85% completion means 15% incomplete.
take the natural log of .15 (the decimal form of 15%). This is -1.897. toss out the negative as this is what you get when working with logs of numbers less than 1. what you are left with is 1.897. This is the number of time constants needed to reach...
the actual motion would equal a harmonic motion at four points in a single cycle: start, mid planet, the antipodal point where the direction would reverse, and mid planet again. but the curve would be a little different in between the points.
I'll have to get more data points, and set up the series on a spreadsheet to get the actual time to accelerate based on the actual acceleration values as you approach the core. This seems like it would be significantly less than 21 minutes (to get to the center) you calculated, so it would be...
Due to increased in the density of the mantle, and the cores, gravity increases slightly as you descend to a depth of about 2000km, from 9.81 m/s2 at the surface to about 10 m/s2 at 2000km deep. it then increases faster to a maximum of about 10.7 m/s2 at 3000km depth, then tapers roughly...