The FoR is the parchutist. and I do take the acceleration of the FE into account. the acceleration of the FE is used to account for the velocity when you calculate R that is why I changed it from "v" to "at". You must remember that the FE model states that the earth accelerates up to him so the air will accelerate faster and faster by him which is well accounted for. We cannot add elements into the system to try and make it reflect reality when the model does not allow it
No, you do not account completely for the acceleration of the FE toward the parachutist. From his FoR, the surfaces of both the FE and the RE are accelerating toward him at 1g. You put the force in the RE equation, but omit it, in error, from the FE equation.
In FE the Force of the surface of the earth is not in the system while the force of gravity is acting upon him in the RE system. how can you be pushed by an unconnected piece? if a car rushes by me the car will not affect me at all, now the wind from it may affect me but not to the extent the car would if it had hit me
You forget that you chose the FoR of the parachutist. You have to deal with the acceleration of the surface toward him equally in both models.
We can simplify this quickly. Imagine a vertical tube perfectly evacuated expect for a ping-pong ball at the top. As the ball falls in the RE model gravity accelerates it down. As the FE surface rises it accelerates up toward the ball. The surface meets the ball at the same time with the same speed in either model.
We don't disagree on any other point. You don't need the air resistance. You don't need the parachute. You just have to face the fact that FE mimics the force of gravity for the constant acceleration of the FE up at 1g. You must add this into your equations.
It is in the presence of these resistive forces that throws the FE theory out of whack. In the absence of resistive forces yes the acceleration in the 2 models would be the same but as soon as you add resistive forces into the mix the results are skewed. this is mainly due to where the forces come from. I suspect you are relating it to the EP and while it is correct that when I jump out of plane I would not be able to tell if I was falling or if the earth was rising up to meet me, however when we develop a model to explain what is happening and predict behavior we can not use EP because we need to state what forces are involved and how they are affecting us.
How can resistive forces throw FE out of whack?
Try this:
Take the parachutist model. Remove air resistance and the parachute. The models agree since there are no resistive forces.
Now add a parachute that magically transforms to provide a constant force of 1N up during the entire descent. The force would be the same in both models. Since equals added to equals are equal, the models are still equal.
Now add air resistance and the parachute. The forces would again be equal. The models are still equal.