  High resolution long-slit spectra obtained with the Phoenix spectrograph on
Gemini South provide our most accurate probe of the three dimensional structure
of the Homunculus around eta Car. The new near-infrared spectra dramatically
confirm the double-shell structure inferred previously from thermal dust
emission, resolving the nebula into a very thin outer shell seen in H2 21218,
and a warmer, thicker inner layer seen in [Fe II] 16435. The thin H2 skin hints
that the most important mass loss during the 19th century eruption had a very
short duration of less than 5 yr. H2 emission traces the majority of the mass
in the nebula, and has an average density of order 10^6.5 cm-3. This emission,
in turn, yields our first definitive picture of the exact shape of the nebula,
plus a distance of 2350pm50 pc and an inclination angle of 41deg (the polar
axis is tilted 49deg from the plane of the sky). The distribution of the H2
emission provides the first measure of the latitude dependence of the speed,
mass loss, and kinetic energy associated with eta Car's 19th century explosion.
Almost 75 percent of the total mass and more than 90 percent of the kinetic
energy in the ejecta were released at high latitudes. This rules out a model
for the bipolar shape wherein an otherwise spherical explosion was pinched at
the waist by a circumstellar torus. Also, the ejecta could not have been
deflected toward polar trajectories by a companion star, since the kinetic
energy of the polar ejecta is greater than the binding energy of the putative
binary system. Instead, most of the mass appears to have been directed poleward
by the explosion itself. [abridged]
