  Massive early-type galaxies are observed to lie on the Mass Plane (MP), a
two-dimensional manifold in the space of effective radius R_e, projected mass
M_p (measured via strong gravitational lensing) and projected velocity
dispersion sigma within R_e/2. The MP is less `tilted' than the Fundamental
Plane, and the two have comparable associated scatter. This means that
c_e2=2*G*M_p/(R_e*sigma^2) is a nearly universal constant in the range
sigma=175-400 km/s. This finding can be used to constrain the mass distribution
and internal dynamics of early-type galaxies. We find that a relatively wide
class of spherical galaxy models has values of c_e2 in the observed range,
because c_e2 is not very strongly sensitive to the mass distribution and
orbital anisotropy. If the total mass distribution is isothermal, a broad range
of stellar luminosity profile and anisotropy is consistent with the
observations, while NFW dark-matter halos require more fine tuning of the
stellar mass fraction, luminosity profile and anisotropy. If future data can
cover a broader range of masses, the MP could be seen to be tilted and the
value of any such tilt would provide a discriminant between models for the
total mass-density profile of the galaxies. [Abridged]
