2.2 Sizes and Shapes of Resolved Objects
It should be recalled that only 40 years ago, the existence of a single solid nucleus at
the heart of cometary activity could still be disputed (although Whipple’s concept of
a solid “dirty snowball” was by far the most accepted theory). Prior to the Halley
fly-bys, the size of the nucleus was estimated by assuming that the nucleus was
active over its entire surface. The thermodynamics of sublimation could then be used
to determine how large the emitting surface area needed to be to produce the
observed water production rate. This minimum surface area could then be used to
determine a lower limit for the radius of the nucleus.
There are numerous assumptions in this approach and hence the observations of
the nucleus of 1P/Halley were of major significance in challenging these assumptions. The picture taken by the Halley Multicolour Camera onboard Giotto (Fig. 1.1)
not merely proved the existence of a solid nucleus but also showed its size to be far
larger than the minimum size needed to produce the observed outgassing.
The sizes of nuclei are usually expressed as dimensions along three axes even
though it is now quite apparent that nucleus shapes are far from regular. Nonetheless
describing nuclei as tri-axial ellipsoids based on these axis dimensions can be useful
as first order approximations to their shapes.
A determination of the shape of 1P/Halley from the spacecraft fly-by data was not
straightforward. The fast fly-bys (~70 km s
À1 relative velocity in all cases) provided
only snapshots while the phase angle of the approaches to the nucleus were all such
that more than half the visible nucleus was unilluminated. The darkness of the
unilluminated limb against a background of illuminated dust did however provide
additional constraints. The dimensions finally derived were 15.3 km  7.8 km  7.4 km
(Keller et al. 1995). The uncertainties on each axis length are of the order of 0.5 km.
At the time, thermal IR observations of small bodies were in their infancy and the
surface reflectance had to be derived by combining the reflected flux at high
heliocentric distance and the estimated cross-sectional area found by the resolved
spacecraft observations. This led to a geometric albedo estimate of 0.04—a remarkably low value which was subsequently confirmed by photometric analyses of the
Vega and Giotto data (Sagdeev et al. 1986a, b).
The subsequent observations of nuclei have shown that low geometric albedos
are usual. Data from spacecraft fly-bys tend to have large errors because the flyby
geometry dictates the minimum phase angle of the observation and obtaining the
geometric albedo requires extrapolation to zero phase. However, observations of the
nucleus of 19P/Borrelly (observed by NASA’s Deep Space 1) and that of 9P/Tempel
1 (observed by Deep Impact) are both consistent with geometric albedos of <0.07
and, taking into account coma contributions in the analysis of the 9P/Tempel 1 data,
probably <0.05 (Table 2.1). Values obtained by combining thermal emission and
photometric observations are fully consistent with this picture.
The irregular shape of 1P/Halley drew considerable attention at the time. The
primary reason was that it challenged the idea that comets are uniformly shrinking
“dirty snowballs” in the way that Whipple expressed them in his rightly celebrated
34
2 The Nucleus
It should be recalled that only 40 years ago, the existence of a single solid nucleus at
the heart of cometary activity could still be disputed (although Whipple’s concept of
a solid “dirty snowball” was by far the most accepted theory). Prior to the Halley
fly-bys, the size of the nucleus was estimated by assuming that the nucleus was
active over its entire surface. The thermodynamics of sublimation could then be used
to determine how large the emitting surface area needed to be to produce the
observed water production rate. This minimum surface area could then be used to
determine a lower limit for the radius of the nucleus.
There are numerous assumptions in this approach and hence the observations of
the nucleus of 1P/Halley were of major significance in challenging these assumptions. The picture taken by the Halley Multicolour Camera onboard Giotto (Fig. 1.1)
not merely proved the existence of a solid nucleus but also showed its size to be far
larger than the minimum size needed to produce the observed outgassing.
The sizes of nuclei are usually expressed as dimensions along three axes even
though it is now quite apparent that nucleus shapes are far from regular. Nonetheless
describing nuclei as tri-axial ellipsoids based on these axis dimensions can be useful
as first order approximations to their shapes.
A determination of the shape of 1P/Halley from the spacecraft fly-by data was not
straightforward. The fast fly-bys (~70 km s
À1 relative velocity in all cases) provided
only snapshots while the phase angle of the approaches to the nucleus were all such
that more than half the visible nucleus was unilluminated. The darkness of the
unilluminated limb against a background of illuminated dust did however provide
additional constraints. The dimensions finally derived were 15.3 km  7.8 km  7.4 km
(Keller et al. 1995). The uncertainties on each axis length are of the order of 0.5 km.
At the time, thermal IR observations of small bodies were in their infancy and the
surface reflectance had to be derived by combining the reflected flux at high
heliocentric distance and the estimated cross-sectional area found by the resolved
spacecraft observations. This led to a geometric albedo estimate of 0.04—a remarkably low value which was subsequently confirmed by photometric analyses of the
Vega and Giotto data (Sagdeev et al. 1986a, b).
The subsequent observations of nuclei have shown that low geometric albedos
are usual. Data from spacecraft fly-bys tend to have large errors because the flyby
geometry dictates the minimum phase angle of the observation and obtaining the
geometric albedo requires extrapolation to zero phase. However, observations of the
nucleus of 19P/Borrelly (observed by NASA’s Deep Space 1) and that of 9P/Tempel
1 (observed by Deep Impact) are both consistent with geometric albedos of <0.07
and, taking into account coma contributions in the analysis of the 9P/Tempel 1 data,
probably <0.05 (Table 2.1). Values obtained by combining thermal emission and
photometric observations are fully consistent with this picture.
The irregular shape of 1P/Halley drew considerable attention at the time. The
primary reason was that it challenged the idea that comets are uniformly shrinking
“dirty snowballs” in the way that Whipple expressed them in his rightly celebrated
34
2 The Nucleus