Concept of strain as applied to time What if we were to measure gravitational force as a function of strain in time $S_t$ as defined by $S_t=\frac{T_\mathrm{ref}-T_\mathrm{local}}{T_\mathrm{ref}}$ where $T_\mathrm{ref}$ is the rate of time at a massless reference clock at infinite distance from mass and $T_\mathrm{local}$ would be the rate of time in the local gravitational field. This would be the equivalent of strain measurement of a solid specimen under tension where we are looking at % elongation.  
Has anyone done any work in this direction, that is looking at changing the units of measure of distance from meters from a singularity to a unit of the warp of spacetime for the purpose of orbital mechanics calculations?
 A: The quantity you describe:
$$ S_t = \frac{T_{ref}-T_{local}}{T_{ref}} $$
is effectively just the time dilation. This is related to the spacetime geometry but does not fully describe it so time dilation alone cannot be used to calculate what happens in a gravitational field.
To see this let's take the specific example of the spacetime round a static black hole. This is described by the metric:
$$ d\tau^2 = \left(1-\frac{r_s}{r}\right)dt^2 - \frac{dr^2}{\left(1-\frac{r_s}{r}\right)} - r^2d\theta^2 - r^2\sin^2\theta d\phi^2 \tag{1} $$
This equation is simpler than it looks at first sight. Suppose we are watching an observer moving in gravitational field and we see that observer move by a distance $dr$, $d\theta$ and $d\phi$ in a time $dt$, then the equation calculates the time that passes for that observer $d\tau$. If the observer isn't moving, so $dr = d\theta = d\phi = 0$ then the equation simplifies to:
$$ d\tau^2 = \left(1-\frac{r_s}{r}\right)dt^2 $$
and that gives us the time dilation i.e. the ratio of the observer's time to the time we measure:
$$ \frac{d\tau}{dt} = \sqrt{1-\frac{r_s}{r}} $$
And this is almost the quantity you describe (your quantity is $1-d\tau/dt$).
The problem is that we get length changes as well as time changes. Suppose our observer measures a small distance $dR$ then we can use equation (1) to find out what we see this distance as. I won't go through the maths but it comes out as:
$$ \frac{dR}{dr} = \frac{1}{\sqrt{1-\frac{r_s}{r}}} $$
That is the distance our observer measures, $dR$, is greater than the distance we measure, $dr$.
And this is why it isn't enough to just consider the time dilation. We need to also consider the changes in the distance otherwise we'll get the wrong result.
A: It's an interesting questions, Schwarzschild radii (SR) could be used as unit you are looking for since space and time warp relative to that and not distance as you are suggesting. 
One SR away from a black hole will have the same time dilating effects and gravitational potential no matter what the size of the black hole. However SR change depending on the size of the BH/mass you calculating against.       
