Angular momentum of Icarus

ICA~US 10, 445-446 (1969)

Angular Momentum of Icarus W I L L I A M K. H A R T M A N N Lunar and Planetary Laboratory University of Arizona, Tucson, Arizona 85721

Received December 30, 1968; revised J a n u a r y 1O, 1969 Inclusion of Icarus in an angular m o m e n t u m density-mass diagram supports a 1967 prediction that asteroidal bodies smaller t h a n about 1017 gm will depart from the planetary rotation law described earlier. Icarus' asteroidal nature and origin b y fragmentation is thereby suggested.

In 1967, the writer and S. Larson pointed out that the asteroids, taken together with the planets, defined a welldetermined relationship between angular momentum density h/M and mass M. Fish (1967) simultaneously and independently made the same remark. Modification of MacDonald's 1963 relation was suggested b y both authors. This finding supported the view that most larger observable asteroids, larger than about 1019 gm (r N 10 km), are "planetary" in nature; i.e., many of them m a y be original accretions with rotations negligibly modified b y subsequent collisions. Alfv~n (1964) had earlier pointed out that the planetary bodies had narrowly restricted rotation periods, in the range about 4 to 25 hr. Alfv~n suggested that planetary bodies should be thought of as having essentially constant periods. The relation found b y Hartmann and Larson, and Fish,

hiM oc M+~/3 is, indeed, a constant period relation. This supported Alfv~n's idea and (by considering the asteroids and the Earth and Moon together as a system) indicated that the range of periods for most bodies is about 8 to 10 hr. Alfv~n also pointed out that if collisions had dominated, the fragments would tend toward equipartition of rotational kinetic energy, producing a law whereby

h/M o: M-116.

Referring to the collision frequency among asteroids, Hartmann and Larson (1967) therefore predicted that "within about an order of magnitude of M = 1017 gm, the collision and fragmentation frequency becomes high enough to cause the [log him vs. log M relation] to flatten out [from the observed slope ÷2/3] or approach the expected value [slope -1/6]." To state the case in other words, the observed relation is a constant-period law: "Planetary" bodies tend to rotate with constant periods of 8 to 10 hours unless tidal forces are involved. The prediction is that the smaller fragments will rotate with shorter periods. There is now some evidence that this prediction was correct. During the 1968 apparition of Icarus, Gehrels (private communication) obtained the results r = 0.51 km ~= 0.03 km and P = 2h 15TM 30 s ± 4s. These optical data (along with other optical determinations) are in good agreement with less precise radar results which indicate 0.3 < r < 0.7 km and 0.9 < P < 3.3 hr, depending on the assumed surface characteristics (Goldstein, 1968). The mass of Icarus is thus some 1015 gin. A new plot of h/M vs. M, including Icarus, shows that this small asteroid" indeed departs significantly from the "planetary" curve defined b y the larger bodies. The departure is larger than for any other asteroidal body. Asteroid 321 has the next largest departure, in the same direction, and is fourth from smallest of

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FIG. 1. Revision of the 1967 plot of angular momentum density vs. mass to include Icarus (x). Dotted line shows MacDonald's (1963) relation; solid line, the 1967 relation; dashed line, the suggested flattening due to partial equipartition of rotational kinetic energy. Probable error of point × is within the size of the symbol. t h e 31 asteroids p l o t t e d earlier, with a n e s t i m a t e d mass o f some l019 gm. I conclude t h a t in Icarus, a t a b o u t 1015 gin, we are perhaps beginning t o see t h e flattening, t h e t e n d e n c y t o w a r d equip a r t i t i o n o f r o t a t i o n a l energy, t h a t was predicted in 1967 to begin in the v i c i n i t y of 101~ gin. The d e p a r t u r e of I c a r u s f r o m t h e " p l a n e t a r y " r o t a t i o n law s u p p o r t s I c a r u s ' origin as a fragmental, r a t h e r t h a n c o m e t a r y or " p l a n e t a r y , " b o d y . Gehrels' discovery o f I c a r u s ' high obliquity, some 74 ° (private c o m m u n i c a tion), also s u p p o r t s a fragmental, non" p l a n e t a r y , " nature. [The large asteroid, 4 Vesta, on the c o n t r a r y , has an obliquity o f only 25 ° (Gehrels, 1967.)] ACKNOWLEDGMENTS The writer thanks S. Sorer for helpful comments, and Dr. T. Gehrels for making his recent

results on Icarus available. This paper was supported by a NASA institutional grant to the University of Arizona. REFERENCES AI~vv~N, H. (1964). On the origin of the asteroids. Icarus 3, 52-56. FISH, F. F. (1967). Angular momenta of the planets, lcarus 7, 251-256. G~.m~LS, T. (1967). Minor planets. I : The rotation of Vesta. Astron. J. 72, 929--938; and Commun. L u n a r Planet. Lab. 7, 169-178. GOT~DS~IN, R. M. (1968). Radar observations of Icarus• Science 162, 903-905. H ~ , W. K., AND L~SO~, S. (1967). Angular momenta of planetary bodies. Icarus 7, 257-260. MAcDonaLD, G. J. F. (1963). The internal constitutions of the inner planets and the moon. Space Sci. Rev. 2, 467-541.