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By Newton’s universal law of gravitation the free-fall acceleration a of a body, such as the satellite shown in Figure 1.3.20, falling a great distance to the surface is not the constant g. Rather, the acceleration a is inversely proportional to the square of the distance from the center of the Earth, a = k/r2, where k is the constant of proportionality. Use the fact that at the surface of the Earth r = R and a = g to determine k. If the positive direction is upward, use Newton’s second law and his universal law of gravitation to find a differential equation for the distance r.
FIGURE 1.3.20 Satellite in Problem 23
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Chapter 1 Solutions
Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term
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