Density and porosity of 67P/C-G constrained
by its shape and rotation
L. Jorda1, S. F. Hviid2, R. Gaskell3, P. Gutiérrez4,
C. Capanna1, P. Lamy1,
OSIRIS Team
1Laboratoire d’Astrophysique de Marseille, France
2Deutsches Zentrum für Luft- und Raumfahrt (DLR), Berlin, Germany
3Planetary Science Institute, Tucson, USA
4Instituto de Astrofísica de Andalucía-CSIC, Granada, Spain
Density of cometary nucleiA challenging measurement from the ground !
● Mass measurements of asteroids & TNOs [ Carry 2012 ]
► Gravitational influence of individual asteroids on other objects
► Orbit of binary/triple asteroids using Kepler's third law
► Deflection/orbit of a S/C from radio ranging measurements
Density of cometary nucleiA challenging measurement from the ground !
● Mass measurements of asteroids & TNOs [ Carry 2012 ]
► Gravitational influence of individual asteroids on other objects
► Orbit of binary/triple asteroids using Kepler's third law
► Deflection/orbit of a S/C from radio ranging measurements
● Mass measurements of comets
► Effect of the recoil force on the nucleus orbit [ Marsden et al. 1973 ]
► Pioneering research by Hans Rickman during the 80's and 90's !
► Ballistic trajectory of Deep Impact plume [ Richardson et al. 2007 ]
► Smooth area as iso-gravity surfaces [ A'Hearn et al. 2011 ]
Density of cometary nucleiA challenging measurement from the ground !
● Volume measurements of small bodies
► Difficult due to irregular shapes [ Simonelli et al., 1993 ]
► From absolute magnitudes and geometric albedos
► 'Shape-from-lightcurves' method [ Kaasalainen et al., 2001 ]
► Direct imaging of small bodies
- During flybys [ Oberst et al. 2004 ] [ Jorda et al., 2012 ] …
- During in-orbit observations [ Thomas et al., 2002 ] …
Density of cometary nuclei
Comet Method Density / kg.m-3 Ref.
1P/Halley NGF 500-1200 Skorov & Rickman (1999)
9P/Tempel 1 BALLIST. 200-1000 Richardson et al. (2007)
NGF 200-700 Davidsson et al. (2007)
19P/Borrelly NGF 290-830 Farnham & Cochran (2002)
67P/C-G NGF 100-370 (<600)* Davidsson & Gutiérrez (2005)
RADAR 600-1000 (surface) Kamoun et al. (2014)
103P/Hartley 2 GRAVITY 140-520 Richardson & Bowling (2014)
D/SL9 SPH 500-900 Asphaug & Benz (1996)
Selection of pre-Rosetta measurements
See also: [ Weissman et al. 2004 ] *Correct mass estimate.
Shape reconstruction
The SPC method [ Gaskell et al., 2008 ]
'StereoPhotoClinometry'
Maplet99x99 surface elements
Shape reconstruction
Maplet images
The SPC method [ Gaskell et al., 2008 ]
Shape reconstruction
X
Y
Z ΩRA = 69.6 ± 0.4°Dec = 64.0 ± 0.1°Obliquity = 52.3°
Rotational parameters
Shape reconstruction
X
Y
Z ΩRA = 69.6 ± 0.4°Dec = 64.0 ± 0.1°Obliquity = 52.3°
Rotational parameters
Spin period
Previous passage* : 12.76137 ± 0.00006 hr
Pre-perihelion** : 12.4041 ± 0.0001 hr
Post-perihelion : 12.060 hr
Decrease of 21 ± 1 min / perihelion
*[ Lowry et al., 2012 ]
**[ Mottola et al., 2014 ]
Shape reconstruction
SPC Model [ Jorda et al., 2016 ]
V = 18.8 ± 0.3 km3
Shape reconstruction
SPC Model [ Jorda et al., 2016 ]
SPG Model [ Preusker et al., 2015 ]
V = 18.8 ± 0.3 km3
V = 18.7 ± 0.4 km3
(northern hemisphere)
Bulk density
SPC shape volume
GM = 666.2 ± 0.2 m3 / s2
M = (9.982 ± 0.003) 1012 kg
Radio science Instrument [ Pätzold et al., 2016 ]
ρ = 532 ± 7 kg / m3
[ Jorda et al. 2016 ]
Bulk density
GM = 666.2 ± 0.2 m3 / s2
M = (9.982 ± 0.003) 1012 kg
Radio science Instrument [ Pätzold et al., 2016 ]
ρ = 533 ± 6 kg / m3
[ Pätzold et al., 2016 ]
SPC & SPG shape volumes
Bulk density
● Among the lowest density objects in the solar system
► Two large TNOs with significantly smaller density [ Carry 2012 ]
► 42355 Typhon
- Scattered disk / Centaur (perihelion inside Neptune's orbit)
- Binary system
- Dimension = 150 km / Albedo = 0.04
- Density = 300 ± 30 kg/m3
► Plutino 1999 TC36
- Triple system
- Dimension = 270x250x130 km / Albedo = 0.08
- Density = 410 ± 30 kg/m3
Bulk porosity
ρice 1000 kg/m3
ρdust
min 2000 kg/m3
Following Kamoun et al. (2014)
max 3500 kg/m3
D/I ratiomin 2
Rotundi et al. (2015)max 6
Bulk porosity
ρice 1000 kg/m3
ρdust
min 2000 kg/m3
Following Kamoun et al. (2014)
max 3500 kg/m3
D/I ratiomin 2
Rotundi et al. (2015)max 6
Porosity = 70-75 % (60-80 %)
= 72-74 % [ Pätzold et al., 2016 ]
Bulk porosityMicro- VS Macro-porosity
● Macro-porosity (m-scale or larger) ?
► Typically 20-40 % for shattered objects [ Richardson et al., 2002 ]
► Pits formed by collapse of large cavities ? [ Vincent et al., 2015 ]
Porosity = 70-75 % (60-80 %)
= 72-74 % [ Pätzold et al., 2016 ]
Bulk porosityMicro- VS Macro-porosity
● Macro-porosity (m-scale or larger) ?
► Typically 20-40 % for shattered objects [ Richardson et al., 2002 ]
► Pits formed by collapse of large cavities ? [ Vincent et al., 2015 ]
● Micro-porosity ?
► High micro-porosity of cometary dust [ Joswiak et al., 2007 ]
[ Niimi et al., 2012 ]
► Fluffy particles at mm-scale [ Langevin et al., 2016 ]
Porosity = 70-75 % (60-80 %)
= 72-74 % [ Pätzold et al., 2016 ]
Density distribution
Any observational evidence for
an inhomogeneous density distribution ?
Density distribution
Any observational evidence for
an inhomogeneous density distribution ?
● Bilobate structure of the nucleus [ Sierks et al., 2014 ]
► Different bulk density for the two lobes ?
► Over-density in the neck ?
● Evidence of layering [ Massironi et al., 2015 ]
► Gradient of density within the two lobes ?
► Layers with different densities ?
Center of Mass
Center of Mass
► Origin of the Cheops BFF
► Stereo NAV solution
► Accuracy ~ 3 m [ Budnik 2015 ]
Center of Figure
► Center of mass for uniform density
► Calculated from the shape model
► Accuracy ~ 3 m [ Jorda et al., 2016 ]
Center of Mass
Offset CoM – CoF
Δx = 18 ± 7 m
Δy = –32 ± 5 m
Δz = 16 ± 11 m
Center of Mass
► Origin of the Cheops BFF
► Stereo NAV solution
► Accuracy ~ 3 m [ Budnik 2015 ]
Center of Figure
► Center of mass for uniform density
► Calculated from the shape model
► Accuracy ~ 3 m [ Jorda et al., 2016 ]
Center of Mass
Center of Mass
► Origin of the Cheops BFF
► Stereo NAV solution
► Accuracy ~ 3 m [ Budnik 2015 ]
Center of Figure
► Center of mass for uniform density
► Calculated from the shape model
► Accuracy ~ 3 m [ Jorda et al., 2016 ]
Offset CoM – CoF
Δx = 18 ± 7 m
Δy = –32 ± 5 m
Δz = 16 ± 11 m
Slightly inhomogeneous density distribution ?
May favor a higher density for the big lobe …
PrecessionDirection of the spin axis Periodogram analysis (PDM)
Period = 276 ± 12 hr
Period = 257 ± 12 hr[ Preusker et al., 2015 ]
● Two independent data sets & methods
● Long period detected : P = 240-290 hr (10-12 days)
● Beat of the rotation and precession periods
Uncertainty ~ 0.03°
Precession
Analysis of the ‘precession’ [ Gutiérrez et al., 2016 ]
The detected period constrains
the ratios of the moments of inertia.
I z /
I x
Iy / I
x
Ratios compatib
le with perio
d
Precession
Analysis of the ‘precession’ [ Gutiérrez et al., 2016 ]
Uniform density
The detected period constrains
the ratios of the moments of inertia.
The shape model allows to compute
the ratios under the assumption of
uniform density.
I z /
I x
Iy / I
x
Ratios compatib
le with perio
d
Precession
Analysis of the ‘precession’ [ Gutiérrez et al., 2016 ]
Iy / I
x
I z /
I x
Uniform density
Not compatible with a uniform density !
The detected period constrains
the ratios of the moments of inertia.
The shape model allows to compute
the ratios under the assumption of
uniform density.Ratios compatib
le with perio
d
Smooth Areas
Map of gravitational slopes Smooth areas:
► Imhotep, Hapi, etc.
► Iso-gravity surface ?
Gravitational slopes:
► Very low
► Compatible with uniform
density
Smooth AreasTopography map of Imhotep
Smooth areas:
► Imhotep, Hapi, etc.
► Similar to 103P's waist
► Iso-gravity surface ?
[ A'Hearn et al., 2011 ]
Waist in 103P/Hartley 2
Smooth AreasEquipotential surface in Hapi
Hapi is a gravitational low filled with dustthat seems to follow an equipotential surface
Calculations performed by S. Hviid (DLR)
Results:
► Still very preliminary !
► Compatible w/uniform density
Uniform density
Mean gravitational slope
Big
lo
be
de
ns
ity
Small lobe density
Smooth AreasEquipotential surface in Hapi
Hapi is a gravitational low filled with dustthat seems to follow an equipotential surface
Calculations performed by S. Hviid (DLR)
Uniform density
Standard deviation of the gravitational slopes
Small lobe density
Big
lo
be
de
ns
ity
Results:
► Still very preliminary !
► Compatible w/uniform density
► May favor higher BL density ?
Reconstruction of the lobes
Reconstruction of the lobes
Reconstruction of the lobes
2.10 km
1.76 km
0.82
km
1.25 km
1.07
km
0.82 km
Reconstruction of the lobes
2.10 km
1.76 km
0.82
km
1.25 km
1.07
km
0.82 km
V = 5.1 ± 0.3 km³(27 %)
V = 12.4 ± 0.6 km³(66 %)
Reconstruction of the lobes
[ Jutzi & Asphaug, 2015 ]
Slow velocity collision during accretion
SPH simulations
Reconstruction of the lobes
[ Jutzi & Asphaug, 2015 ]
Slow velocity collision during accretion
Abydos landing site
NAC_2014-10-22T00.50.03 NAC_2014-12-12T17.32.12 NAC_2014-12-13T05.27.52
Philae ? Philae ?
Identification by Lamy et al.
Abydos landing site3D reconstruction with MPCD
[ Capanna et al., 2015 ]
Abydos landing site3D reconstruction with MPCD
[ Capanna et al., 2015 ]
Abydos landing site3D reconstruction with MPCD
[ Capanna et al., 2015 ]
Conclusion● Bulk properties of CG
► Complex shape not retrieved by lightcurves analysis
► Underdense & highly porous object
► NGF mass in agreement with Rosetta measurement
● Density & porosity
► Compatible with the very low strengths [ Groussin et al., 2015 ]
► Porosity in agreement with CONSERT [ Kofman et al., 2015 ]
► Implications for the collisional history ? [ Morbidelli & Rickman, 2015 ]
► Work needed to understand the effect of collisions on density …
Conclusion● Evidences for an inhomogeneous density of comet CG ?
► None in gravity data [ Pätzold et al., 2016 ]
► Weak from smooth areas as iso-gravity surfaces
► Small but significant CoM-CoF offset [ Jorda et al., 2016 ]
► Ratios of the moments of inertia [ Gutiérrez et al., 2016 ]
► Weak evidence of higher surface density [ Kamoun et al., 2014 ]
► Radial change of the dielectric constant [ Ciarletti et al., 2015 ]
● The density distribution of CG must fulfill all these constraints
► Uniform lobe density does not seem to fulfill them
► Smooth areas as iso-gravity surfaces [ A'Hearn et al., 2011 ]
► Future tests on a layered density model …
