Icarus 329 (2019) 207–221 Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Small body shapes and spins reveal a prevailing state of maximum topographic stability T ⁎ James E. Richardsona, , Kevin J. Gravesb, Alan W. Harrisc, Timothy J. Bowlingd a Planetary Science Institute, 1106 Chalfant St, South Bend, IN 46617, USA b Department of Earth, Atmospheric, & Planetary Sciences, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN 47907, USA c More Data!, 4603 Orange Knoll Ave, La Canada, CA 91011, USA d Southwest Research Institute, 1050 Walnut Street, Suite 300, Boulder, CO 80302, USA ARTICLE INFO ABSTRACT Keywords: Over the past thirty years, spacecraft missions, Earth-based radar experiments, and telescopic observations have Asteroids revolutionized our knowledge of Main Belt asteroids, near-Earth asteroids, and comet nuclei. As a result of this Rotation effort, we now possess high resolution shape models and well-constrained spin rates, pole orientations, and basic Asteroids surface properties for a few dozen such small bodies. Here we present the results of a geomorphological ex- Surfaces amination of 32 such small body shape models along with their associated spin properties, and show that small Comets body shape, gravity, and spin combine to gradually drive the surface towards a condition of maximum topo- Nucleus Mars graphic stability; that is, a state of low topographic variation, low slopes, and low surface erosion (mass-wasting) Satellites rates. Of the 32 bodies investigated, 15 (47%) reside within this ‘zone of maximum topographic stability’, and when asteroid lightcurve-derived rotation rate and body elongation estimates are included, 1941 (70%) of 2791 well-observed asteroids reside within this zone. This finding indicates that given a mobile surface layer and sufficient time, small body surfaces naturally tend to erode, and their spin states gradually evolve, towards a state of maximum topographic stability, which also corresponds to a state of lowest internal stress. This erosional effect is most prominent on bodies several kilometers and larger in diameter, where YORP induced spin-state changes are small. 1. Introduction looking for common properties and trends with respect to surface properties and processes. Eight shape models derived from spacecraft For many years, the only small bodies for which we had detailed optical data were used, consisting of four asteroids, two comet nuclei, shapes and images were the two Martian moons, Phobos and Deimos, and the two Martian moons (Thomas, 2014). Twenty-four shape models obtained during the Viking missions of the late 1970s (Thomas, 1979). derived from Arecibo and Goldstone planetary radar data were used, Then, in 1991 and 1994, the Galileo spacecraft flew by Main Belt as- consisting of two Main Belt and twenty-two near-Earth asteroids, with teroids 951 Gaspra (Belton et al., 1992) and 243 Ida (Belton et al., two options for asteroid 1950 DA (Benner, 2013). These shape models, 1996), giving us our first close-up views of an asteroid's surface and listed in Table 1, were selected based upon the degree of surface cov- shape. At about the same time, Hudson and Ostro (1994) pioneered erage obtained (> 65% preferred); the shape model resolution techniques for using Earth-based radar systems to obtain detailed achieved (> 1000 polyhedron facets preferred); and the degree to shapes and physical characteristics from near-Earth asteroids, begin- which the body has been characterized in the scientific literature (see ning with 4769 Castalia. These two methods – spacecraft and planetary the reference list in the far-right column of Table 1). Each small body radar observations – have since produced a steady stream (about 1–2 was then analyzed using the surface gravitational properties approach new objects per year) of highly-resolved asteroid surface, shape, and originally presented in Richardson and Bowling (2014), which also spin characterizations. contains a detailed Section 2.1 Background, describing the history and The purpose of this geomorphological study was to investigate the literature leading up to this study. shape, gravity, and spin of 32 publicly available small body datasets, ⁎ Corresponding author. E-mail addresses: [email protected] (J.E. Richardson), [email protected] (K.J. Graves), [email protected] (A.W. Harris), [email protected] (T.J. Bowling). https://doi.org/10.1016/j.icarus.2019.03.027 Received 8 October 2018; Received in revised form 17 January 2019; Accepted 18 March 2019 Available online 07 April 2019 0019-1035/ © 2019 Elsevier Inc. All rights reserved. J.E. Richardson, et al. Table 1 Selected small body shape models. −3 −3 No. Name a (km) b (km) c (km) Period (h) c/a ωsc Class ρmeasured (kg m) Error ρoptimum (kg m ) Range ρassumed (kg m ) Group Polygons Source 4179 Toutatis 4.26 2.03 1.70 128.8080 0.40 0.0195 Sk –– – – 2300 A 39,996 Ostro et al. (2001) 4486 Mithra 2.35 1.65 1.44 67.5000 0.61 0.0372 S –– – – 2300 A 5996 Brozovic et al. (2010) M2 Deimos 7.8 6.0 5.1 30.3120 0.65 0.1037 C 1471 ± 166 ––1471 A 5040 Thomas (1993) 9P Tempel 1 6.3 5.9 5.2 40.7000 0.83 0.1481 – 400 ± 200 ––400 A 32,040 Thomas et al. (2007) 2100 Ra-Shalom 2.3 2.3 2.0 19.7970 0.87 0.1572 C –– – – 1500 A 2292 Shepard et al. (2000) 4660 Nereus 0.51 0.33 0.24 15.1000 0.47 0.1664 Xe –– – – 2300 A 2292 Brozovic et al. (2009) 2063 Bacchus 1.11 0.53 0.50 15.0000 0.45 0.1676 Sq –– – – 2300 A 508 Benner et al. (1999) 52760 1998 ML14 1.1 1.1 1.0 14.9800 0.91 0.1678 S ––600 200–10,000 2300 B 1092 Ostro et al. (2001) 25143 Itokawa 0.54 0.29 0.21 12.1320 0.39 0.2250 QS 1950 ± 140 ––1950 A 196,608 Abe et al. (2006) – 2002 CE26 Alpha 3.5 3.3 3.1 15.6000 0.89 0.2590 C 890 ± 290 500 300–1500 890 B 2292 Shepard et al. (2006) 8567 1996 HW1 3.8 1.6 1.5 8.7624 0.39 0.2868 Q –– – – 2300 A 2780 Magri et al. (2011) 216 Kleopatra 217 94 81 5.3850 0.37 0.3425 M 4270 ± 860 2900 1900–5500 4270 B 4092 Ostro et al. (2000) 10115 1992 SK 1.39 0.90 0.91 7.3182 0.65 0.3434 S ––960 580–2310 2300 A 1016 Busch et al. (2006) 208 951 Gaspra 18.2 10.5 8.9 7.0420 0.49 0.3569 S –– – – 2300 A 32,040 Thomas et al. (1994) M1 Phobos 26.8 22.4 18.4 7.6530 0.69 0.3636 D 1876 ± 10 2200 710–3600 1876 B 32,040 Willner et al. (2010) 16 Psyche 279 232 186 4.1959 0.67 0.4282 M 4500 ± 1400 3200 2200–5500 4500 B 2292 Shepard et al. (2017) 433 Eros 34.4 11.2 11.2 5.2700 0.33 0.4426 S 2670 ± 30 2200 1400–4000 2670 B 129,600 Thomas et al. (2002) 33342 1998 WT24 0.47 0.43 0.40 3.6970 0.85 0.4611 E ––5000 3700–7900 5000 B 7996 Busch et al. (2008) 103P Hartley 2 2.323 0.745 0.723 18.3400 0.31 0.4647 –– – 200 140–350 200 B 20,584 Thomas et al. (2013) 1627 Ivar 15.38 7.28 7.10 4.7952 0.46 0.5027 S ––2450 1700–4100 2500 B 9996 Crowell et al. (2017) 243 Ida 53.6 24.0 15.2 4.6300 0.28 0.5106 S 2600 ± 500 2300 1500–4800 2600 B 32,040 Thomas et al. (1996) 1620 Geographos 5.11 2.10 1.85 5.2233 0.36 0.5160 S ––2000 1300–4000 2000 B 4092 Hudson and Ostro (1999) 1580 Betulia 6.59 5.85 4.19 6.1384 0.64 0.5921 C ––1100 700–2600 1100 B 2292 Magri et al. (2007) 4769 Castalia 1.6 1.0 0.7 4.0700 0.44 0.5923 S ––2500 1600–5100 2500 B 4092 Hudson and Ostro (1994) 6489 Golevka 0.69 0.57 0.49 6.0289 0.71 0.6028 Q ––1100 600–2800 1100 B 4092 Hudson et al. (2000) 101955 Bennu 0.57 0.54 0.51 4.2975 0.90 0.7902 C 1260 70 ––1260 C 2692 Nolan et al. (2013) 341843 2008 EV5 0.42 0.41 0.39 3.7250 0.93 0.8355 C –– – – 1500 C 3996 Busch et al. (2011) 66391 1999 KW4 Alpha 1.53 1.50 1.35 2.7645 0.88 0.9823 S 1970 ± 240 ––1970 C 9168 Ostro et al. (2006) 29075 1950 DA (Pro) 1.28 1.24 1.19 2.1216 0.93 1.0373 EM –– – – 3000 C 2036 Busch et al. (2007) 29075 1950 DA (Retro) 1.60 1.45 1.20 2.1216 0.75 1.0373 EM –– – – 3000 C 1016 Busch et al. (2007) 136617 1994 CC Alpha 0.69 0.67 0.64 2.3886 0.93 1.0833 Sk 2170 ± 610 ––2170 C 3996 Brozović et al. (2011) 54509 YORP (2000 PH5) 0.15 0.13 0.09 0.2029 0.60 10.8461 –– – – – 3000 C 572 Taylor et al. (2007) – 1998 KY26 0.03 0.03 0.03 0.1784 1.00 12.3356 –– – – – 3000 C 4092 Ostro et al. (1999) Icarus 329(2019)207–221 J.E. Richardson, et al. Icarus 329 (2019) 207–221 2. Spin state and topography axis, generally near the equatorial, extreme ends of the body, will mark areas of topographic high (red-pink).