Small Body Surface Environment

The surface of an asteroid or comet nucleus is an unconfined granular pile at accelerations between 1e-2 and 1e-5 m/s2 [2], where cohesion and van der Waals attraction between grains exceed weight and escape velocity is of the order of a mechanism’s own tip speed. What follows sets out the gravitational regime, the force hierarchy that replaces weight as the dominant term in regolith mechanics, the measured bearing strength and packing state of the near subsurface, the low-gravity impact and ejecta regime, the thermal field, and the ionizing radiation environment.

Gravitational regime

Surface acceleration on small bodies spans 1e-2 to 1e-5 m/s2 [2]. A body of 1 km radius and 2000 kg/m3 bulk density produces about 5e-4 m/s2, roughly 50 micro-g [1].

Body	Surface acceleration	Source
Eros (18 km)	0.2 to 0.6 milli-g	[1]
Itokawa (0.18 km)	6 to 9 micro-g	[1]
1999 KW4 primary	30 micro-g down to near zero at the equator	[1]

Bennu is 492 m in diameter with a bulk density of 1190 kg/m3 [5]. Its escape velocity is 20 cm/s and its equatorial rotational surface velocity is 10 cm/s at a rotation period of about 4.3 h [6]. Departure speed for material lifted from the surface is therefore of the same order as the tip speed of a slow-moving mechanism.

Lithostatic pressure inside a spherical body of 2000 kg/m3 follows P(R) = 5.6e-4 R^2 (1 - R^2) Pa, so interior pressures reach the kilopascal level only for radii above about 1300 m [1]. Below that, the material is effectively unconfined at every depth.

Rotation sets the second limit. A cohesionless body of 2000 kg/m3 disrupts at a spin period near 2.3 h [1]. The observed spin barrier is not absolute. Asteroids above about 300 m diameter are not seen rotating faster than 2.0 h, but (60716) 2000 GD65, diameter 2.3 +0.6/-0.7 km, completes a rotation in 1.9529 h [17]. At a bulk density of 2000 kg/m3 a cohesive stress of 150 to 450 Pa is required to hold it together, of the same order as lunar regolith, and the same analysis gives about 100 Pa for the smaller fast rotator (335433) 2005 UW163.

The force hierarchy at milli-g and below

Weight is not the dominant force on a small grain at these accelerations. The van der Waals attraction between two contacting grains is F_c = 3.6e-2 S^2 r newtons, where r is grain radius in meters and S is a surface cleanliness factor that tends to 1 on an airless body and falls to about 0.1 in a terrestrial atmosphere [1]. The underlying constants are a Hamaker constant of 4.3e-20 J and an interparticle separation of 1.5e-10 m, both taken from lunar regolith.

The grain radius at which cohesion equals weight (bond number of unity) moves by three orders of magnitude across the gravity range:

Gravity	Grain radius at unity bond number	Comparable body	Source
1 g	6.5e-4 m	Earth	[1]
0.1 g	2e-3 m	Moon	[1]
0.01 g	6.5e-3 m	Vesta	[1]
1 milli-g	2e-2 m	Eros	[1]
0.1 milli-g	6.5e-2 m	Toutatis	[1]
1 micro-g	6.5e-1 m	Itokawa	[1]

At 1 micro-g a half-meter boulder is held to its neighbors as firmly as a 0.65 mm sand grain is held on Earth [1]. Expressed as bond number, a 1 mm grain has a value of 20 at 1 milli-g and 2e6 at 1 micro-g [2].

Two further forces enter at the extremes of grain size. Solar radiation pressure reaches unity bond number at about 100 micrometer grain radius in microgravity, and equals cohesion at about 100 micrometer [1]. Electrostatic force at the terminator field strength of 1e5 V/m equals cohesion at about 0.3 m grain radius, while under nominal photoemission the crossover falls to nanometer grains. Gravity is therefore the weakest of the four terms over most of the particle size range that a mechanism has to handle.

Bulk cohesive strength of an assemblage follows sigma_c = 3e-4 / d Pa with d the mean grain diameter in meters: 300 Pa at 1 micrometer, 30 Pa at 10 micrometer and 3 Pa at 100 micrometer [2]. Strengths inferred from body-scale observation are of the same order: at least 60 to 85 Pa for 1950 DA, 50 to 100 Pa for 2013 P/R3, and about 25 Pa for 2008 TC3.

Measured bearing strength of the near subsurface

The OSIRIS-REx contact with Bennu on 20 October 2020 is the only direct measurement of near-subsurface geotechnical properties on a rubble pile: contact was at 10 cm/s with a 32 cm diameter annular head, the arm spring took no compression, and the spacecraft inertial measurement unit sampled acceleration at 200 Hz through a rigid load path [3].

Quantity	Measured value	Source
Contact velocity	10 cm/s	[3]
Peak acceleration	0.014 m/s2	[3]
Peak contact force before gas release	10 to 15 N	[3]
Penetration at 1.2 s after contact	2 to 3 cm	[3]
Penetration at end of pre-gas interval	5.95 to 6.91 cm in 0.605 to 0.705 s	[3]
Head tilt taken up by a 5 cm rock	about 7 deg	[3]
Disturbed surface area	0.51 m2 against a 0.08 m2 footprint	[3]
Inferred bulk density, upper 6 to 7 cm	440 to 600 kg/m3	[3]
Inferred packing fraction	0.2 to 0.45	[3]
Inferred compressive strength	2 to 200 Pa	[3]
Inferred bulk cohesion	0.2 to 20 Pa	[3]

The measured near-subsurface density is 37 to 50 percent below the bulk density of the asteroid, and the packing fraction is about half the random close packing that a gravity-dominated deposit would reach [3]. Cohesion at the sampling site is orders of magnitude below the value of up to 4000 Pa measured on the Moon. Independent limits agree: the excavated region produced by the gas release requires material below 1 Pa, the Bralgah crater ejecta blanket implies effective strength at or below 2 Pa, and the Hayabusa2 impact experiment on Ryugu gave an effective surface strength below 1.3 Pa [3].

Source: [3], CC BY 4.0.

The transition is set by packing fraction rather than by cohesion alone. For weakly cohesive regolith below about 10 Pa, a packing fraction at or below 0.5 keeps contact force under about 60 N and makes the response drag dominated, while a packing fraction at or above 0.6 pushes force above 60 N for friction angle at or above 20 deg and stops penetration within the first few centimeters for friction angle at or above 30 deg [3]. The same threshold appears in the fitted force law: closely packed regolith resists intrusion once friction angle reaches 28 deg or cohesion reaches 50 Pa, whereas in loose packing the depth is set by an inertial term [4].

The intrusion force law fitted to the touchdown separates a quasi-static and an inertial term, F_pressure = 80 mu rho a^2 g |z| with mu = tan(phi), and F_drag = 3.2 rho a^2 U^2 [4]. For a design case of a 1 m boulder striking cohesionless regolith of 2.2 g/cm3 at friction angle 40 deg and packing fraction 0.5, arriving at 20 cm/s, the predicted burial depth is 0.15 m. Cratering strength at the Bennu surface is below 100 Pa, and the Ryugu subsurface below 1 m depth is about 100 Pa.

Anchoring and reaction budgets follow directly. A 10 to 15 N contact force produced a 0.014 m/s2 acceleration on the spacecraft [3]; any tool that must react more than a few newtons against such a surface either drives itself off the body or plunges through the loose upper layer.

Low-gravity impact, penetration and ejecta

Parabolic flight and suborbital campaigns bracket the regime. The PRIME experiment covered impact speeds of 4 to 230 cm/s and COLLIDE covered 1 to 120 cm/s, into targets of 75 to 250 micrometer grains [7].

Condition	Result	Source
About 1e-2 g	Ejecta only above 20 cm/s impact speed, otherwise the projectile embeds	[7]
Below 1e-4 g	Ejecta above 10 cm/s, and the projectile can rebound	[7]
Coefficient of restitution, 1e-2 g	0.43 +/- 0.14	[7]
Coefficient of restitution, below 1e-4 g	0.15 +/- 0.04	[7]
Quartz sand / JSC-1 restitution	0.38 +/- 0.15 / 0.45 +/- 0.16	[7]
Restitution across 5 to 100 cm/s	Falls by about a factor of 10	[7]
Ejecta velocity scaling	Impact energy to the power 0.50	[7]

Restitution of the Itokawa surface inferred from the Hayabusa landing was 0.84 [1], an order of magnitude above the microgravity laboratory value, which is the measure of how far a competent boulder field departs from a granular bed.

Penetrometry under parabolic flight covers the quasi-static end of the same problem. Penetration velocities of 3 to 35 mm/s over about 22 s of microgravity per parabola gave 42 mm of penetration at 3 mm/s, at Froude numbers of 0.18 to 1.8 [9]. Flat tips produce the largest reaction force, above conical and hemispherical tips, and cohesive targets give reaction forces of nearly the same magnitude as their 1 g counterparts, which means low gravity does not relieve the tool loads when the material is cohesive. Drop towers give shorter windows: 1.8 m of fall yields 0.49 s at 0.16 g and 0.48 s at 0.14 g, and a 0.9 m tower yields 0.28 s of microgravity [8].

Sampler simulation reproduces the same sensitivity. Smoothed particle hydrodynamics models of a brush sampler used bulk modulus 3.33 MPa, shear modulus 370 kPa, bulk density 1.5 g/cm3, internal friction angles of 20, 42 and 60 deg and cohesion of 0, 0.5 and 1 kPa, run at both 9.81 m/s2 and the Phobos value of 5.7e-3 m/s2 with motor speeds of 100 to 500 rpm [10]. Discrete element sampling simulations at 10 cm/s contact into regolith of 1600 kg/m3 bulk density, 36 percent porosity and 0.8 to 1.2 cm grains showed collected mass falling sharply between strengths of 50, 150 and 300 Pa [2].

Self-generated particle environment

Bennu ejects particles from its own surface without external cause. Ejection speeds run from 0.05 to more than 3 m/s at ejection energies of 8 to 270 mJ [6]. The 6 January 2019 event yielded 124 photometrically measured particles from under 1 cm to 8 cm in size, and the 19 January event gave speeds of 0.06 to 1.3 m/s. Surface-relative ejection speeds cluster at 10 to 25 cm/s, and particles that fail to escape enter temporary orbits at 15 to 20 cm/s. A vehicle operating close to such a body is inside a sparse population of centimeter debris moving at speeds comparable to its own approach velocity.

Thermal environment

Thermal inertia is the governing surface thermal parameter and is low.

Surface	Thermal inertia (J/m2/K/s^0.5)	Source
Bennu, pre-launch disk average	310 +/- 70	[5]
Bennu, global average on arrival	350 +/- 20	[5], [19]
Bennu, variation over a full rotation	below 10	[19]
Bedrock reference value	1500	[19]
Ryugu, global average	225 +/- 45	[11]
Ryugu, thermal infrared imager estimate	200 +/- 7	[11]
MASCOT landing site, regional average	181 +/- 102	[11]
MASCOT landing site, individual rock	180 (+65 / -40)	[11]

Thermal inertia does not predict particle size on this surface. The simplified models that translate thermal inertia into a characteristic particle size, assuming particles smaller than the diurnal skin depth give a lower value than bedrock at 1500 J/m2/K/s^0.5, predict a Bennu surface dominated by 0.5 to 5 cm particles [19]. The surface is instead dominated by boulders above 1 m, with about 200 boulders larger than 10 m and the largest exceeding 30 m, distributed evenly enough that thermal inertia varies by under 10 J/m2/K/s^0.5 across a rotation. Bennu’s geometric albedo is 4.4 +/- 0.2 percent at 550 nm [19]. Candidate reconciliations are low boulder thermal inertia, dust coating the boulders, a mixture of particulate regolith and boulders, or high boulder porosity. Micrometer-scale particles are present despite the expectation that small airless bodies carry coarser regolith.

A thin dust layer decouples the observed thermal signature from the substrate. A layer of 10 to 100 micrometer thickness with a thermal inertia of 25 J/m2/K/s^0.5 changes the apparent thermal inertia of the surface by more than 20 percent, and on Ryugu the diurnal skin depth masked by such a layer is about 10 mm [12]. A worked case gives a sand-like layer of 58 mm at 216 J/m2/K/s^0.5 over a substrate at 700 J/m2/K/s^0.5. The thermal conductivity of a Ryugu boulder is about 0.1 W/m/K, which is an insulator: heat rejected into the surface by a landed vehicle does not conduct away [12].

Comet nuclei swing much harder. Diurnal temperature change on 67P at perihelion reaches about 230 K, with variations of order 100 K away from perihelion [13]. Seasonal thermal stress reaches tens of MPa and penetrates about 0.25 m, which is enough to fracture the near-surface layer when thermal inertia is at or above 50 J/m2/K/s^0.5. Published strengths for the hard layer are a 10 to 50 cm thickness, Young modulus at or above 7 MPa with an upper limit of 980 MPa, and compressive strength anywhere from 70 kPa to 9 MPa [13]. The lower layer is far weaker, with tensile strength from hundreds of kPa down to about 1 kPa [13]. An anchoring design has to hold in either.

The same forcing acts at grain scale on asteroids. Modeled microstructures on airless surfaces reach peak tensile stresses of order 100 MPa, controlled by the coefficient of thermal expansion and Young modulus of the constituent minerals and amplified at grain boundaries [14]. Thermal fatigue is therefore a regolith production mechanism and a reason to expect fresh fracture surfaces rather than rounded clasts.

Individual grain stiffness

Nanoindentation of returned Itokawa grains gives reduced Young modulus of 83.0 +/- 0.1 and 86.0 +/- 0.04 GPa on one 131 micrometer particle at 5 and 10 mN load, and 111.0 +/- 0.2 and 101.0 +/- 0.05 GPa on a 149 micrometer particle [15]. Individual grains are therefore competent silicate; the weakness of a small-body surface is entirely in the packing, not in the material.

Surface roughness and site selection

Bennu and Ryugu both proved rougher on arrival than the pre-encounter models used for design. Bennu’s disk-averaged thermal inertia measured before launch, 310 +/- 70, was consistent with the 350 +/- 20 found on arrival [5], yet the surface carried no smooth deposit at the scale the sampler had been sized for. Sampleability had to be re-derived in flight from particle size-frequency distributions and rock tilt efficiency mapped facet by facet across candidate regions of interest. Bennu, unlike Eros and Itokawa, has no extensive ponded fine deposits, and spectral and thermal data indicate minimal dust coverage at the surface [3].

Radiation

Small bodies have no magnetic field and no atmosphere. A vehicle on the surface sees the unattenuated interplanetary galactic cosmic ray and solar energetic particle environment over the sky not occluded by the body, with the body itself providing the only shielding mass. The design environment is the Badhwar-O’Neill galactic cosmic ray model, whose 2014 revision derives the solar modulation parameter from time-delayed sunspot number and improves the fit to measured ion spectra below 4 GeV/n over the 2011 version [18]. No measured surface radiation dataset from an asteroid or comet nucleus has been published; the environment is taken from interplanetary models rather than from in-situ measurement.

Simulants and ground test

Asteroid simulant fidelity is assessed against a figure of merit rather than against a single property, because a simulant that matches bulk density can still fail on grain shape, strength and porosity [16]. Fine simulant measured at ambient pressure gives a Young modulus of 0.258 MPa and a shear yield stress of 3499 Pa [8]. Reduced-gravity mechanical testing is limited by the available free-fall window, which caps the achievable strain rate and the number of parameter points in a campaign [8], [9].