It seems I am late to the party, but as you invited me in from another thread, I will try to respond summing it all up.
In many ways, this is quite analogous to electrostatic interactions.
The force between 2 charged particles is given by F=kQq/d^2.
But you can easily describe the nature of the elctric field around a single particle.
That is given by E (noting this is to denote the field, not an energy):
E=kQ/d^2.
This field exists even when you only have one particle.
It generates a force on another charged particle as:
F=qE.
Then the acceleration is given as a=(q/m)*E.
The same can be done with gravity, noting that "q" for gravity is m.
Using this method for gravity, there is clearly a force, even if you want to jump straight to the acceleration, skipping the force.
You could do the same with electrostatics. a=kQq/mr^2.
That doesn't mean no force is involved or that a charged particle can accelerate other charged particles without a force.
The fact that gravitational mass and inertial mass is always observed to be the same was one of the big puzzles about gravity (and still is to some extent).
However it was mostly addressed by relativity which has gravity not actually being a force and instead having it be the curvature of space time.
A mass (or energy density) would bend spacetime with the extent of curvature depending on mass/energy density and the distance to the object.
Then, anything else would merely follow the curvature of spacetime in an inertial path.
In this model, there is no real force, and instead you have an inertial force.
how do they bend space-time at such a large scale as quoted when atomic particles don’t have the ability of bend space-time unless in a collection?
They can bend space time. Everything can.
It is just a single atom all by itself will curve it by an insignificant amount.
But if you have a massive amount of these, those insignificant amounts build up.
It is like if you had a container with absolutely nothing in it, and put it a single molecule of water, that is still basically nothing in it. But but in a massive amount and you end up with a container full of water.
Then why don t you consider these slight distortion of space-time individually instead of taking a celestial body as a whole. it will limit the bending of space time to the actual size of celestial body.
Because doing it all at once is a much simpler calculation.
What would you rather do, a single calculation or roughly 10^50 of them (for Earth)?
It will not limit it to the edge of the body.
Even a tiny mass bends spacetime extremely far away. It is just that it bends it by an extremely tiny amount.
As for your energy equations, you can't just take completely different energy equations and equate them like that.
They are fundamentally different equations, with different meanings.
The full equation would be more like E=rest energy + kinetic energy + potential energy.
Where potential energy is in turn composed of gravitational potential energy, electrostatic potential energy and so on.
If you want to do it from the individual components, then you also throw in binding energy.
All you are doing is converting it from energy to specific energy.
I asked "Do pilots adjust for curvature when they fly parallel to the ground"? just like moving jet on the runway
They do so automatically by maintaining altitude.
They need to adjust their attitude to be able to maintain their altitude.
There is no specific requirement to adjust specifically for the curve as it is already taken care of.