  We discuss the neutrino oscillation physics of a very long neutrino factory
baseline over a broad range of lengths (between 6000 km and 9000 km), centered
on the ``magic baseline'' ($\sim$ 7500 km) where correlations with the leptonic
CP phase are suppressed by matter effects. Since the magic baseline depends
only on the density, we study the impact of matter density profile effects and
density uncertainties over this range, and the impact of detector locations off
the optimal baseline. We find that the optimal constant density describing the
physics over this entire baseline range is about 5% higher than the average
matter density. This implies that the magic baseline is significantly shorter
than previously inferred. However, while a single detector optimization
requires fine-tuning of the (very long) baseline length, its combination with a
near detector at a shorter baseline is much less sensitive to the far detector
location and to uncertainties in the matter density. In addition, we point out
different applications of this baseline which go beyond its excellent
correlation and degeneracy resolution potential. We demonstrate that such a
long baseline assists in the improvement of the $\theta_{13}$ precision and in
the resolution of the octant degeneracy. Moreover, we show that the neutrino
data from such a baseline could be used to extract the matter density along the
profile up to 0.24% at $1 \sigma$ for large $\sin^2 2 \theta_{13}$, providing a
useful discriminator between different geophysical models.
