Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 13, Problem 28E
What is the period of revolution about the Sun for an asteroid with a semi-major axis of 3 AU in the middle of the asteroid belt?
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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 13 Solutions
Astronomy
Ch. 13 - Why are asteroids and comets important to our...Ch. 13 - Give a brief description of the asteroid belt.Ch. 13 - Describe the main differences between C-type and...Ch. 13 - In addition to the ones mentioned in Exercise...Ch. 13 - Vesta is unusual as it contains what mineral on...Ch. 13 - Compare asteroids of the asteroid belt with...Ch. 13 - Briefly describe NASA’s Spaceguard Survey. How...Ch. 13 - Who first calculated the orbits of comets based on...Ch. 13 - Describe the nucleus of a typical comet and...Ch. 13 - Describe the two types of comet tails and how each...
Ch. 13 - What classification is given to objects such as...Ch. 13 - Describe the origin and eventual fate of the...Ch. 13 - What evidence do we have for the existence of the...Ch. 13 - Give brief descriptions of both the Kuiper belt...Ch. 13 - Give at least two reasons today’s astronomers are...Ch. 13 - Suppose you were designing a spacecraft that would...Ch. 13 - Suppose you were designing a spacecraft that would...Ch. 13 - Suppose a comet were discovered approaching the...Ch. 13 - We believe that chains of comet fragments like...Ch. 13 - Why have we found so many objects in the Kuiper...Ch. 13 - Why is it hard to give exact diameters for even...Ch. 13 - Refer to Example 13.1. How would the calculation...Ch. 13 - Refer to Example 13.1. How would the calculation...Ch. 13 - The calculation in Example 13.1 refers to the...Ch. 13 - If the Oort cloud contains 1012 comets, and ten...Ch. 13 - The mass of the asteroids is found mostly in the...Ch. 13 - Make a similar estimate for the mass of the Kuiper...Ch. 13 - What is the period of revolution about the Sun for...Ch. 13 - What is the period of revolution for a comet with...
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