Question regarding gravitational pull between 2 objects with an object separating them For illustration sake, envision three objects lined up in a row. The center object would be bigger than the other two. How would the gravities of the masses of the objects on the sides of the bigger object affect each other? 
And do we have a formula to represent how the gravities affect each other? 
 A: The gravitational force between two objects is not affected by the presence of other objects (other than that those other objects may alter the trajectory of the objects in question, and therefore alter their distances). So in the situation you describe, the forces on the side objects due to gravity from the other side object will be the same as if the center object was not there.
A: Consider three masses $m_1$, $m_2$ and $m_3$ initally located along a line, with distances $x_1$, $x_2$ and $x_3$ from the combined center of mass. As a convention we have $x_1 < x_2 < x_3 $.
This means that at all times $m_1 x_1 + m_2 x_2 + m_3 x_3 = 0$.
There are three pairs of gravitational attractions acting on the bodies. $$\begin{aligned} 
  F_{12} & = G \frac{m_1 m_2}{(x_2-x_1)^2} & F_{23} & = G \frac{m_2 m_3}{(x_3-x_2)^2} & F_{31} & = G \frac{m_3 m_1}{(x_1-x_3)^2} 
\end{aligned} $$
Summing up all the forces at each body, you get three equations of motion
$$ \begin{aligned} 
  F_{12} + F_{31} & = m \ddot{x}_1 &
  -F_{12} + F_{23} & = m \ddot{x}_2 & 
  -F_{23} - F_{31} & = m \ddot{x}_3
\end{aligned} $$
These equations need to be solved numerically with a simulation, and care must be taken that $x_1 < x_2 < x_3 $ is maintained, otherwise the forces will have to switch signs.
