Consider a Newtonian mechanics gravity field with a center of mass $m$ at position ${\bf v}$ like so:
$$F({\bf v}) = \sum_{k} G\cdot m\cdot m_k\cdot \frac{({\bf v-v_k})}{\|({\bf v-v_k})\|^3}$$
, assuming we have a set of mass centers $\bf v_k$ each having mass $m_k$
or we can rewrite using ${\bf F} = m{\bf a}$:
$${\bf a}({\bf v}) = \sum_{k} G\cdot m_k\cdot \frac{({\bf v-v_k})}{\|({\bf v-v_k})\|^3}$$
It is easy to imagine if we have two equally large masses $m_1=m_2$, we will have a plane of locally highest potential energy in "the middle" of these points. By continuity this surface should slowly morph into some other shape than a plane as we slowly continously alter the relation between $m_1$ and $m_2$.
Can we calculate some algebraic expression for this curve? Like a level-set of some function?