8.01SC | Fall 2016 | Undergraduate

Classical Mechanics

Week 2: Newton's Laws

5.2 Worked Example: Gravity Superposition

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The center of two spherical planets of masses \(\displaystyle m_1 \) and \(\displaystyle m_2 \) are separated by a distance \(\displaystyle d \). Consider the origin of the coordinate system to be at the center of planet 1. At what location \(\displaystyle x \) measured from the center of planet 1 will a third planet of mass \(\displaystyle m \) experience zero gravitational force? Assume \(\displaystyle m_1 \ne m_2 \).

Express your answer in terms of the gravitational constant \(\displaystyle G \), \(\displaystyle m_1 \), \(\displaystyle m_2 \) and \(\displaystyle d \) as needed.

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