  Using precise relative astrometry from the Hubble Space Telescope and the W.
M. Keck Telescope, we have determined the orbits and masses of the two
dynamically interacting satellites of the dwarf planet (136108) Haumea,
formerly 2003 EL61. The orbital parameters of Hi'iaka, the outer, brighter
satellite, match well the previously derived orbit. On timescales longer than a
few weeks, no Keplerian orbit is sufficient to describe the motion of the
inner, fainter satellite Namaka. Using a fully-interacting three point-mass
model, we have recovered the orbital parameters of both orbits and the mass of
Haumea and Hi'iaka; Namaka's mass is marginally detected. The data are not
sufficient to uniquely determine the gravitational quadrupole of the
non-spherical primary (described by $J_2$). The nearly co-planar nature of the
satellites, as well as an inferred density similar to water ice, strengthen the
hypothesis that Haumea experienced a giant collision billions of years ago. The
excited eccentricities and mutual inclination point to an intriguing tidal
history of significant semi-major axis evolution through satellite mean-motion
resonances. The orbital solution indicates that Namaka and Haumea are currently
undergoing mutual events and that the mutual event season will last for the
next several years.
