Please clarify the question. One way of doing this is to express the problem in mathematical notation.
we have calculated the acceleration due to gravity from a particular altitude down to the surface
If we assume an airless body (eg the Moon), and calculate the gravitational acceleration as a function of the radius from the center of the Moon:
Gravitational Acceleration = g(r).
g: gravitational acceleration
r: radius from center of the Moon
For "normal" velocities and "normal" masses, g(r) can be approximated by Newton's law of gravitation:
g(r) = GM/r2
Where:
G: Gravitational Constant
M: Mass of the Moon
r: radius from center of the Moon
Assuming that there is no tangential velocity (which could put it in an orbit that
never hits the Moon's surface), you calculate the final impact velocity v
_{f} by integrating this acceleration g(r) from initial radius R
_{i} to the Moon's radius R
_{m}, and adding any initial radial velocity v
_{i}.
what would happen if we accelerated an object down to the surface at exactly this rate of increasing acceleration?
Here I am confused. If we let the object free-fall, it would experience acceleration g(r) without us having to do anything.
However, the active voice "we accelerated" implies that we do
not let if free-fall, but do something to it. What is this "something"?
Is it to double the acceleration? So the object accelerates at 2g(r)?
Are there unstated assumptions different from what I have assumed above?
Something else?