An FFI - hmmm. Fatal Familial Insomnia? 
Iām surmising that GMT is unable to offer values of mnay of its internal variables. No worries.
Using the above equation, from gmt_map.c, I get 6367477.33489 meters, for WGS-84. Presuming that current.proj.ECC is equivalent to the square of the first eccentricity (= 2f - f^2, where f = 1/298.257223563).
I am unable to locate that particular equation in the literature (yet).