is positive the hyperbolas curve towards you. You can show this using the analemmatic sundial design program that I sent to you and others. Put different values for the solar declination in cell F19 (F17 on earlier versions). Look at chart 1 or 4 to see the path of the shadow. Check this against the observations made by students. I have some pieces of scrap plastic pipe in the basement. I am going to see if I can cut these into rings to make a simple armillary sphere to demonstrate these concepts. Cheers, Roger Bailey Walking Shadow Designs N 51 W 115 Today the solar declination is -22.3 degrees. At your latitude in Lisbon (38.7) the altitude of the sun at noon is 90-38.7-22.3 = 29 degrees. Here at latitude 51 the noon altitude is only 16.7 degrees, about half as high. No wonder that I am planning another trip to Portugal! -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Rui Farinha Sent: January 7, 2002 6:58 AM Cc: Sundial, Mailinglist Subject: About shadows, heights and other ones... Sorry the Off-Topic and my english... Hi Roger Bailey and other dear friends: Two questions: 1) Last week i red a magazine called "Cosinus" (a french publication to kids). One of the articles was about the highest full moon in the year being the one closest to the Winter solstice (Northern Hemisphere) - during this day we could "watch" the "lowest sun" to a given latitude and the biggest shadow. I'm writing something about this "curiosity" ("the highest and lowest sun" and "the highest and lowest moon" during an year) to the school journal but i would like to know more about this subject (calculations, pictures, schemes, etc.) that could help me being more accurate. Could you or anyone help me with this subject? (Internet sites or so). 2) I'm also doing (with students) the well known activity: determining the N-S (and E-W) directions by marking the end of a stick shadow during several hours of a day and then, connect all the points obtained and see the curved line and so on... I'm also trying to see the line that we obtain during solstices and equinoxes days and dates between this ones to make comparisons (by the way, speaking in mathematical terms, what can we consider this curves?). I will try to compare the curved lines with the ones obtained in dates close to the ones wehave work but in Southern Hemisphere (contact schools in Brasil or other countries). A) Does anyone knows sites about this activities and astronomical explanations with draws and pictures? B) Does anyone knows schools that have made this activities included in astronomy or geography projects? (I've already searched google in english, portuguese and spanish but i'm not satisfied with the materials i obtained). Thank you very much. Sorry if i wasn't very clear explaining my doubt but my english... Rui Farinha
