Hi,
this should work:
dilation = N[1/((1 - (SetPrecision[0.999999999999999999999999^2, Infinity]))^(1/2)), 1000]
It was just a little numerical problem. The term
((1.000000000000000000000000 - (0.999999999999999999999999^2))^(1/ 2))
is numerically zero:
0.*10^-12
Cheers,
Marco