ASTR340 Problem Set #1 - Spring 2008 - Prof. Alberto Daniel Bolatto, Assignments of Astronomy

Download ASTR340 Problem Set #1 - Spring 2008 - Prof. Alberto Daniel Bolatto 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. 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. C. What do you think about Aristotle’s theory internal consistency? 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? B. Who proposed the Heliocentric model first and when? What was the motivation? 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? 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) 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) 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) 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) 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? 5. Kepler’s third law [20 pts.] A. The first extrasolar planet (i.e., a planet orbiting another star) was found around the solar-type star 51 Pegasus in 1995. Its period is 4.2308 days (a very short year!). What would be its distance to 51 Pegasus? (Hint: solar-type means its mass is very similar to the mass of the Sun) B. We do not have (currently) any direct means of imaging the planet around 51 Pegasus to confirm its distance to the star. But we can apply the general form of Kepler’s third law to double stellar systems, where we can also make orbital distance measurements. Every system measured has been consistent with the predictions of Kepler’s third law. What do you think this means about the predictive power of Newtonian physics? Please contrast this situation with the predictive power of the Ptolemaic system.