The Strength of Cometary Surface Material: Relevance of Deep Impact Results for Future Comet Mission

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The Strength of Cometary Surface Material
Relevance of Deep Impact Results for Future Comet
Missions

• J. Biele1, S. Ulamec1, L. Richter1, E. Kührt2,
  J. Knollenberg2, D. Möhlmann2
• 1 DLR, Institute for Space Simulation /
  Cologne, Germany
• 2 DLR Institute for Planetary Research, Berlin,
  Germany

Background Image Comet P/Churyumov-Gerasimenko
22.3.2003 by Herman Mikuz / Crni Vrh Observatory
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Abstract

• In the view of the ongoing Rosetta Mission, which
  was launched in March 2004 and will arrive at the
  target comet, 67P/Churyumov-Gerasimenko in 2014,
  where a Lander is going to be delivered, the
  results of the Deep Impact Mission (in particular
  regarding comet surface properties) have been
  acknowledged with highest interest.
• Analysis of the velocity of dust ejecta after the
  impact indicates very soft surface material of
  comet Tempel 1 with strength of only 65 Pa
  (AHearn, M.F. et al., Deep Impact Excavating
  Comet Tempel 1, Science 310, 258-264, 14 Oct.
  2005).
• We will critically discuss this result and
  estimate the real compressive strength of
  cometary surface materials. Modelling the
  touchdown of PHILAE (the ROSETTA Lander) results
  in a maximum depth of the order of 20 cm.
  Experimental studies are being prepared to
  investigate low velocity penetration of blunt
  bodies into dust-rich, fluffy comet analogue
  materials.

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Motivation

• Initial interpretations of DI mission results
  have inferred an extremely low (lt65 Pa) (shear)
  strength of comet Tempel 1 surface material
• Questions were raised (bad news?) whether a
  comet lander (e.g. Rosettas Philae) could
  land/dock and stay on such weak material

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Which strength?

• Values discussed in context with Deep Impact
  refer to shear strength ? cohesion tensile
  strength
• During impacts, due to very high strain rates,
  the dynamic strength is usually higher than the
  (quasi-)static strength
• In the case of soft landing (v ? 1 m/s, typical
  area 500 cm2, actually more a docking maneuvre)
  compressive strength is the relevant parameter
  It is typically at least one order of magnitude
  higher than tensile strength!

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Data about strength, I

• Comets
• Break-up of SL-9 before its impact into Jupiter
  an upper limit of the tensile strength on km
  scales was derived to 100 Pa (essentially
  strengthless). Tidal disruption of comets
  indicate low global tensile strengths in the
  order of 100 - 1000 Pa. N.B. strength derived
  from comet splittings is NOT the relevant
  strength for Deep Impact because strength is a
  scale-dependent phenomenon (see below) (at least
  if the target is not homogeneous on all scales
  and contains flaws of different sizes) and,
  therefore, we need estimates of the strength of
  porous ices or ice/dust mixtures on meter scales.
  
• Images by Stardust from comet Wild-2 cometary
  surface must have a finite strength to support
  the observed topographic features because of the
  small gravity, some 10 Pa might suffice (Belton
  2004).
• Comets probably have surface crusts (of the order
  of 1 dm) of a stronger material than the
  underlying matrix (KOSI experiments!). Can DI
  differentiate between them?
• Another source of information about possible
  strength values of cometary surfaces on dm-m
  scales stems from the analysis of meteoroids
  associated with certain comets which enter the
  earth atmosphere at high speeds and finally
  break-up and create a light flash. Wetherill
  (1982) gives values for tensile strengths of
  these fireballs ranging from 1 kPa to 1 MPa.

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Data about strength, II

• Laboratory measurements
• Snow small scale (cm) shear strength in the
  relevant density range of 300-500 kg m-3 is of
  the order of 10 -100 kPa. Petrovic, 2002 and
  Mellor, 1975. Tensile strength is nearly
  independent on temperature, while compressive
  strength shows a remarkable increase with
  decreasing temperatures.
• Simulating possible cometary analogue material
• KOSI, Jessberger and Kotthaus (1989)
  small-scale compressive strength of porous
  mixtures of crystalline ice and dust between 30
  kPa and 1 MPa with increasing strength for an
  increasing dust fraction
• Bar-Nun Laufer (2003) 20 kPa for their
  amorphous ice samples with a density of about 250
  kg m-3.

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More about strength

• Dynamic and quasi-static strength
• The strength values given above are derived from
  quasi-static experiments whereas, in principle,
  the dynamic strength for high strain rates is the
  relevant measure for impacts. Although
  measurements of dynamic strengths are limited it
  is well known that the strength increases with
  strain-rate (Ai Ahrens, 2004) resulting in
  values about an order of magnitude higher (or
  even more) than the quasi-static strength for the
  same material. It is further interesting that
  this effect might be even stronger for porous
  materials (Stewart Ahrens, 1999)
• Size dependence of the strength
• Different theories indicate that the strength
  decreases with increasing size d according to
  d-q where the exponent q is between 0.5 (fractal
  aggregate with D2.5, Xu 2005) and 0.6 (Weibull
  theory, Petrovic 2002).

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Perspective some of the weakest known materials
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Estimates on tensile strength of cometary
material - conclusion

• Theoretical tensile strength of powders (Van der
  Waals forces only) scale with 1/r (r is the
  particle radius) e.g., from Chokshi et al.
  (1993) Kührt and Keller (1994) derive a
  theoretical strength of 100 Pa and 100 kPa for
  grains of 1mm and 1µm, respectively. Sirono and
  Greenberg (2000) derive 300 Pa for the tensile
  and 6000 Pa for the compressive strength for a
  medium composed of ice grains linked into chains
  by intermolecular forces.
• From the discussion above the conclusion can be
  drawn that the cometary surface on meter scales
  has a reasonable lower limit of the tensile
  strength of about 1 kPa whereas the probable
  upper limit can be taken as 100 kPa.
• However, the space missions to comet nuclei since
  1986 have shown that no comet nucleus observed
  seems to resemble the next.. surprises
  are always possible!

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Compressive strength

• Theory of soil mechanics (failure of of geologic
  materials, e.g., Terzaghi 1954)
• Cohesion is the static part in tensile/shear
  strength.
• Dynamically, there is a friction part and the
  total shear strength can be written as
  Mohr-Coulombs law (equivalently, but more
  complex, by the Drucker-Prager criterion, see
  HolsappleMichel 2006)
• with c cohesion and ? friction angle being
  material constants. These constants actually
  depend on the size of the bearing area and on the
  range of the normal force s
• Now in bearing capacity theory, the following
  expression for the bearing strength (compressive
  strength for e.g. circular or square loads) of a
  soil (if gravity can be neglected) is given as

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Complete expression for compressive strength
(bearing strength)
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Bearing capacity factors
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Low velocity penetration of blunt bodies into
fluffy (porous, granular) comet surfaces

• working model vltltcsound breaking the
  compressive strength C and accumulation of
  material in front (snow shovel effect)
• Experiments (dropping 10cm-discs into
  Regolith-analogue material with very low c lt 100
  Pa) started at DLR Cologne to verify the
  mechanical model.
• For not too low C equivalent to the simple energy
  conservation equation,final depth v2m/2CA (v
  touchdown velocity m mass A projected frontal
  area)
• Otherwise, by numerical integration of the
  equations of motion

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DLR model penetration depth of Philae as a
function of compressive strength, C
Transitions feet only, feetlegs,
feetlegsbaseplate
C in Pa
Modelled penetration depths of Philae as a
function of compressive strength
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Equations of motion
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Experiments

• Preliminary experiments have been conducted
  impact of flat steel cylinders (0.6, 1.2, 1.8 kg,
  10 cm diameter), 0.66-2.8 m/s into Mars analog
  soil (50 grounded olivine, 50 quartz sand,
  density 1400-1900 kg/m3, c?40 Pa, F ?25 from
  shear experiments on the surface predicted
  bearing capacity 2000 Pa for a few cm
  penetration)
• From penetration depth, effective compressive
  strength in the 2-15 kPa range, increasing with v
  higher than anticipated (observed penetration y
  ? constlog(v0), anticipated y
  ?1/2v02/(tA/m-g))
• Might be due to three effects
• Influence of gravity and density (q and ? terms)
  surpass cohesion term in compressive strength
• Compaction of deeper levels provide much higher c
  than the measured surface layer
• Deviations of reality from standard model

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Experiments cont.-
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Strength derivation DI

• The DI team calculated the (shear) strength s by
  the formula
• The derivation of this formula is not clear to us
• New evaluation (200 100) Pa same formula, times
  correction factors
• The method used by the DI team to derive the
  shear strength at the surface of comet Tempel 1
  neglects acceleration by gases and is therefore
  not conclusive.
• Simplified (1D-) gas dynamic dust/gas
  calculations J. Knollenberg, March 2006
  constrained by OSIRIS measurements of the gas
  mass and a dust distribution according to
  NewburnSpinrad (1985) show the acceleration of
  dust by gas is a significant factor also during
  the first minutes after the impact

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Does DI give us a reliable value for the shear
strength?

• By the impact shock itself (before the material
  is actually excavated!) , the material is
  stressed (fractured) and its tensile strength is,
  thus, modified. Therefore, the pristine material
  properties can most likely not be determined with
  the applied method. Besides, it appears to be
  extremely model-dependent to infer quasi-static
  properties from supersonic impacts.
• Due to the impact a non-negligible amount of gas
  (H2O, CO2, CO) has been released from an extended
  source modifying the velocity distribution of the
  ejected dust particles. Thus, the detection of a
  minimum velocity of dust grains cannot be
  directly related to the material strength. The
  grains do not follow ballistic trajectories.
• Holsapple and Housen (LPSC 2006) conclude that
  within the large uncertainties .., any strength
  between 0 and 12 kPa could furnish the amount of
  total mass estimated. So, either gravity or
  strength craters can be consistent with the
  observations.. Even with a strength of 12 kPa,
  the plume would be attached to the comet surface
  for all times after about the first 20 min ..
  The role of gas pressure is mentioned.

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Dust acceleration due to gases

• Simplified (1D-) gas dynamic dust/gas
  calculations J. Knollenberg, March 2006
  constrained by OSIRIS measurements of the gas
  mass and dust distribution according to
  NewburnSpinrad (1985) show
• Dust velocities of 150 m/s are only possible if
  most particles have r lt 10µm and
• the dominant dust acceleration takes place within
  the first 5-10 km above the nucleus, thus
• the acceleration of dust by gas is a significant
  factor also during the first minutes after the
  impact

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Comet strengths conclusion

• We conclude that, unfortunately, neither DI nor
  other comet observations seem to provide yet firm
  data on the strength of cometary material.
• It should be always kept in mind that different
  definitions of strength exist and that they
  depend on scale and strain rate

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Philae Lander

• Separation from the Orbiter
• Descent (gravity)
• Activation of cold gas system (optional)
• Attitude control with flywheel
• Soft landing
• Fixation to ground

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Consequences of extremely soft surface for Philae

• Even a tensile strength as low as 50 Pa, which
  corresponds to a compressive strength (Nc of
  regolith is typically 15) in the order of 1 kPa
  would result in a penetration depth of the
  Rosetta Lander of only about 0.2m.
• Since Rosettas target comet, Churyumov-Gerasimenk
  o, has a much higher mass than the initial target
  comet Wirtanen, landing Philae has become more
  demanding for hard soils
• Actually, a softer comet surface will help Philae
  to land safely!

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Conclusions

• Results of DI do not really contradict with
  initial Engineering model, applied for Philae
• We have great confidence in a succesful landing
  on Churyumov-G. if the comets surface properies
  are similar ti those of Temple !

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References

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