PHY 102 1nd Edition Lecture 2Outline of Last Lecture I. Humankind has always been in contact with surroundingsA. Sensesa. Outside Worldi. Celestialii. Terrestrialiii. In-betweenII. Gods were createda. PriestsIII. Astronomya. How it beganb. Egyptians and BabyloniansIV. Greek AstronomyV. Pythagorasa. Theoryb. ParallaxVI. Abandon theory if observation is wrong!VII. Platoa. TheoryVIII. Retrogression/retrograde motionIX. Eudoxosa. TheoryOutline of Current Lecture I. Eudoxos (continued)II. Angle of Measurementa. Definitioni. Two names associated with the measurementsii. 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 LectureI. Eudoxos (continued)a. Concentric = distance between planet and earth is fixedb. Simplicity and symmetry has been retained at the expense of having to deal with several spheresc. Homocentric modeli. Disagreement between theory and observation: planets seemed to be brighter when they retrogressed1. They got closer to earth (cannot happen if circling around in a perfect sphere)II. Age of Measurementa. 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 objectsi. Aristarchus and Eratosthenes1. Aristarchus worked with Moon and Sun2. Eratosthenes worked with Earthii. 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 makesc. 1/3 (33%) the size of Earthi. Improvement: 27% of the size of Earthiii. How far is the moon?1. Aristarchus: Look at anglesa. Use geometryi. Formlua: (size/height of stick) = (distance/distance to stick)1. How to: Full moon, take a short stick, hold itas far away from your eyes as you can, makesure it barely covers the moon, make a ratiob. Distance to the moon is about 25 times Earth’s diameteri. Improvement: 30 timesc. Angle is important *iv. How far is the Sun?1. Aristarchus found the Earth-Sun distance to be 20 times Earth-Moon distancev. How big is the Sun? 1. Since the angular sizes of the sun and moon are about the same insky, the sun must be 20 times bigger than the moona. Moon is about 1/3 Earthi. So the sun should be 7 times bigger than Earth1. If the Sun is 7 times bigger, it cannot go around the earth; it must be the other way around2. Almost 1800 Years before Copernicus, Aristarchus discovered heliocentrisma. For the same reason that Pythagorean astronomy did not prevail (undetectibility of Earth’s motion/parallax), Aristarchus’ heliocentrism died outvi. 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 shadowb. 360 degrees subtends the entire circumferencei. Proportion: (circumference/360) = (C1C2/θ)c. Distance = 500 miles, angle difference = 7.2 degrees(Circumference/360) = (500/7.2)Circumference of Earth = 25,000 milesC = 2πr25000 = 2πrr = 3,978