Horizons: Exploring the Universe (MindTap Course List)
Horizons: Exploring the Universe (MindTap Course List)
14th Edition
ISBN: 9781305960961
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 19, Problem 5P

What is the maximum angular diameter of the largest asteroid, Ceres, as seen from Earth? Can Earth-based telescopes detect surf ace features? Can the Hobble Space Telescope’ (Hint: Use the small-angle formula in Reasoning with Numbers 3-1.) (Notes: The angular resolution of Earth-based telescopes is about 1 arc second and of HST about 0.1 arc second. Ceres’ average distance from the Sun is 2.8 AU.)

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At what average distances (in AU) from the Sun would you expect to find Kirkwood gaps where the orbital period of asteroids are respectively four-ninths, and two-fifths, of the orbital period of Jupiter? (Hint: use Kepler's third law.) inner gap at AU outer gap at AU Compare your results with the figure. 7:2 3:1 8,3 5;2 7:3 9:4 2;1 9:5 7:4 53 8:5 3:2 Resonances Gap Gap Gap Gap GapGap Gap Distance from sun (AU) O The results agree with the figure. O The results do not agree with the figure.
Consider an asteroid that orbits in a relatively circular orbit with a semimajor axis a = 2 au from the Sun. A typical asteroid has an albedo, or reflectivity, A ~ 0.3. At our closest approach to the asteroid, we make a measurement of the flux coming from the asteroid to be F = 3 × 10-15 w m-2. What is the radius of the asteroid in km? Include a labelled diagram along with your calculations.
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