A study of lunar and solar eclipses
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1 A study of lunar and solar eclipses Rosa M. Ros International Astronomical Union Technical University of Catalonia, Spain
2 Goals Understand why the Moon has phases Understand the cause of lunar eclipses Understand why there are solar eclipses Determine distances and diameters of the Earth-Moon-Sun system
3 Vision of lights and shadows System Earth-Moon-Sun: phases and eclipses Relative positions and shadows
4 Model of the dark side of the Moon 2 volunteers: one in the center (the Earth) and the other revolving around it (the Moon). Place the Moon facing the Earth and have it revolve around the Earth by 90 and rotate itself also by 90º, repeat the process until the initial position is reached
5 Model with flashlight (Sun) to explain the phases of the Moon 5 volunteers: one in the center (the Earth) and the other 4 simulate the 4 phases of the Moon with masks (1 completely illuminated, 2 partially illuminated and 1 completely dark)
6 Distances and diameters of the system Earth-Moon-Sun Earth Diameter km 4 cm Moon Diameter km 1 cm EM Distance km 120 cm Sun Diameter km 440 cm = 4.4 m ES Distance km 4700 cm = 0.47 km
7 Simulation of Phases of the Moon Direct the small moon of the model to the Moon and we can see both with the same phase
8 Errors Phases of the Moon depend on Sun's position
9 Moon Phases and Eclipses
10 Lunar eclipses only when the Moon is full Eclipses: Moon
11 Simulation of a Moon Eclipse
12 Moon Eclipse
13 Moon Eclipses Lunar eclipses can be visible to half of the Earth (night side) Rosa M. Ros
14 Eclipses: Sun Solar eclipses occur only when there is New Moon
15 Simulation of a Solar Eclipse
16 Detail of solar eclipse Dar ejemplos o contar anécdotas de la vida real Mostrar interés por la situación de la audiencia, si resulta apropiado Rosa M. Ros
17 Qué significa esto Agregar una declaración de su opinión acerca del tema Resumir los puntos principales que desee que la audiencia recuerde Rosa M. Ros
18 Solar eclipses are visible only in a small region of the Earth Solar Eclipse
19
20 Observations It can only occur: a lunar eclipse when is full Moon and a solar eclipse when is new Moon A solar eclipse is seen only in a small area of the Earth It is very difficult for Earth and Moon to be "well aligned, thus an eclipse cannot occur every time that there is new or full Moon
21 Finally... as an example... Next total solar eclipse in Spain: August 12, 2026 (last one 2004 in a different area) Each year there are 0 to 3 lunar eclipses
22 Distances and diameters in another small model (to visualize and better understand the distances to the Sun) Earth Diameter km 2.1 cm Moon Diameter km 0.6 cm EM Distance km 60 cm Sun Diameter km 220 cm ES Distance km 235 m
23 Painting the Sun
24 Looking at the small Sun from the Moon
25 Flip page" eclipse simulator 1. Trim and number the pictures in order 2. Paste each picture on a spiral notebook. 3. Turn the pages quickly to use the demonstrator.
26 Determination of Diameters Measure the diameter of the Moon (using some photos) Measure the diameter of the Sun (using pinhole camera)
27 Determination of the Moon diameter Photos that can show the Earth's shadow cone, represented by a cardboard
28 Determination of the Sun s diameter: with pinhole camera, observations and measurements
29 Determination of the Sun s diameter we can establish the proportion and calculate the Sun s diameter L = 150,000,000 km Earth-Sun distance, l = tube length, d = diameter of the Sun on semi-transparent paper
30 Aristarchus Experiment 310 to 230 BC Established relationships between distances Earth-Moon- Sun and their diameters (but could not determine any absolute value), had to wait until Eratosthenes 1) Distance Earth-Moon and Earth-Sun 2) Radius Moon and Radio Sun 3) Distance Earth-Moon and Moon Radius or distance Earth-Sun and Sun Radius 4) Cone of Terrestrial Shadow and Moon Radius 5) Relate all
31 1) Distance Earth-Moon and Earth-Sun cos a = EM / ES therefore ES = EM /cos a
32 1) Distance Earth-Moon and Earth-Sun Aristarchus a = 87º then ES = 19 EM Now a = 89º 51 therefore ES = 400 EM Rosa M. Ros
33 2) Radius of the Moon and of the Sun From the Earth, lunar and solar diameters are observed to be equal to 0.5 Therefore, the radius is Rs = 400 RM Rosa M. Ros
34 3) Distance Earth-Moon and Moon diameter from the Earth is 0.5 º With 720 times this diameter, we can discover the circular trajectory of the Moon 2 RM 720 = 2 p EM EM = 720 RM/ p Moon Radius Rosa M. Ros
35 3) Earth-Sun distance and By analogy ES = 720 Rs/ p Sun radius Aristarchus 1st heliocentric model
36 Cone of Terrestrial Shadow In a lunar eclipse, Aristarchus observed that the time required for the Moon to cross the shadow cone of the Earth was twice the time necessary for the surface of the Moon remain covered (i.e. 2:1) It really is 2.6:1 Rosa M. Ros
37 5) Relate all (x+tl+ts)/rs = (x+tl) / RT = x/(2.6 RL)
38 Solving the system follows (everything related to Earth s radius): RM = (401 / 1440) RE EM = (401 / ( 2 p) ) RE Rs = (2005 / 18) RE ES = (80200 / p) RE We assume RE= 6645 km RM = 1850 km (real 1738 km) EM = km (real km) Rs = km (real km) ES = km (real km)
39 Eratosthenes Experiment 280 to 192 BC Rosa M. Ros
40 Eratosthenes again Two cities on the same meridian Simultaneous observations
41 p = p - a + b + g therefore g = a - b where a and b are measured in radians Eratosthenes Rosa M. Ros
42 Eratosthenes We measure the length of the plumb line (or stick) and its shadow a = arctan (stick)/(shadow) Rosa M. Ros
43 by proportionality 2p RE / 2p = d/ g is deduced Eratosthenes RE = d/g g we know g = a - b d is the distance between cities (map) Rosa M. Ros
44 Our results with the method of Eratosthenes Ripoll- Barcelona a = radian b = radian g = radian d = 89.4 km RE = 6600 km (real 6645 km) Rosa M. Ros
45 Conclusions We now understand the eclipses Have established sizes relationships for the Earth-Moon-Sun system It is verified that by observing and formulating the data obtained, we can learn much more about the universe
46 Many Thanks for your attention!
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