Determination of the Gravity Field and Rotational Dynamics of an Asteroid by Tracking an
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Photoelectric photometry of six earth-approaching asteroids is presented. The selection criterion was that they were close enough in 1986 to be observed by radar. Rotation periods were obtained for 1986 DA, 3199, 3103, and 1983 RD. 1986 JK and 1986 RA showed no detectable brightness variations during the monitoring time on several nights each, and therefore were either seen pole-on or have long rotation periods. Asteroids 1986 JK and 1986 RA are of taxonomic class C, 1986 DA and 3103 of class X, 1983 RD of class Q, and only 3199 of the class S that was previously believed to be predominant among earth-approaching asteroids.
Based on Wilson's (1977) article on the magnetic effects on space vehicles and other celestial bodies, the magnetic damping of rotation is considered. The inadequacy of the interstellar magnetic field in overcoming solar wind shielding and thus influencing the rotation of bodies is described. The ionospheric shielding of the interstellar field is discussed along with the permeability and magnetic damping by the solar or stellar wind. Star formation and angular momentum is discussed and attention is given to the magnetic damping of unshielded small bodies. Calculations of the rate for damping through random particle impact are made. Theories concerning the rotation of asteroids and the origin of meteorites are reviewed. The shielding process of ionospheric plasmas is outlined and the damping effect of the geomagnetic field on the rotation of artificial satellites is evaluated.
Photometry and colorimetry of 951 Gaspra were obtained on nine nights during the 1990 opposition. A composite lightcurve constructed using data from eight of those nights yielded a synodic rotational period of 7.04346 +/- 0.00006 hours, a mean absolute V magnitude of 11.8026 +/- 0.0025, and a slope parameter of 0.285 +/- 0.005. The apparent discrepancy can be easily resolved by realizing that their determination is based primarily on data obtained after opposition. Different phase functions pre- and post-opposition are a natural consequence of a changing aspect during an opposition. If the sub-Earth latitude on Gaspra is at a less equatorial aspect after opposition than it was before opposition, then we would expect to see a shallower phase function (corresponding to a larger numerical value of the slope parameter). Adding weight to this hypothesis is the last observation of the opposition, made in May after Gaspra had passed post opposition quadrature, which is displaced toward brighter absolute magnitudes relative to the rest of our data, indicating an even more poleward sub-Earth latitude than earlier in the opposition. Because the orbits of Earth and Gaspra are nearly coplanar, a substantial change in sub-Earth latitude during the opposition would not have been possible unless the obliquity of the asteroid's rotational axis is not small.
The effects of asteroid collisional history on sizes and spins of present-day objects are discussed. Collisional evolution studies indicate that collisions have altered the spin-rates of small bodies, but that the largest asteroids may have retained their primordial rotation rates. Most asteroids larger than 100 km diam have probably been shattered, but have gravitationally recaptured their fragments to form a rubble-pile structure. Large angular momentum asteroids appear to have Maclaurian spheroidal or Jacobi-ellipsoid-like shapes; some of them may have fissioned into binaries. An integrated size and spin collisional evolution model is presented, with two critical parameters: one which determines the spin rates for small fragments resulting from a shattering collision, and the other determines the fraction of impact angular momentum that is retained by the target.
The Yarkovsky effect is a thermal radiation force which causes objects to undergo semimajor axis drift and spin up/down as a function of their spin, orbit, and material properties. This mechanism can be used to (i) deliver asteroids (and meteoroids) with diameter D < 20 km from their parent bodies in the main belt to chaotic resonance zones capable of transporting this material to Earth-crossing orbits, (ii) disperse asteroid families, with drifting bodies jumping or becoming trapped in mean-motion and secular resonances within the main belt, and (iii) modify the rotation rates of asteroids a few km in diameter or smaller enough to explain the excessive number of very fast and very slow rotators among the small asteroids. Accordingly, we suggest that nongravitational forces, which produce small but meaningful effects on asteroid orbits and rotation rates over long timescales, should now be considered as important as collisions and gravitational perturbations to our overall understanding of asteroid evolution.
The main goal of the research is to carry on an extensive study of physical properties (colors and variability) of asteroids in the 1 to 10 km diameter range and of cometary cores, with the use of a charge coupled device (CCD) camera, PMT photometer, or both. Particular attention is paid to asteroids being observed by radar because the greatest gain is found from the combination of radar results with the data obtained by optical techniques. To satisfy the goal, 100 nights/year have been scheduled on the 2.3 m and 1.5 m telescopes. During the past 2 years small asteroids were observed. Out of 22 asteroids for which periods of rotation could be precisely measured, 17 have periods of rotation less than 5 hours. This indicates that small objects rotate faster. By now researchers know 14 asteroids with rotation periods in the 2 hour range. At the same time they confirmed the existence of a number of exceptionally slow rotators e.g., 1367 Nongoma with P = 5.65 days. Taxonomic observations lead to a conclusion that Apollo, Amor, and Aten asteroids represent a variety of classes and are not predominantly of class S. Apollo asteroid 3361 Orpheus was found to belong to the rare class V. In collaboration with Dr A. Harris of JPL the opposition effect was studied for 30 Urania and 64 Angelina. Seven comets: P/Helin, P/Brooks 2, P/Klemola, P/Borrelly, Wilson (1986 1) and Shoemaker (1987 o) were monitored for variability. The results were negative with the exception of P/Brooks 2 for which 0.35 mag amplitude was detected.
The new mechanism of angular momentum drain is proposed to account for the relatively slow rotation rates of intermediate-sized asteroids. Impact ejecta on a spinning body preferentially escape in the direction of rotation, systematically draining away spin angular momentum and leading to the counterintuitive result that collisions can reduce the spin of midsized objects. The existing theory of asteroid rotation is reviewed, and the escape of ejecta from hypervelocity impacts on bodies of different sizes and physical properties is described. The effect of this mass loss on asteroidal rotation is calculated and shown to be a significant brake on the spins of intermediate-sized asteroids. Finally, this new process is incorporated in a revised theory of collisional evolution, its predictions are compared with observational data, and its applications are discussed.
Asteroid 951 Gaspra appears to be in an obliquity resonance with its spin increasing due to the YORP effect. Gaspra, an asteroid 5.8 km in radius, is a prograde rotator with a rotation period of 7.03 hours. A three million year integration indicates its orbit is stable over at least this time span. From its known shape and spin axis orientation and assuming a uniform density, Gaspra's axial precession period turns out to be nearly commensurate with its orbital precession period, which leads to a resonance condition with consequent huge variations in its obliquity. At the same time its shape is such that the Yarkovsky-O'Keefe-Radzievskii-Paddack effect (YORP effect for short) is increasing its spin rate. The YORP cycle normally leads from spin-up to spin-down and then repeating the cycle; however, it appears possible that resonance trapping can at least temporarily interrupt the YORP cycle, causing spin-up until the resonance is exited. This behavior may partially explain why there is an excess of fast rotators among small asteroids. YORP may also be a reason for small asteroids entering resonances in the first place.
Orbital and landing operations about near-Earth asteroids are different than classical orbital operations about large bodies. The major differences lie with the small mass of the asteroid, the lower orbital velocities, the larger Solar tide and radiation pressure perturbations, the irregular shape of the asteroid and the potential for non-uniform rotation of the asteroid. These differences change the nature of orbits about an asteroid to where it is often common to find trajectories that evolve from stable, near-circular orbits to crashing or escaping orbits in a matter of days. The understanding and control of such orbits is important if a human or robotic presence at asteroids is to be commonplace in the future.
Spacecraft motion in close proximity to irregularly shaped, rotating bodies such as asteroids presents a unique dynamical environment as compared to most space missions. There are several fundamental novelties in this environment that spacecraft must deal with. These include the possibility of orbital instabilities that can act over very short time spans (on the order of hours for some systems), possible non-uniform rotation of the central gravity field, divergence of traditional gravity field representations when close to the asteroid surface, dominance of perturbing forces, an extremely large asteroid model parameter space that must be prepared for in the absence of reliable information, and the possibility of employing new and novel trajectory control techniques such as hovering and repeated landings on the asteroid surface. An overview of how these novelties impact the space of feasible close proximity operations and how different asteroid model properties will affect their implementation is given. In so doing, four fundamental types of close proximity operations will be defined. Listed in order of increasing technical difficulty these are: (1) close, stable orbits; (2) low-altitude flyovers; (3) landing trajectories; and (4) hovering trajectories. The feasibility and difficulty of implementing these operations will vary as a function of the asteroid shape, size, density, and rotation properties, and as a function of the spacecraft navigation capability. Additional information is contained in the original extended abstract.
In 1971 asteroid Vesta was observed in a region of the sky in which it had never been observed before. Its photometric lightcurve had two distinct maxima. Those observations have been the only strong evidence to support a rotation period of about 10 hr 41 min. Lightcurves made in 1982, when Vesta was at the same aspect as 1971, do not show two different maxima. It is concluded that there was a systematic error in the 1971 observations. At this time a definitive statement cannot be made about the true period of Vesta, although the 5 hr 20 min period does appear more plausible. Radar echoes in 1988 and 1992 should resolve the problem. The shorter rotation period was assumed and the photometric astrometry method applied. The sidereal period is 5 hr 20 min 31.68 sec (0.2225889 + or 0.0000002 days), the rotation is prograde, and the coordinates of the north pole are 103 deg longitude and + 43 deg latitude with an uncertainty of about 6 deg.
Results from an observational program to detect weak silicate features on M-type asteroids will be presented. Results include nearly full-rotational coverage of asteroids 69 Hesperia, 110 Lydia, 201 Penelope and 216 Kleopatra. Additional information is contained in the original extended abstract.
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Photoelectric observations of 1915 Quetzalcoatl on March 2, 1981 show that this asteroid has a rotational period of 4.9 + or - 0.3 hr and a lightcurve amplitude of 0.26 magnitudes. B-V and U-B colors are found to be 0.83 + or - 0.04 and 0.43 + or - 0.03, respectively, consistent with Quetzalcoatl being an S-type asteroid. Additional observations from March 31, 1981, give a linear phase coefficient of 0.033 mag/deg and a mean B(1,0) magnitude of 20.10. The resulting estimated mean diameter for Quetzalcoatl is only 0.37 km, making it one of the smallest asteroids for which physical observations have yet been made.
The general problem of satellite and particle dynamics about a uniformly rotating tri-axial ellipsoid with constant density is formulated.