Title: The tumbling rotational state of 1I/`Oumuamua,
Abstract: The discovery of 1I/2017 U1 ('Oumuamua) has provided the first glimpse of a
planetesimal born in another planetary system. This interloper exhibits a
variable colour within a range that is broadly consistent with local small
bodies such as the P/D type asteroids, Jupiter Trojans, and dynamically excited
Kuiper Belt Objects. 1I/'Oumuamua appears unusually elongated in shape, with an
axial ratio exceeding 5:1. Rotation period estimates are inconsistent and
varied, with reported values between 6.9 and 8.3 hours. Here we analyse all
available optical photometry reported to date. No single rotation period can
explain the exhibited brightness variations. Rather, 1I/'Oumuamua appears to be
in an excited rotational state undergoing Non-Principal Axis (NPA) rotation, or
tumbling. A satisfactory solution has apparent lightcurve frequencies of 0.135
and 0.126 hr-1 and implies a longest-to-shortest axis ratio of 5:1, though the
available data are insufficient to uniquely constrain the true frequencies and
shape. Assuming a body that responds to NPA rotation in a similar manner to
Solar System asteroids and comets, the timescale to damp 1I/'Oumuamua's
tumbling is at least a billion years. 1I/'Oumuamua was likely set tumbling
within its parent planetary system, and will remain tumbling well after it has
left ours.