by assuming a surface reflectance or by using observations of the thermal flux as
described above.
Size and axis determination of irregular small bodies has reached a high level of
sophistication using light curve analysis in combination with other techniques
(e.g. stellar occultation and radar delay-Doppler). An example of this was the
prediction made for the asteroid (21) Lutetia which was the target of a fly-by by
the Rosetta spacecraft 4 years before it reached 67P. The spin axis determined prior
to the fly-by was found to be accurate to within 2
, while the size determinations
were within 2% of the Rosetta-derived values (Carry et al. 2012).
There are several issues that make achievement of comparable accuracies for
cometary nuclei extremely challenging. Firstly, cometary nuclei are, typically, at
least a factor of 10 smaller in dimension than (21) Lutetia and hence signal levels are
appreciably lower. Second, the activity of comets as they approach the Sun can
influence the observed cross-sectional area. To study a “bare” nucleus with no dust
coma requires observation at )2.7 AU thereby further reducing signal levels. Third,
we shall see that nuclei are extremely dark and small absolute variations in the
surface reflectance can have large effects on the observed fluxes from the object.
Approaches to tackling these problems have been studied for more than two
decades. For example, modelling of the dust coma of the comet can be used to
remove the signal resulting from activity and thereby obtain the signal from the bare
nucleus alone. This has been performed using Hubble Space Telescope observations
of a number of comets (Lamy et al. 2004). An accurate knowledge of the point
spread function (PSF) of the instrument in combination with PSF correction techniques enhances the accuracy of the determination. Issues concerning surface reflectance can also be addressed by looking at the thermal light curve which will deviate
from following the reflected light curve if reflectance variations are present. This has
become possible for cometary nuclei using space-borne infrared observatories such
as Spitzer. A recent compilation of rotation periods for some of the numbered
comets, derived from multiple observational methods, has been provided by
Kokotanekova et al. (2017).
Further complexity arises from deviations of objects from regular (spherical to
tri-axial ellipsoidal) shapes. Observed light curves can deviate markedly from simple
sine curves. This is clearly evident in unresolved observations of 67P taken by the
OSIRIS instrument on Rosetta before the spacecraft made its rendezvous (Fig. 2.7).
Attempts to determine the shape of the nucleus prior to the start of the Rosetta
rendezvous manoeuvres using numerical models to fit the details of the light curves
were subsequently shown to be somewhat less successful than expected. The highly
irregular shape of the nucleus (with two parts linked by a “neck”) was not predicted.
As can be seen in Fig. 2.7, 67P was found to have a rotation period of 12.404 h
prior to rendezvous. It had been expected, however, that variations in both the
rotation period and the orientation of the rotation axis would occur as a result of
torques produced by activity and mass loss (Gutierrez et al. 2005). The sublimation
from the surface is anisotropic even in the simplest situation where gas emission is
solely related to the cosine of the incidence angle. The irregular geometries of nuclei
combined with possible deviations from isolation-driven activity can lead to
2.4 Rotational Properties
43
described above.
Size and axis determination of irregular small bodies has reached a high level of
sophistication using light curve analysis in combination with other techniques
(e.g. stellar occultation and radar delay-Doppler). An example of this was the
prediction made for the asteroid (21) Lutetia which was the target of a fly-by by
the Rosetta spacecraft 4 years before it reached 67P. The spin axis determined prior
to the fly-by was found to be accurate to within 2
, while the size determinations
were within 2% of the Rosetta-derived values (Carry et al. 2012).
There are several issues that make achievement of comparable accuracies for
cometary nuclei extremely challenging. Firstly, cometary nuclei are, typically, at
least a factor of 10 smaller in dimension than (21) Lutetia and hence signal levels are
appreciably lower. Second, the activity of comets as they approach the Sun can
influence the observed cross-sectional area. To study a “bare” nucleus with no dust
coma requires observation at )2.7 AU thereby further reducing signal levels. Third,
we shall see that nuclei are extremely dark and small absolute variations in the
surface reflectance can have large effects on the observed fluxes from the object.
Approaches to tackling these problems have been studied for more than two
decades. For example, modelling of the dust coma of the comet can be used to
remove the signal resulting from activity and thereby obtain the signal from the bare
nucleus alone. This has been performed using Hubble Space Telescope observations
of a number of comets (Lamy et al. 2004). An accurate knowledge of the point
spread function (PSF) of the instrument in combination with PSF correction techniques enhances the accuracy of the determination. Issues concerning surface reflectance can also be addressed by looking at the thermal light curve which will deviate
from following the reflected light curve if reflectance variations are present. This has
become possible for cometary nuclei using space-borne infrared observatories such
as Spitzer. A recent compilation of rotation periods for some of the numbered
comets, derived from multiple observational methods, has been provided by
Kokotanekova et al. (2017).
Further complexity arises from deviations of objects from regular (spherical to
tri-axial ellipsoidal) shapes. Observed light curves can deviate markedly from simple
sine curves. This is clearly evident in unresolved observations of 67P taken by the
OSIRIS instrument on Rosetta before the spacecraft made its rendezvous (Fig. 2.7).
Attempts to determine the shape of the nucleus prior to the start of the Rosetta
rendezvous manoeuvres using numerical models to fit the details of the light curves
were subsequently shown to be somewhat less successful than expected. The highly
irregular shape of the nucleus (with two parts linked by a “neck”) was not predicted.
As can be seen in Fig. 2.7, 67P was found to have a rotation period of 12.404 h
prior to rendezvous. It had been expected, however, that variations in both the
rotation period and the orientation of the rotation axis would occur as a result of
torques produced by activity and mass loss (Gutierrez et al. 2005). The sublimation
from the surface is anisotropic even in the simplest situation where gas emission is
solely related to the cosine of the incidence angle. The irregular geometries of nuclei
combined with possible deviations from isolation-driven activity can lead to
2.4 Rotational Properties
43