Chapter 4.6, Problem 80AE

Gravitational Force According to Newton’s Law of Universal Gravitation, the attractive force $F$ between two bodies is given by

$F=G\frac{m_1{m}_2}{r^2}$

where $m_1,m_2=$ the masses of the two bodies

$r=$ distance between the two bodies

$G=gravitationalconstant=6.6742\times {10}^{-11}newtons\cdot mete{r}^2\cdot kilogra{m}^{-2}$

Suppose an object is traveling directly from Earth to the moon. The mass of Earth is $5.9742\times {10}^{24}$ kilograms, the mass of the moon is $7.349\times {10}^{22}$ kilograms, and the mean distance from Earth to the moon is $384,400$ kilometers. For an object between Earth and the moon, how far from Earth is the force on the object due to the moon greater than the force on the object due to Earth?

Source: www.solarviews.com;en.wikipedia.org