  We investigate the relationships among the angular orbital elements --- the
longitude of the ascending node, Omega, the inclination, i, and the argument of
perihelion, omega --- of the Kreutz system's faint, dwarf sungrazers observed
only with the SOHO/STEREO coronagraphs; their published orbits were derived
using a parabolic, purely gravitational approximation. In a plot of i against
Omega the bright Kreutz sungrazers (such as C/1843 D1, C/1882 R1, C/1963 R1,
etc.) fit a curve of fixed apsidal orientation, whereas the dwarf members are
distributed along a curve that makes with the apsidal curve an angle of 15 deg.
The dwarf sungrazers' perihelion longitude is statistically invariable, but
their perihelion latitude increases systematically with Omega. We find that
this trend can be explained by a strong erosion-driven nongravitational
acceleration normal to the orbit plane, confirmed for several test dwarf Kreutz
sungrazers by orbital solutions with nongravitational terms incorporated
directly in the equations of motion on a condition of fixed apsidal
orientation. Proceeding in three steps, we first apply Marsden et al.'s
standard formalism, solving for the normal acceleration only, and eventually
relax additional constraints on the nongravitational law and the acceleration's
radial and transverse components. The resulting nongravitational accelerations
on the dwarf sungrazers exceed the maximum for catalogued comets in
nearly-parabolic orbits by up to three orders of magnitude, topping in
exceptional cases the Sun's gravitational acceleration! A mass-loss model
suggests that the dwarf sungrazers' nuclei fragment copiously and their
dimensions diminish rapidly near the Sun, implying the objects' imminent demise
shortly before they reach perihelion.
