PHY 102 1nd Edition Lecture 2 Outline of Last Lecture I Humankind has always been in contact with surroundings A Senses a Outside World i Celestial ii Terrestrial iii In between II Gods were created a Priests III Astronomy a How it began b Egyptians and Babylonians IV Greek Astronomy V Pythagoras a Theory b Parallax VI Abandon theory if observation is wrong VII Plato a Theory VIII Retrogression retrograde motion IX Eudoxos a Theory Outline of Current Lecture I Eudoxos continued II Angle of Measurement a Definition i Two names associated with the measurements ii How big is the moon iii How far is the moon These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute iv How far is the sun v How big is the sun vi How big is Earth Current Lecture I Eudoxos continued a Concentric distance between planet and earth is fixed b Simplicity and symmetry has been retained at the expense of having to deal with several spheres c Homocentric model i Disagreement between theory and observation planets seemed to be brighter when they retrogressed 1 They got closer to earth cannot happen if circling around in a perfect sphere II Age of Measurement a One of the most crucial developments in Greek astronomy was the attention given albeit for a very short while to the sizes and distances of objects i Aristarchus and Eratosthenes 1 Aristarchus worked with Moon and Sun 2 Eratosthenes worked with Earth ii How big is the moon 1 Aristarchus Look at the eclipse of Moon a What is the eclipse of the moon i Earth s shadow covers the moon it disappears 1 Earth is bigger than the moon b By measuring the angle of the triangle the shadow makes c 1 3 33 the size of Earth i Improvement 27 of the size of Earth iii How far is the moon 1 Aristarchus Look at angles a Use geometry i Formlua size height of stick distance distance to stick 1 How to Full moon take a short stick hold it as far away from your eyes as you can make sure it barely covers the moon make a ratio b Distance to the moon is about 25 times Earth s diameter i Improvement 30 times c Angle is important iv How far is the Sun 1 Aristarchus found the Earth Sun distance to be 20 times EarthMoon distance v How big is the Sun 1 Since the angular sizes of the sun and moon are about the same in sky the sun must be 20 times bigger than the moon a Moon is about 1 3 Earth i So the sun should be 7 times bigger than Earth 1 If the Sun is 7 times bigger it cannot go around the earth it must be the other way around 2 Almost 1800 Years before Copernicus Aristarchus discovered heliocentrism a For the same reason that Pythagorean astronomy did not prevail undetectibility of Earth s motion parallax Aristarchus heliocentrism died out vi How big is Earth 1 Eratosthenes Compare shadow angles in two different cities a Shadow angle tip of your head to the tip of the shadow b 360 degrees subtends the entire circumference i Proportion circumference 360 C1C2 c Distance 500 miles angle difference 7 2 degrees Circumference 360 500 7 2 Circumference of Earth 25 000 miles C 2 r 25000 2 r r 3 978 miles