Steven J. Ostro, Jean-Luc Margot, Lance A. M. Benner, Jon D. Giorgini, Daniel J. Scheeres, Eugene G. Fahnestock, Stephen B. Broschart, Julie Bellerose, Michael C. Nolan, Christopher Magri, Petr Pravec, Petr Scheirich, Randy Rose, Raymond F. Jurgens, Eric M. De Jong, Shigeru Suzuki.

*Science* **314**, 1276-1280 (2006)

**ABSTRACT**

**
High-resolution radar images reveal near-Earth asteroid
(66391) 1999 KW4 to be a binary system. The ~1.5-km diameter
primary (Alpha) is an unconsolidated
gravitational aggregate with spin period ~2.8 h, bulk
density ~2 g/cm^3, porosity ~ 50%, and an oblate shape
dominated by an equatorial ridge at the object's potential
energy minimum. The ~0.5-km secondary (Beta) is
elongated and probably is denser than Alpha. Its average
orbit about Alpha is circular with radius ~2.5 km and
period ~17.4 h, and its average rotation is synchronous
with the long axis pointed toward Alpha, but librational
departures from that orientation are evident. Exotic
physical and dynamical properties may be common
among near-Earth binaries.
**

Daniel J. Scheeres, Eugene G. Fahnestock, Steven J. Ostro, Jean-Luc Margot, Lance A. M. Benner Stephen B. Broschart, Julie Bellerose, Jon D. Giorgini, Michael C. Nolan, Christopher Magri, Petr Pravec, Petr Scheirich, Randy Rose, Raymond F. Jurgens, Eric M. De Jong, Shigeru Suzuki

*Science* **314**, 1280-1283 (2006)

**ABSTRACT**

**
Dynamical simulations of the coupled rotational and orbital dynamics of binary near-Earth
asteroid (66391) 1999 KW4 suggest that it is excited due to perturbations from the sun during
perihelion passages. Excitation of the mutual orbit will stimulate complex internal motions,
including periodic fluctuations in the orbit and in the magnitude of the angular momentum of
the primary component, and oscillations in the rotational dynamics and orbital mechanics of
the smaller component that cause its attitude relative to uniform rotation to have large
variation within some orbits and to hardly vary within others. The primary's proximity to
its rotational stability limit suggests an origin from spin-up and disruption of a loosely
bound precursor within the past million years.
**

**Another animation showing the KW4 system viewed from Earth as it moved across the sky
from 2001 May 21 to June 12 is available
here.
**

**
ANIMATIONS OF RADAR IMAGES:
**

**
Goldstone radar images from May 21-29.
**

**
Arecibo radar images from May 29.
**

Fig. 1. Single-date, multi-run sums. Sums of delay-Doppler radar images obtained with Arecibo (left) and Goldstone (right) on each observation date. These sums are long time exposures (table S1) that show the orbital phase coverage of the secondary component (Beta) in each observing sequence. The pairs of Arecibo time exposures on May 26-28 correspond to radar setups with slightly different Doppler frequency resolutions (table S1). The radar is toward the top, rotation and orbital motion are counterclockwise, and each image has a height of 5625 m (37.5 microseconds of roundtrip time delay) and 117.2 cm s-1 of line-of-sight velocity (Doppler frequency of 18.6 Hz at Arecibo's 2380- MHz transmitter frequency or 66.9 Hz at Goldstone's 8560- MHz frequency). Vertical smear of the primary component (Alpha) due to motion about the system barycenter is evident in the long Goldstone exposures.

Fig. 3. Examples of images and fit results. Each three-frame horizontal collage shows an Arecibo radar image used in the estimations, the corresponding image synthesized from the shape model, and a plane-of-sky (POS) view of that model. Each three-frame collage consists of three squares with 2.0- km sides for Alpha and 0.8-km sides for Beta. In the delay- Doppler images, the radar is toward the top and the object rotates counterclockwise. In the POS frames, north is toward the top and the arrow represents the spin vector. The Alpha collages show images obtained on (top to bottom) May 26, 26, 27, 27, 27, 28, 28, 29, 29. The Beta collages show images obtained on May 26, 26, 27, 27, 28, 28, 29, 29, 29. See (29) for tabulation of all images used in the shape modeling and corresponding three-frame collages.

Fig. 4. Principal-axis views of the Alpha (top) and Beta shape models. Yellow-shaded regions were not viewed in Arecibo images at incidence angles less than 70 degrees. Since their modeling relied heavily or entirely on Goldstone images, which are weaker than the Arecibo images, the accuracy of our reconstruction probably is lower there than for the rest of the model.

Fig. 5. Principal-axis views of the Alpha (top) and Beta shape models. Colors indicate effective gravitational slope (the angular deviation from the local downward normal of the total acceleration vector due to gravity and rotation), calculated using the model densities (Table 2). Alpha's slopes average 28º with a maximum of 70º, while Beta's average 9º with a maximum of 18º.Principal-axis views of the Alpha (top) and Beta shape models. Colors indicate effective gravitational slope (the angular deviation from the local downward normal of the total acceleration vector due to gravity and rotation), calculated using the model densities (Table 2). Alpha's slopes average 28º with a maximum of 70º, while Beta's average 9º with a maximum of 18º.

Table 1. Relative orbit of Beta about Alpha. Least-squares estimates of the elements of the average 2001-2002 relative orbit are given in the J2000 equatorial frame along with their standard errors and correlation matrix. The epoch, T, which corresponds to calendar date 2001 May 26 09:55:00.5 represents the time at which Beta is at pericenter. # and i correspond to a pole direction at right ascension = 15.4º + 3º and declination = -66.1º + 2º. Our estimate of PORBIT from Beta-Alpha delay-Doppler differences, 1045.34 + 2.16 min, is marginally compatible with our estimate of PORBIT, 1048.18 + 1.15 min, from modeling of mutual events observed in optical lightcurves during 2001 June 3-12 (2) with the orbital pole fixed at the radar estimate (26). [A decrease in the number of revolutions of Beta around Alpha by one between the 2001 and 2002 epochs of the radar measurements corresponds to an increase in orbital period of 2.04 min. There are solutions that fit the radar data with an orbital period of 1047.38 min, but not without a statistically unacceptable increase (25%) in the chi-square value.]

Table 2. Alpha and Beta model characteristics. The Alpha model has 4586 vertices and 9168 facets, with mean edge length 39 m and effective angular resolution of 3º. The Beta model is a spherical harmonics representation of degree and order 8 realized with 1148 vertices and 2292 facets, with mean edge length 26 m and effective angular resolution of 7º. The positive side of Alpha's longest principal axis (+x) is on the plane of the sky and approaching Earth on 2001 May 25 at 12:23:21. We assumed uniform internal density and principal-axis rotation about the z axis. The dynamically equivalent equal-volume ellipsoid (DEEVE) is the homogeneous ellipsoid having the same moment-of-inertia ratios and volume as the model. The assigned standard errors include our assessment of systematic effects. The uncertainties in the components' individual masses include contributions from the uncertainty in the system's total mass (Table 1) and from the uncertainty in the determination of the mass ratio. Uncertainties in densities and other ratios are calculated using Fieller's Theorem. Our value for Alpha's spin period agrees with the value, 2.7650 +- 0.0004 h, derived from lightcurves by Pravec et al. 2006. Digital versions of the models in Wavefront format are available at http://echo.jpl.nasa.gov/asteroids/shapes/kw4a.obj and ../kw4b.obj.

Evolution of KW4's orbit (A) semi-major axis and (B) eccentricity over 2 weeks, computed for the relaxed and excited orbit and Beta states.

(A) Rotational angular velocity and (B) total angular acceleration of Beta, shown in the Beta fixed frame, for the relaxed and excited cases. (C) shows Alpha's orbit in a Beta-fixed frame. The large y variations are due primarily to Beta's attitude libration about the Beta-Alpha line.(A) Rotational angular velocity and (B) total angular acceleration of Beta, shown in the Beta fixed frame, for the relaxed and excited cases. (C) shows Alpha's orbit in a Beta-fixed frame. The large y variations are due primarily to Beta's attitude libration about the Beta-Alpha line.

Curves of constant geopotential about Alpha (A) without and (B) with Alpha's pole-on shape superimposed. Four equilibrium points, orbits that are stationary in the frame rotating with Alpha, are indicated by "e" and lie just at the body's surface. Alpha's surface lies outside of the innermost curve, defined for the equilibrium point with the lowest potential value.

Last update: 2011 October 10