The pole orientation of asteroid 433 Eros determined by photometric astrometry

Refinements to the pole-determination method photometric astrometry (PA) were completed in 1983 (R. C. Taylor and E. F. Tedesco, 1983, Icarus54, 13–22). A goal is to redo the pole analysis for every asteroid whose pole had been determined from earlier versions of PA: Previous PA poles are reviewed in this paper. Asteroid 433 Eros is in that collection and has redone. The result are prograde rotation; a sidereal period of 0.219588 ± 0.000005 day; and a north pole at 22° longitude, +9° latitude. The uncertainty of the pole is 10°. The pole position of Eros determined by C.D. Vesely (1971, In Physical Studies of Minor Planets (T. Gehrels, Ed.), pp. 133–140, NASA SP-267) and Dunlap (1976, Icarus28, 69–78), using earlier versions of photometric astrometry, were within 21 and 7°, respectively, of the present result.     

Radar observations of asteroid 1580 Betulia

Radar observations of the asteroid 1580 Betulia, made at a wavelength of 12.6 cm, show a mean radar cross section of 2.2 ± 0.8 km² and a total spectral bandwidth of 26.5 ± 1.5 Hz. Combining our bandwidth measurements with the optically determined rotation period sets a lower limit to the asteroid's radius of 2.9 ± 0.2 km.     

Radar observations of asteroid 1 Ceres

Radar observations of asteroid 1 Ceres were made at a 12.6-cm wavelength from the Arecibo Observatory in March/April 1977. The measurements, made with a received circular polarization orthogonal to that transmitted, yield a radar cross section of (0.04 ± 0.01)πR², for R = 510 km. The corresponding radar reflectivity is less than that measured for any other celestial body. Within the accuracy of measurement, no significant variation of cross section with rotational phase is apparent. The shape of the power spectrum suggests that Ceres is rougher at the scale of the observing wavelength than the Moon and inner planets, but smoother than the outer three Galilean satellites.     

Radar and photoelectric observations of asteroid 2100 Ra-Shalom

Results of 13-cm-wavelength radar observations and V-filter photoelectric observations of Ra- Shalom during its 1981 Aug–Sep apparition are reported. The radar data yid detections of echoes in the same sense of circular polarization as transmitted (i.e., the SC sense) as well as in the opposite (OC) sense. The estimate of the ratio of SC to OC echo power, μ_c = 0.14 ± 0.02, indicates that most, but certainly not all, of the backscattering is due to single reflections from surface elements that are fairly smooth at decimeter scales. The value obtained for the OC radar cross section on Aug 26 (1.2 ± 0.3 km²) is about three times larger than those obtained on Aug 23, 24, and 25. The echo bandwidth appears to be within about 1.5 Hz of 5.0 Hz on each date. The photoelectric data suggest a value, P_syn = 19.79 hr, for the synodic rotation period, and yield a composite lightcurve with two pairs of extrema. Combining this value for P_syn with a firm lower bound (4 Hz) on the maximum echo bandwidth yields a lower bound of 1.4 km on the maximum distance between Ra-Shalom's spin axis and any point on its surface.     

Radar observations of asteroid 1998 ML14

Abstract— Goldstone and Arecibo delay‐Doppler radar imaging of asteroid 1998 ML 14 shortly after its discovery reveals a 1 km diameter spheroid with prominent topography on one side and subdued topography on the other. The object's radar and optical properties are typical for S‐class near‐Earth asteroids. The gravitational slopes of a shape model derived from the images and assumed to have a uniform density are shallow, exceeding 30° over only 4% of the surface. If 1998 ML14's density distribution is uniform, then its orbital environment is similar to a planetary body with a spheroidal gravitational field and is relatively stable. Integration of a radar‐refined orbit reveals that the 1998 apparition was the asteroid's closest approach to Earth since at least 1100 and until 2283, when it approaches to within 2.4 lunar distances. Outside of that time interval, orbit uncertainties based on the present set of observations preclude reliable prediction.     

Radar observations of asteroid 1999 JM8

Abstract— We report results of delay‐Doppler observations of 1999 JM8 with the Goldstone 8560 MHz (3.5 cm) and Arecibo 2380 MHz (13 cm) radars over 18 days in July‐August 1999. The images place thousands of pixels on the asteroid and achieve range resolutions as fine as 15 m/pixel. The images reveal an asymmetric, irregularly shaped object with a typical overall dimension within 20% of 7 km. If we assume that 1999 JM8's effective diameter is 7 km, then the absolute magnitude, 15.15, and the average Goldstone radar cross section, 2.49 km², correspond to optical and radar albedos of 0.02 and 0.06, establishing that 1999 JM8 is a dark object at optical and radar wavelengths. The asteroid is in a non‐principal axis spin state that, although not yet well determined, has a dominant periodicity of ?7 days. However, images obtained between July 31 and August 9 show apparent regular rotation of features from day to day, suggesting that the rotation state is not far from principal axis rotation. 1999 JM8 has regions of pronounced topographic relief, prominent facets several kilometers in extent, numerous crater‐like features between ?100 m and 1.5 km in diameter, and features whose structural nature is peculiar. Arecibo images provide the strongest evidence to date for a circular polarization ratio feature on any asteroid. Combined optical and radar observations from April 1990 to December 2000 permit computation of planetary close approach times to within ± 10 days over the interval from 293 to at least 2907, one of the longest spans for any potentially hazardous asteroid. Integration of the orbit into the past and future shows close approaches to Earth, Mars, Ceres, and Vesta, but the probability of the object impacting Earth is zero for at least the next nine centuries.     

Radar observations of the asteroid 2011 UW158

In July 2015 intercontinental bistatic radar observations of the potentially dangerous asteroid 2011 UW158 during its close approach to the Earth were carried out. The asteroid was illuminated at a frequency of 8.4 GHz with the 70-m DSS-14 antenna of the Goldstone Deep Space Communications Complex, while the signal reflected from the asteroid was received with the 32-m radio telescopes of the Quasar VLBI network at the Zelenchukskaya and Badary Observatories. The spectra of the reflected radio signals were obtained. The sizes and rotation period of the asteroid consistent with photometric observations and the ratio of the powers of the reflected signals with left- and right-hand circular polarizations were determined. The derived values suggest that the asteroid has an inhomogeneous surface and a prolate shape. The observations of the Doppler shift of the reflected signal frequency were obtained, which allowed the orbital parameters of the asteroid to be improved.     

Video techniques applied to astrometry

In this work we report on the application of video techniques to the astrometry of fast moving objects in the Solar System. Various phenomena may be observed for astrometric purposes, and two-dimensional photometry is well adapted for this. In this paper we describe in particular the method used to acquire and analyse such observations and we also give the first results obtained concerning two observations of mutual phenomena of the Galilean satellites of Jupiter which occurred during the last (1985) campaign of observations.     

On quasi-satellite periodic motion in asteroid and planetary dynamics

Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is known that quasi-satellite motion is associated with a family of periodic solutions, called family f, which consists of 1:1 resonant retrograde orbits. In our study, we determine the critical orbits of family f that are continued both in the elliptic and in the spatial models and compute the corresponding families that are generated and consist the backbone of the quasi-satellite regime in the restricted model. Then, we show the continuation of these families in the general three-body problem, we verify and explain previous computations and show the existence of a new family of spatial orbits. The linear stability of periodic orbits is also studied. Stable periodic orbits unravel regimes of regular motion in phase space where 1:1 resonant angles librate. Such regimes, which exist even for high eccentricities and inclinations, may consist dynamical regions where long-lived asteroids or co-orbital exoplanets can be found.     

Radar observations and the shape of near-Earth asteroid 2008 EV5

We observed the near-Earth ASTEROID 2008 EV5 with the Arecibo and Goldstone planetary radars and the Very Long Baseline Array during December 2008. EV5 rotates retrograde and its overall shape is a 400 ± 50 m oblate spheroid. The most prominent surface feature is a ridge parallel to the asteroid’s equator that is broken by a concavity about 150 m in diameter. Otherwise the asteroid’s surface is notably smooth on decameter scales. EV5’s radar and optical albedos are consistent with either rocky or stony-iron composition. The equatorial ridge is similar to structure seen on the rubble-pile near-Earth asteroid (66391) 1999 KW4 and is consistent with YORP spin-up reconfiguring the asteroid in the past. We interpret the concavity as an impact crater. Shaking during the impact and later regolith redistribution may have erased smaller features, explaining the general lack of decameter-scale surface structure.     

Radar observations at 3.5 and 12.6 cm wavelength of asteroid 433 Eros

A study of the asteroid 433 Eros using 3.5 and 12.6 cm radar waves indicates that the surface is very much rougher than any planetary or lunar surface observed by this method. A surface completely covered with sharp edges, pits, subsurface holes, or embedded chunks with scale sizes on the order of our wavelengths seems to be indicated. A model based on a rough rotating triaxial ellipsoid having radii in the rotation equator of 18.6 and 7.9 km agrees well with our data, although a strong wobble in the apparent center frequency of the spectra as rotation progresses indicates that one side may be more reflective than the other, or more likely, that the projected axis of rotation does not equally divide the projected area.     

The dynamics of globally active triaxial comets, with applications to asteroid rotation

It is demonstrated how globally distributed outgassing activity on a triaxial comet nucleus bridges the gap between the intuitive Sekanina model, used for comet orbit solutions, and the physics of the problem. In this activity and shape limit, it is shown how a recoil force component, which originates from a day-side restricted sublimation process, is necessary to describe the comet's rotational evolution. Modifications of the non-gravitational force cosines are suggested, with a fundamentally different interpretation than before. Applications to asteroid rotation yield that the ability of specular reflection, of solar photons on an asteroid's surface, to change the asteroid's rotation period and equatorial obliquity, is not dependent on the overall shape of the asteroid.     

Radar observations of asteroid 25143 Itokawa (1998 SF36)

Abstract— We observed 25143 Itokawa, the target of Japan's Hayabusa (MUSES‐C) sample‐return mission, during its 2001 close approach at Arecibo on twelve dates during March 18‐April 9 and at Goldstone on nine dates during March 20‐April 2. We obtained delay‐Doppler images with range resolutions of 100 ns (15 m) at Arecibo and 125 ns (19 m) at Goldstone. Itokawa's average circular polarization ratio at 13 cm, 0.26 ± 0.04, is comparable to that of Eros, so its cm‐to‐m surface roughness probably is comparable to that on Eros. Itokawa's radar reflectivity and polarization properties indicate a near‐surface bulk density within 20% of 2.5 g cm^?3. We present a preliminary estimate of Itokawa's shape, reconstructed from images with rather limited rotation‐phase coverage, using the method of Hudson (1993) and assuming the lightcurve‐derived spin period (12.132 hr) and pole direction (ecliptic long., lat. = 355°, ?84°) of Kaasalainen et al. (2003). The model can be described as a slightly asymmetrical, slightly flattened ellipsoid with extents along its principal axes of 548 times 312 times 276 m ± 10%. Itokawa's topography is very subdued compared to that of other asteroids for which spacecraft images or radar reconstructions are available. Similarly, gravitational slopes on our Itokawa model average only 9° and everywhere are less than 27°. The radar‐refined orbit allows accurate identification of Itokawa's close planetary approaches through 2170. If radar ranging planned for Itokawa's 2004 apparition succeeds, then tracking of Hayabusa during its 2005 rendezvous should reveal Yarkovsky perturbation of the asteroid's orbit.     

Pole orientation of asteroid 44 Nysa via photometric astrometry,including a discussion of the method's application and its limitations

The results of photometric astrometry, a method of determining the orientation of a rotation axis, as applied to asteroid 44 Nysa are presented. The pole orientation of Nysa was found to be λ₀ = 100°, β₀ = +60° with an uncertainty of 10°. The sidereal period is 0^d.26755902 ± 0.00000006, and the rotation prograde. Refinements to, and limitations of, the application of the method of photometric astrometry are discussed. In light of the results presented herein, we believe that all photometric astrometry pole determinations of the past should be redone.     

Applications of interferometers in space to astrometry and planetary detection

Optical and infrared interferometers located outside the Earth's atmosphere should attain fully coherent performance over baselines as long as desired. This new capability should lead, if problems of compensating for angular stability can be solved, to extremely precise measurements of the angular distance between a star and one or more references. This property can be used for astrometric planetary detection, as well as for parallax and proper motion measurements. In addition, the interferometer's high rejection of stray radiation allows the construction of a sensitive direct planetary detection device.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

Radar constraints on asteroid regolith properties using 433 Eros as ground truth

Abstract— Radar data enable us to estimate an asteroid's near‐surface bulk density, thus providing a joint constraint on near‐surface porosity and solid density. We investigate two different approaches to simplifying this joint constraint: estimating solid densities by assuming uniform porosities for all asteroids; and estimating porosities by assuming uniform mineralogy within each taxonomic class. Methods used to estimate asteroids' near‐surface solid densities from radar data have not previously been calibrated via independent estimates. Recent spacecraft results on the chondritic nature of 433 Eros now permit such a check, and also support porosity estimation for S‐class objects. We use radar albedos and polarization ratios estimated for 36 main‐belt asteroids and nine near‐Earth asteroids to estimate near‐surface solid densities using two methods, one of which is similar to the uncalibrated algorithms used in previous studies, the other of which treats Eros as a calibrator. We also derive porosities for the same sample by assigning solid densities for each taxonomic class in advance. Density‐estimation results obtained for Eros itself are consistent with the uncalibrated method being valid in the mean; those derived for the full sample imply that uncalibrated solid densities are, at most, a few tens of percent too large on average. However, some derived densities are extremely low, whereas most porosity estimates are physically plausible. We discuss the relative merits of these two approaches.     

Radar studies of magnetosphere dynamics

Ionospheric radars are an important tool for studying magnetospheric dynamics. The nature of such instruments is described and their application to a number of important problems is discussed, emphasizing South African work. A study of the theory of reflection from irregularities is discussed. The nature of ULF pulsations of more than one type has been elucidated by radar studies. An improvement of the understanding of magnetospheric convection has been achieved. A new HF radar experiment being developed for operation at SANAE, Antarctica, is described. An HF radar will be operated at SANAE in conjunction with the British radar at Halley to provide vector information about magnetospheric convection within that part of the magnetosphere which maps to a large portion of the Antarctic continent. The radar will be part of the SuperDARN international network of radars.     

The PRIMA facility phase-referenced imaging and micro-arcsecond astrometry

This article describes dual-field interferometry, in particular PRIMA, the phase-referenced imaging and micro-arcsecond astrometry facility of the very large telescope interferometer. It uses the simultaneous detection of fringes of two stars in a narrow angle and the accurate measurement of their respective positions. PRIMA aim is threefold: (i) to increase the VLTI limiting magnitude with off-axis fringe tracking, (ii) to reconstruct images with a resolution of 2 mas in K-band, 10 mas in N-band, and (iii) to perform differential narrow-angle astrometry with an accuracy of 10 μas. This article exposes the fundamental and technical limitations of such a technique and presents how PRIMA will try to solve the practical problems of measuring 100-m long optical paths with nanometric accuracy in a ground based interferometer.     

Relativity in astrometry,Celestial mechanics and geodesy

Book review

Relativity in astrometry, Celestial mechanics and geodesySoffel, M. H.: 1989, Springer Verlag, DM 98. (Hardcover) (ISBN 3-540-18906-8)     

Averaged rotational dynamics of an asteroid in tumbling rotation under the YORP torque

The secular effect of YORP torque on the rotational dynamics of an asteroid in non-principal axis rotation is studied. The general rotational equations of motion are derived and approximated with an illumination function expanded up to second order. The resulting equations of motion can be averaged over the fast rotation angles to yield secular equations for the angular momentum, dynamic inertia and obliquity. We study the properties of these secular equations and compare results to previous research. Finally, an application to several real asteroid shapes is made, in particular we study the predicted rotational dynamics of the asteroid Toutatis, which is known to be in a non-principal axis state.