What Newtonian Law can be used to determine the presence of a force?

!st Law

What wold be a good strategy to calculate forces for a symmetric arrangement of charges.

Calculate the Scalar Electrostatic Potential and use the gradient.

How could the first microcomputers used 50 years ago in the first trip to the moon manage to navigate from the earth to the moon with such relatively primitive computers in running real time?

They simply used a five parameter approximation (quartic polynomicl) to the navigation equations. They just used the position and first four time derivatives (velocity, acceleration, jerk, and snap) of the three dimensions of the position.vector. This was used with an inertial navigation system and checked with position relative to a known star location.