Overview
Newton originally formulated his theory of gravity by postulating that gravity was a force defined by the following equation
{% \vec{F} = - \frac{GmM}{r^2} \vec{e}_r %}
When there are several particles, the total force on a test particle is the sum of the gravitational forces from
each of the other particles.
{% \vec{F} = - \sum_{i=1}^N \frac{G m m_i}{r_i^2} \vec{e}_i %}