In celestial mechanics, Kepler’s equation is important. It reads x = y − ε sin y, in which x is a planet’s mean anomaly, y its eccentric anomaly, and ε the eccentricity of its orbit. Taking ε = 0.9, construct a table of y for 30 equally spaced values of x in the interval 0? x ?π. Use Newton’s method to obtain each value of y. The y corresponding to an x can be used as the starting point for the iteration when x is changed slightly.
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