For 67P, effects of torques could be easily observed using imaging data over the
duration of the near-comet activities of Rosetta to reconstruct the nucleus orientation. This was performed by the European Space Operations Centre in Darmstadt
and values provided in the form of reconstructed SPICE kernels (Acton 1996).
Figure 2.8, which was produced using these results, shows that the rotation period
of the comet changed by nearly 25 min during the perihelion passage initially rising
during the approach to the Sun but falling rapidly within the 150 day period about
perihelion itself. The first derivative is also plotted in Fig. 2.8 as a rate of change of
the angular velocity (dΩ N /dt) with time computed over a 50 h moving average. This
indicates that the maximum torque was around 30 days post perihelion which is
consistent with the lag with respect to perihelion of the maximum emission from the
nucleus of 67P of 33 Æ 8 days found from photometric analyses (Ferrin 2007) and
measurements of the hydrogen emission that will be discussed later (Fig. 3.48).
A spin-down (a decrease in the rotational angular velocity) of 41P/Tuttle–
Giacobini–Kresák has been observed by Schleicher et al. (2019) (see also Bodewits
et al. 2018) indicating that an increasing angular velocity due to torques is not
universal. On the other hand, 49P/Arend–Rigaux has been shown to have a very
small rotation period change of <14 s per apparition (Eisner et al. 2017) over a
measurement period of 28 years.
The spin-up observed for 67P and 9P/Tempel 1 can ultimately result in splitting
of the nucleus if the tensile strength of the comet is low. The critical periods for
spheroids have been derived analytically by Davidsson (2001). For the most probable case of an oblate spheroid, the critical period is given by
P crit ¼
π
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Gρ N A G
4
þ
T S
ρa 2
q
ð2:36Þ
where ρ N is the bulk density of the object, a is its semi-major axis, T S is its tensile
strength, and A G arises from the geometry of the object through
Fig. 2.8 The rotation
period of 67P over the
duration of the Rosetta nearcomet activities. Solid line:
The rotation period itself
(left axis). Broken line: The
first derivative in units of
[deg day
À2
]. The data have
been smoothed over using a
51 h boxcar smoother. The
maximum of the derivative
can be seen around 30 days
post-perihelion
46
2 The Nucleus
duration of the near-comet activities of Rosetta to reconstruct the nucleus orientation. This was performed by the European Space Operations Centre in Darmstadt
and values provided in the form of reconstructed SPICE kernels (Acton 1996).
Figure 2.8, which was produced using these results, shows that the rotation period
of the comet changed by nearly 25 min during the perihelion passage initially rising
during the approach to the Sun but falling rapidly within the 150 day period about
perihelion itself. The first derivative is also plotted in Fig. 2.8 as a rate of change of
the angular velocity (dΩ N /dt) with time computed over a 50 h moving average. This
indicates that the maximum torque was around 30 days post perihelion which is
consistent with the lag with respect to perihelion of the maximum emission from the
nucleus of 67P of 33 Æ 8 days found from photometric analyses (Ferrin 2007) and
measurements of the hydrogen emission that will be discussed later (Fig. 3.48).
A spin-down (a decrease in the rotational angular velocity) of 41P/Tuttle–
Giacobini–Kresák has been observed by Schleicher et al. (2019) (see also Bodewits
et al. 2018) indicating that an increasing angular velocity due to torques is not
universal. On the other hand, 49P/Arend–Rigaux has been shown to have a very
small rotation period change of <14 s per apparition (Eisner et al. 2017) over a
measurement period of 28 years.
The spin-up observed for 67P and 9P/Tempel 1 can ultimately result in splitting
of the nucleus if the tensile strength of the comet is low. The critical periods for
spheroids have been derived analytically by Davidsson (2001). For the most probable case of an oblate spheroid, the critical period is given by
P crit ¼
π
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Gρ N A G
4
þ
T S
ρa 2
q
ð2:36Þ
where ρ N is the bulk density of the object, a is its semi-major axis, T S is its tensile
strength, and A G arises from the geometry of the object through
Fig. 2.8 The rotation
period of 67P over the
duration of the Rosetta nearcomet activities. Solid line:
The rotation period itself
(left axis). Broken line: The
first derivative in units of
[deg day
À2
]. The data have
been smoothed over using a
51 h boxcar smoother. The
maximum of the derivative
can be seen around 30 days
post-perihelion
46
2 The Nucleus