  The central surface brightness ($\mu_V(0)$) of the dwarf spheroidal
satellites of our own Galaxy is found to correlate with their distance from the
Galactic Center ($R_{GC}$). This observational evidence suggests that
environmental effects could strongly influence their structure. This suggestion
is further supported by a clear-cut bivariate correlation linking $\mu_V(0)$ to
a linear combination of $M_V$, the absolute integrated magnitude, and $R_{GC}$,
which seems to be shared also by the M31 spheroidals. Possible implications for
the Fundamental Plane of elliptical galaxies and Dark Matter content of dwarf
spheroidals are also briefly discussed.

Astrophysics