Solved: Spacecraft that study the Sun are often placed at the so-called L1 Lagrange

Chapter 8, Problem 71

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Spacecraft that study the Sun are often placed at the so-called L1 Lagrange point, located sunward of Earth on the SunEarth line. L1 is the point where Earths and Suns gravity together produce an orbital period of one year, so that a spacecraft at L1 stays fixed relative to Earth as both planet and spacecraft orbit the Sun. This placement ensures an uninterrupted view of the Sun, without being periodically eclipsed by Earth as would occur in Earth orbit. Find L1s location relative to Earth. (Hint: This problem calls for numerical methods or solving a higher-order polynomial equation.)