Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 30, Problem 28E
Why are we limited to finding life on planets orbiting other stars to situations where the biosphere has created planet-scale changes?
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A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).
Chapter 30 Solutions
Astronomy
Ch. 30 - What is the Copernican principle? Make a list of...Ch. 30 - Where in the solar system (and beyond) have...Ch. 30 - Give a short history of the atoms that are now in...Ch. 30 - What is a biomarker? Give some possible examples...Ch. 30 - Why are Mars and Europa the top targets for the...Ch. 30 - Why is traveling between the stars (by creatures...Ch. 30 - What are the advantages to using radio waves for...Ch. 30 - What is the “cosmic haystack problem”? List as...Ch. 30 - What is a habitable zone?Ch. 30 - Why is the simultaneous detection of methane and...
Ch. 30 - What are two characteristic properties of life...Ch. 30 - What are the three requirements that scientists...Ch. 30 - Can you name five environmental conditions that,...Ch. 30 - Would a human have been possible during the first...Ch. 30 - If we do find life on Mars, what might be some...Ch. 30 - What kind of evidence do you think would convince...Ch. 30 - What are some reasons that more advanced...Ch. 30 - What are some answers to the Fermi paradox? Can...Ch. 30 - Why is there so little evidence of Earth’s...Ch. 30 - Why was the development of photosynthesis a major...Ch. 30 - Does all life on Earth require sunshine?Ch. 30 - Why is life unlikely to be found on the surface of...Ch. 30 - In this chapter, we identify these characteristic...Ch. 30 - Given that no sunlight can penetrate Europa’s ice...Ch. 30 - Why is Saturn’s moon Enceladus such an exciting...Ch. 30 - In addition to an atmosphere dominated by...Ch. 30 - How can a planet’s atmosphere affect the width of...Ch. 30 - Why are we limited to finding life on planets...Ch. 30 - Suppose astronomers discover a radio message from...Ch. 30 - The light a planet receives from the Sun (per...Ch. 30 - Think of our Milky Way Galaxy as a flat disk of...
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