Question 582155
Suppose d is the distance between this object and Earth, m_1 is the mass of the object, m_2 and m_3 are the masses of the Earth and moon, respectively. Then r-d or 384000-d is the distance between the object and the Moon. We want the following inequality to be true:


*[tex \LARGE G \frac{m_1 m_2}{d^2} < G \frac{m_1 m_3 }{(r-d)^2}]


G and m_1 cancel, leaving


*[tex \LARGE \frac{m_2}{d^2} < \frac{m_3}{(r-d)^2} \Rightarrow m_2 (r-d)^2 < m_3 d^2 \Rightarrow m_2 (r-d)^2 - m_3 d^2 < 0]


Since m_2, m_3, and r are known, solve the quadratic in terms of d (you will have to expand, simplify first), replace m_2, m_3, r in, and find the smallest d such that the gravitational force from the Moon is greater than the force from the Earth.