Astronomy 111 Exam Review Problems (Real exam will be Tuesday Oct 25, 2016)

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1 Astronomy 111 Exam Review Problems (Real exam will be Tuesday Oct 25, 2016) Actual Exam rules: you may consult only one page of formulas and constants and a calculator while taking this test. You may not consult any books, nor each other. All of your work must be written on the attached pages, using the reverse sides if necessary. The final answers, and any formulas you use or derive, should be indicated clearly and explained. Exams are due an hour and fifteen minutes after we start, and will be returned to you during the next lecture. Exam problems will be based on problem set and workshop problems! The exam will cover classes and problems/workshops prior to the time of exam. We may not have covered topics like Jeans escape or atmospheric scale height. Notes: There are xx problem parts in all, each of which is worth a maximum of ten points. You will be asked to chose a subset of these to work on. You will be graded on your best xx problem parts. Please specify which problem parts you do not want graded. This list of problem is vastly longer than the actual exam will be!!1

2 Problem 1: Venus has an equatorial radius of 6052 km. Its semi-major axis is 0.72 AU. The Sun has a radius of 7 x cm. a) During a Venus transit (such as occurred June 8, 2004 and June 5, 2012), what is the angular diameter of Venus in arcseconds (as seen from the Earth)? b) What minimum diameter telescope would you need to be able resolve the Venus transit at visible wavelengths (as seen from the Earth)?!2

3 Problem 1: (continued) c) During a Venus transit, what fraction of the Sun s light is blocked by Venus? d) Consider a transit on a distant star similar to the Sun. The transit is caused by a Venus sized extra solar planet. The viewer is very distant from the star. What change in the observed magnitude of the star does this transit cause? Does the magnitude of the star increase or decrease during the transit?!3

4 Problem 2: At a pressure of 1 atmosphere, water freezes at 273K and boils at 373K. We say that a planet is in the habitable zone if its equilibrium temperature is within the range allowing liquid water. Assume that the planet has an albedo similar to that of Earth. The equilibrium temperature of the Earth (at 1AU from a solar type star and with Earth s albedo) is 263 K. a) How does the equilibrium temperature of a planet depend upon the planet s distance from the star R and the luminosity of the star, L? Write your answer in the following form: L r T eq = X(in Kelvin) L AU and find the exponents α,β and the constant X. b) What are the inner and outer radii (in AU from the star) of the habitable zone near a star that is 100 as luminous as the Sun (such as a red giant)? The Sun will become a red giant in a few billion years. Speculate on which moons and satellites in our solar system might become nice places to live during this time.!4

5 Problem 2: (continued) c) Consider the possibility that the planet is not in a circular orbit. What is the maximum eccentricity for the planet s orbit that would allow the planet to remain in the habitable zone during its entire orbit. Assume that the semi-major axis puts the planet right in the middle of the habitable zone.!5

6 Problem 3: A dust particle is in a nearly circular orbit about a star of mass M, and has a ratio of radiation pressure to gravitational force of β. The particle experiences forces due to gravity from the central star and radiation pressure from the central star. Ignore drag forces such as Poynting Robertson drag. a) As a function of distance r from the star, what is the period, P, of the particle s orbit about the star? b) The particle is trapped in the 2:1 mean motion resonance outside a planet with semi-major axis ap. Because of radiation pressure, the dust particle does not have the same semi-major axis that a larger object in this resonance would have. What is the semi-major axis of the dust particle in terms of the planet s semi-major axis and β?!6

7 Problem 4: Pluto has a mass of g and Charon has a mass of g. Charon is in orbit about Pluto with a semi-major axis of km. Pluto and Charon are in an orbit around the Sun with a semi-major axis of 39.5AU and eccentricity of e=0.25. a) At what distance (in km) from Pluto is the Center of Mass of the Pluto/Charon system? b) How far away (in AU) from the Earth would Pluto and Charon be at perihelion? Assume that they are at opposition.!7

8 Problem 4: (continued) c) Pluto is observed to have visual magnitude of mv=7.5. Charon is 1.9 magnitudes fainter than Pluto. What visual magnitude are the two bodies observed together?!8

9 Problem 5: The scale height of a planetary atmosphere is approximately given by h=kt/gm where T is the temperature, g is the surface gravitational acceleration, k is Boltzmann s constant and m is the mean molecular mass of particles in the atmosphere. a) How does the scale height of a planetary atmosphere depend on (scale with) the mass and radius of the planet? b) Assume that the temperature of the atmosphere is set by an equilibrium between the radiation absorbed from the Sun and that emitted by the planet. How does the scale height depend on the distance of the planet from the Sun?!9

10 Problem 5: (continued) c) By what factor would the scale height of Pluto s atmosphere change between perihelion and aphelion? Pluto has an eccentricity of d) Consider a planet with mass M which has a satellite with mass Ms. The satellite has radius Rs and is on an eccentric orbit (around the planet) with semi-major axis a and eccentricity e. How much larger (by what factor) is the tidal force on the satellite at periapse compared to that at apoapse?!10

11 Problem 6: In this problem you are asked to describe various terms discussed in lecture and in the text. Please supplement your description with examples, equations or with a description of a setting where you would use this term. a) Describe 2 (out of 6) of the following terms 1. Obliquity 2. Right ascension and Declination 3. Sidereal rotation period 4. Kepler s laws 5. Mean motion 6. Escape Velocity b) Describe 2 (out of 4) of the following terms 1. Spectral resolution 2. Diffraction limit 3. Absolute Magnitude 4. Signal to noise!11

12 Problem 7: (continued) c) Describe 2 (out of 4) of the following terms 1. Poynting-Robertson Drag 2. Radiation pressure 3. Albedo 4. Yarkovski Effect d) Describe 2 (out of 4) of the following terms 1. Thermal conductivity 2. Greenhouse effect 3. Optical depth 4. Jean s escape!12

Astronomy 111 Review Problems Solutions

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