An object which experiences two gravitational force

1. The problem statement, all variables and given/known data

Let there be a Voyager 5 with two Earth’s(I mean they have the same mass and density etc)
At start,Voyager 5 will be stationary.
I want to calculate the path of the Voyager and if possible,draw it on a graph.

2. Relevant equations
##F=\frac{GMm}{r^2}##

3. The attempt at a solution
I know I have to find the resultant force and accelerate the voyager in that direction.
My problem is that if I move it a little bit,the forces will change both direction and magnitude.Then I will again have to find the resultant force and accelerate it.This would be boring.
Is this really that difficult?Is there any other way?
I need your help here. 🙂

Attached Images
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