Subject: How can the earth-moon distance be calculated for historical values?

I am dealing with the below text:
 
"since tidal forces are inversely proportional to the cube of the distance, 
the recession rate (dR/dt) is inversely proportional to the sixth power of the 
distance. So dR/dt = k/R^6, where k is a constant = (present speed: 0.04 
m/year) x (present distance: 384,400,000 m)^6 = 1.29x10^50 m^7/year. 
Integrating this differential equation gives the time to move from Ri to Rf as 
t = 1/7k(Rf^7 - Ri^7). For Rf = the present distance and Ri = 0, i.e. the 
earth and moon touching, t = 1.37 x 10^9 years."
 
I say k would not remain contant (for all values of t) for the following two 
reasons.

1)  Tidal coupling requires deformation of the orbital bodies.  (Clearly, 
perfectly rigid bodies would not transfer energy between them by strictly 
tidal means).  Many deformable bodies do not deform in a linear manner in 
relation to the force applied.
2)  Even if the deformation is strictly linear, the difference between earth's 
rotational period verses the orbital period will change, and that will 
influence how quickly energy is transferred between bodies.  That must be 
accounted for with a changing k.  (For an extreme example, if the moon was 
moved to geosych orbital distance, tides would be stationary, and no energy 
transfer would occur).

Re: How can the earth-moon distance be calculated for historical values?