| Introduction: Landslides were observed on a few comet’s nuclei, e.g. [1], [2]. The
mechanism of their origin is not obvious because of very low gravity. According to [2]
fluidization and multiphase transport of cometary material could be an explanation. We
consider another option, namely, earthquakes resulted from meteoroids impacts as a trigging
mechanism.
Material of comets: Comets nuclei are believed to built of soft materials like snow and
dust. The recent landing of Philae on the comet 67P/Czuriumow-Gierasimienko indicates a
different situation. According to [1]: “thermal probe did not fully penetrate the
near-surface layers, suggesting a local resistance of the ground to penetration of >4
megapascals, equivalent to >2 megapascal uniaxial compressive strength”. Here we
assume that elastic properties of comet’s nuclei could be similar to elastic properties
of dry snow, namely Young modulus is assumed to be 106 – 108Pa, see [3] and
[4].
The model and results: We consider cometary nucleus in the shape of two spheres (with
radius 1400 m each) connected by a cylinder (with radius of 200 m and length of 200 m).
Density is 470 kg m−3. This shape corresponds approximately to shapes of some
comets (e.g. 67P/Churyumov- Gerasimenko [1], 103P/Hartley 2 [5]) A few vibration
modes of such body are possible. In present research we consider 3 modes: bending,
lengthening-shortening along axis of symmetry, and torsion. We calculated periods of basic
oscillation in each of these modes for different values of Young modulus - Table
1.
Table 1 Basic results of calculations
Young modulus [MPa]Periods [s] of vibrationMaximum
acceleration
[m s−2]
4 110 - 950 0.0001- 0.0004
40 38 – 290 0.0004- 0.0014
400 12 – 92 0.0012- 0.0045
Rotation and nutation: the impact results in changing of rotation of the comet. In
general, the vector of angular velocity will be a subject to nutation that results in
changing of centrifugal force, and consequently could be an additional factor triggering
landslides.
Discussion: Let assume that the comet are hit by small meteoroid of the mass of 1 kg and
velocity 20 km s−1. The mode of excited vibrations and their amplitudes depends on many
factors. Of course, the energy of vibration cannot exceed energy released during impact.
Generally a few modes of vibration are excited but for some special place of impact and the
special velocity vector of the impactor one mode could take most of the energy and this mode
will prevail. In calculations for Table 1 we assume that only one mode is generated. The
maximum values of acceleration of the surface resulting from the impact are given in Table
1.
The acceleration of the cometary surface could be vertical, horizontal or inclined with
respect to local gravity or local normal to the surface. Note that acceleration is often higher
than acceleration of the gravity of the comet. Consequently, the vibrations could throw
loose material into space that could lead to massive instability of loose material,
i.e. to landslides. It could be alternative mechanism to that presented in [2] (i.e.
fluidization).
Acknowledgement: The research is partly supported by Polish National Science Centre
NCN) (decision 2014/15/B/ST 10/02117)
References
[1] T. Spohn, et al. (2015) Thermal and mechanical properties of the near-surface layers
of comet 67P/Churyumov- Gerasimenko. Science 31 July 2015: Vol. 349 no. 6247
DOI: 10.1126/science.aab0464
[2] Belton M. J.S., Melosh J. (2009). Fluidization and multiphase transport of particulate
cometary material as an explanation of the smooth terrains and repetitive outbursts on
9P/Tempel 1. Icarus 200 (2009) 280–291
[3] Reuter B. (2013) On how to measure snow mechanical properties relevant to slab
avalanche release. International Snow Science Workshop Grenoble – Chamonix Mont-Blanc
- 2013 007
[4] Ball A.J. (1997) Ph. D. Thesis: Measuring Physical Properties at the Surface of a
Comet Nucleus, Univ.of Kent U.K.
[5] Thomas P.C. et al.(2013) Shape, density, and geology of the nucleus of Comet
103P/Hartley 2. Icarus 222 (2013) 550–558 |