you could make up a problem and involve some mechanics to solve it, imagine you have a trolley with 4 freely mounted wheels, you are going to accelerate the trolley with a constant force, the wheels don't slip under acceleration, what is the acceleration rate of the trolley ? ignore air drag and...
the aerodynamic drag force is proportional to the square of the speed
power required is : ( aerodynamic drag force overcome (+ rolling resistance if you want) ) * speed
if fuel consumption is energy consumed, is this power * time ?
if you took one car and increased the engine horsepower but at the same engine rpm, you would need to lengthen the gearing to suit the higher potential top speed.
why don't you set up an excel sheet, with inputs for mass 1, mass 2, and centre to centre distance, put in some example values, then process through the appropriate maths to reveal an orbit time, then adjust the centre to centre distance if required to close in on the required result, trial and...
assume the particle is of negligable mass, then the equation for gravitational acceleration is : g = (G * M) / d^2
use substitution, call the distance from A = 1, then find the distance B
Say you had a fixed journey of say 10,000 m to travel in a given time, i.e. at a given speed, then with a fixed set of vehicle variables (drag coefficient, rolling resistance coefficient, vehicle mass) you could figure the energy required (Power required * time) to complete the journey, then...
i would be tempted to apportion an effective moment of inertia to shafts B & C (this takes into account the relative rotation rates)
Select an arbitrary rotation rate for shaft A (say 10 rad/sec)
Calculate the rotational KE of each shaft at this rate
The effective moment of inertia of shafts B...