  Asteroid binaries found amongst the Near-Earth objects are believed to have
formed from rotational fission. In this paper, we aim to study the dynamical
evolution of asteroid systems the moment after fission. The initial condition
is modelled as a contact binary, similar to that of Boldrin et al. (2016). Both
bodies are modelled as ellipsoids, and the secondary is given an initial
rotation angle about its body-fixed $y$-axis. Moreover, we consider six
different cases, three where the density of the secondary varies, and three
where we vary its shape. The simulations consider 45 different initial tilt
angles of the secondary, each with 37 different mass ratios. We start the
dynamical simulations at the moment the contact binary reaches a spin fission
limit, and our model ensures that the closest distance between the surfaces of
the two bodies is always kept at 1 cm. The forces, torques and gravitational
potential between the two bodies are modelled using a newly developed surface
integration scheme, giving exact results for two ellipsoids. We find that more
than 80% of the simulations end with the two bodies impacting, and collisions
between the bodies are more common when the density of the secondary is lower,
or when it becomes more elongated. When comparing with data on asteroid pairs
from Pravec et al. (2019) we find that variations in density and shape of the
secondary can account for some of the spread seen in the rotation period for
observed pairs. Furthermore, the secondary may also reach a spin limit for
surface disruption, creating a ternary/multiple system. We find that secondary
fission typically occurs within the first five hours after the contact binary
separates, and is more common when the secondary is less dense or more
elongated.
