My School’s Analemma & Remembering Eratosthenes

My School’s Analemma&Remembering Eratosthenes Lisbon eTwinning Metting 21/10/2006 Arlindo Fragoso

Lisbon eTwinning Metting - 21/10/06 My School’s Analemma • Because of the obliquity of the ecliptic, the Sun moves not just in the east-west direction in the sky, but also in the north-south direction. This means that even if the Sun moved along the sky at a constant rate, its speed in the east-west direction would vary because its speed in the north-south direction varies, so that the real Sun would go faster in the east-west direction than the mean Sun near midsummer and midwinter, and slower near the beginning of spring and autumn. That is why the Sun moves along the analemma from west to east near the top and bottom of the analemma (around midwinter and midsummer, December and June), and from east to west near the middle of the analemma (around the beginning of spring and autumn, March and September).

Lisbon eTwinning Metting - 21/10/06 My School’s Analemma • The Earth's orbit is an ellipse, which is a circle that is slightly squashed in one direction. Because the Earth's orbit around the Sun is not a circle, the apparent speed of the Sun in the sky varies slightly with time. Around 3 January it is greatest (about 3 percent faster than average), and around 7 July it is smallest (about 3 percent slower than average). This adds to the east-west motion in the analemma. Because the apparent speed of the Sun in the sky is faster in December than in June, the southern (September to March) part of the analemma is wider than the northern (March to September) part. • The analemma is 47 degrees long (two times the obliquity of the ecliptic) and, at its widest part, about 8 degrees wide.

Lisbon eTwinning Metting - 21/10/06 My School’s Analemma

Lisbon eTwinning Metting - 21/10/06 My School’s Analemma • By studying the sun's azimuth on a second-by-second basis, it was established that the vertical analemma corresponded to an exposure schedule for precisely 12:28:16 UT+2, for it is at this time that azimuth for the summer and winter solstice line-up perfectly. The ephemeris of the sun at this time was also used to examine the range in altitude from January 1st to December 31st in order to arrive at an imaging schedule for the analemma. More specifically, the altitude was identified for the upper apex (June 21) and the cross-over points (Aug 30); this range was divided by seven so as to derive an offset that could be successively subtracted from the altitude on June 21st so as to identify the corresponding dates with that target altitude for imaging. A similar approach was adopted for the lower loop where a divisor of 14 was applied to the range in altitude between the cross-over point (Aug 30) and the lower apex (Dec 21).

Lisbon eTwinning Metting - 21/10/06 My School’s Analemma

Lisbon eTwinning Metting - 21/10/06 My School’s Analemma www.perseus.gr/Astro-Solar-Analemma.htm http://en.wikipedia.org/wiki/Analemma http://www.analemma.de/english/analem.html http://www.analemma.com/Pages/framesPage.html http://analyzer.depaul.edu/paperplate/analemma.htm Software http://research.microsoft.com/projects/GroupShot/ MSR Group Shot helps you create a perfect group photo out of a series of group photos. With Group Shot you can select your favorite parts in each shot of the series and Group Shot will automatically build a composite image.

Lisbon eTwinning Metting - 21/10/06 Remembering Eratosthenes • The main objective of the experiment is to measure the terrestrial circumference. We propose a realistic procedure, working with two groups located in different regions around the world, working in a coloborative way, no mather the period of the year.

Lisbon eTwinning Metting - 21/10/06 Remembering Eratosthenes

Lisbon eTwinning Metting - 21/10/06 Remembering Eratosthenes • The first step is to determine the geographical orientation and, therefore, the North-South direction using the Vitruvio's method. This is made placing a vertical stick into the ground, embedding it partially in a way that it stays perpendicular to the soil (this is very important). The stick can have between 20 and 50cm above the ground. • In the morning, mark on the ground the position of the extremity of the shade produced by the stick. Them make a circle centering it in the stick and passing it by the former marked point. In the afternoon, when the shade comes back to reach the drawn circle, mark this position with another point. Next, measure the distance between the marked points and determine, in the soil, the half of this distance. The straight line joining the stick and this point is the North-South direction.

Lisbon eTwinning Metting - 21/10/06 Remembering Eratosthenes Determination of Latitude • The vertical stick and the N-S direction will be used again. In a clear day, the group should be prepared before the solar noon. As soon as the shade reaches the N-L direction (it occurs when the Sun reaches its highest position in the sky, and is called solar noon), note down its size. The length of the stick above the ground must be written down too. The local time of the phenomenon is basic for the experiment and must carefully be registered by each team and converted for Greenwich Mean Time (GMT).

Lisbon eTwinning Metting - 21/10/06 Remembering Eratosthenes The angular altitude of the sun at noon (a), can be obtained by tg (a) = h / s. Get the latitude by the following formula: f = δ - ( 90º – a) [shade directed to South] f = δ+ ( 90º – a) [shade directed to North] where δ is the solar declination. The values for solar declinations along the year can be found, for example, in the Astronomical Ephemeris.See http://solardat.uoregon.edu/SolarPositionCalculator.html

Lisbon eTwinning Metting - 21/10/06 Remembering Eratosthenes • Remembering Eratosthenes http://www.rio.rj.gov.br/planetario/eratostenes/english/era2.html • Surface Distance Between Two Points of Latitude and Longitude http://www.wcrl.ars.usda.gov/cec/java/lat-long.htm • Eratosthenes Experiment: A Worldwide Science and Math Experiment - September 22, 2006 http://youth.net/eratosthenes/welcome.html • www.sover.net/~rc/deep_secrets/measuring/index.html • www.eduref.org/Virtual/Lessons/Mathematics/Geometry/GEO0004.html • http://ithacasciencezone.com/earthzone/lessons/03dimens/mearth/index.htm • www.britannica.com/eb/article-217489/geometry • www.k12science.org/noonday/ • www.phys-astro.sonoma.edu/observatory/eratosthenes/

My School’s Analemma & Remembering Eratosthenes