Astronomy Problem Set: Theories, Geocentric vs Heliocentric, Eratosthenes, Kepler - Prof. , Assignments of Astronomy

Download Astronomy Problem Set: Theories, Geocentric vs Heliocentric, Eratosthenes, Kepler - Prof. and more Assignments Astronomy in PDF only on Docsity! PROBLEM SET #1 ASTR340 – SPRING 2008 Due Date: 14th February 2008 (yes, Valentine’s day) Book Chapters: 1 and 2 1. What constitutes a scientific theory? [20 pts.] A. Please name and explain the main properties of a scientific hypothesis according to the scientific method. 1) Relevant 2) Consistent 3) Predictive 4) Testable 5) Simple (Ockham’s Razor) B. Aristotle hypothesized that heavier bodies fall faster than lighter bodies, which seems true enough in every-day experience. Assume that cube A is lighter than cube B, and thus falls more slowly. What does the theory predict will happen if I glue (or tie with a rope) cube A to cube B and throw the composite A+B body out of the window? Will A+B fall faster or slower than either A or B? Explain your reasoning. A possibility would be that, being A+B heavier than either A or B, it falls more rapidly than either of the two. Another possibility would be that if A is lighter (thus falls more slowly) than B, then when I tie them with an arbitrarily short rope A will slow down the fall of B (like a parachute). C. What do you think about Aristotle’s theory internal consistency? It’s difficult to decide, based on just that hypothesis, what to predict. It could go either way. It seems that this hypothesis lacks internal consistency and/or predictive power. 2. Location, location, location [20 pts.] A. Outline three good arguments for the Geocentric view. Why should the Earth be at rest at the center of the Universe? 1) We have no perception of motion on the surface of the Earth 2) Stars do not have a perceptible parallax motion 3) We are the acme of creation. How could we not be at the center? B. Who proposed the Heliocentric model first and when? What was the motivation? Aristarchus of Samos. His measurements show that the Sun was much larger than the Earth. How come the Sun is moving around us? The Sun should be at the center (of the Universe) C. What was the observation that finally proved geocentrism could not be correct? What was the prediction from the Geocentric model and what was actually observed? Galileo’s observations of the phases of Venus were not compatible with the Geocentric view. It was clear that Venus was, when almost full, farther than the Sun, which would be impossible in the Geocentric system. 3. Erathostenes the astronaut [20 pts.] A. On a given day the Apollo 11 flagpole on Mare Tranquillitatis casts no shadow (the Sun is directly overhead, that is, at 0 degrees from the zenith). At precisely the same time, the flagpole on the Apollo 17 landing site, situated 590 km almost directly north of Mare Tranquillitatis in the Taurus-Littrow region, casts a pretty noticeable shadow. How far away from the zenith (in degrees) is the Sun at the Apollo 17 landing site? (Hint: the radius of the Moon is 1,737 km) About 19.5 degrees (angle=590/1,737 radians=590/1,737 *180/pi degrees) B. If the flagpole is 2 meters in height, how long is its shadow? (Hint: look at the definition of the tangent of an angle) About 71 cm (2m*tan (19.5 deg)=length of shadow) 4. The size of the Universe [20 pts.] A. Parallax is the change in apparent position of an object against the background, as the observer moves. In annual parallax, the observer is carried ±150,000,000 km by the Earth in its orbit around the Sun. Think about a right triangle with the 90 degree vertex on the Sun, another vertex at the Earth, and a third at a very distant star. If the angle subtended by Earth-Sun distance as seen from the star is 1 arcsecond (1” is 1/3,600 of a degree, or π/(180*3,600) radians), what would be the distance from the Sun to the star? That distance is called a “parsec”, and it is a common distance unit in astronomy, useful because parallax P[”]=1/D[parsec]. (Hint: sketch a drawing and recall the definition of tangent of an angle) D=150,000,000 km/tan (1/3,600 deg)~3x1013 km B. Barnard’s star in the constellation of Ophiuchus was discovered in 1916 by Edward Emerson Barnard and it is known to be at a distance of 5.96 light years, the closest neighbor of the Sun after Proxima and Alpha Centauri. What is its parallax? (Hint: one parsec is approximately 3.27 light-years. Recall the definition of parsec and why it is a useful distance unit for computing parallaxes) Distance to Barnard’s star [parsec] = 1/P[”] = 1/(5.96/3.27) = 0.55” C. Did Tycho Brahe stand any chance of measuring Barnard’s star parallax? What do you think this means about a crucial objection leveled against the Heliocentric model? No, this is such a small angle that it is impossible to measure with the naked eye. Since this is one of the nearest stars, it is clear that it was impossible to measure any parallax motion before the invention of the telescope. The lack of parallax, which was a key objection against Heliocentrism that swayed many people (c.f., Tycho Brahe), just implies that the Universe is VERY LARGE. 5. Kepler’s third law [20 pts.]