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Ostro et al.: Asteroid Radar Astronomy 151 Asteroid Radar Astronomy Steven J. Ostro Jet Propulsion Laboratory, California Institute of Technology R. Scott Hudson Washington State University Lance A. M. Benner and Jon D. Giorgini Jet Propulsion Laboratory, California Institute of Technology Christopher Magri University of Maine at Farmington Jean-Luc Margot California Institute of Technology Michael C. Nolan Arecibo Observatory Radar is a uniquely powerful source of information about the
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  Ostro et al.:Asteroid Radar Astronomy 151151 Asteroid Radar Astronomy Steven J. Ostro  Jet Propulsion Laboratory, California Institute of Technology R. Scott Hudson Washington State University Lance A. M. Benner and Jon D. Giorgini  Jet Propulsion Laboratory, California Institute of Technology Christopher Magri University of Maine at Farmington Jean-Luc Margot California Institute of Technology Michael C. Nolan  Arecibo Observatory Radar is a uniquely powerful source of information about the physical properties and orbitsof asteroids. Measurements of the distribution of echo power in time delay (range) and Dop-pler frequency (radial velocity) produce two-dimensional images that can provide spatial reso-lution as fine as a decameter if the echoes are strong enough. With adequate orientationalcoverage, such images can be used to construct detailed three-dimensional models, define therotation state precisely, and constrain the object’s internal density distribution. As of May 2002,radar signatures have been measured for 75 main-belt asteroids (MBAs) and 105 near-Earthasteroids (NEAs). We summarize specific results for radar-detected asteroids, which span 4 or-ders of magnitude in diameter and rotation period. Radar has revealed both stony and metallicobjects, principal-axis and complex rotators, smooth and extremely rough surfaces, objects thatmust be monolithic and objects that probably are not, spheroids and highly elongated shapes,contact-binary shapes, and binary systems. Radar also has expanded accurate orbit-predictionintervals for NEAs by as much as several centuries. 1.INTRODUCTION One of the goals of this book is to outline developmentssince  Asteroids II  (  Binzel et al., 1989), which was completedin 1988. The subsequent 13 years have seen critical devel-opments in technical aspects of asteroid radar astronomy,including increases in sensitivity and versatility of tele-scopes, the evolution and optimization of observationaltechniques, and the invention of analytical methods to opti-mize extraction of information from radar images. Observa-tions commensurate with those developments have raisedthe number of radar-detected asteroids from 52 (19 NEAs +33 MBAs) in mid-1988 ( Ostro, 1989) to 180 (105 NEAs +75 MBAs) in May 2002 and have produced an enormousbody of information about the physical properties of aster-oids. An equally significant development since  Asteroids II  is an increase in the number of persons lead-authoring aster-oid radar papers at an average rate of one person per year.The following sections outline the technical develop-ments and observational highlights of the past 13 years,summarize the major conclusions drawn from the explo-sive increase in data, and discuss current problems and chal-lenges to be faced during the coming decade. See Ostro (2002a) for a list of radar-detected asteroids, Ostro (1993,2002b) for reviews of planetary radar principles and tech-niques, Ostro (1994) for a discussion of radar’s role in NEOhazard identification and mitigation, and  Harmon et al. (1999) for a review of radar observations of comets. 2.STRATEGIES, TELESCOPES, ANDTECHNICAL DEVELOPMENTS2.1.Telescopes and Observing Strategies The basic strategy of an asteroid radar experiment is tomeasure the distribution of echo power in time delay andDoppler frequency, usually in the opposite sense (OC) of circular polarization as transmitted as well as in the samesense (SC) as a function of the object’s orientation andplane-of-sky (POS) direction. SC echo would be absent in  152  Asteroids III  mirrorlike backscattering from surface elements for whichsize and radius of curvature are huge compared to the wave-length, but would become increasingly significant if thereis near-surface “roughness” at scales near the wavelengthor any kind of multiple scattering. Hence SC/OC is a mea-sure of near-surface structural complexity (see section 3).The achievable delay/Doppler resolution depends first of all on the echo’s signal-to-noise ratio (SNR), the ratio of echo power to the root-mean-square receiver noise. TheSNR depends primarily on the target’s distance R tar , diam-eter D tar , and rotation period P; the telescope’s effective areaA and transmitter power P tx ; and the integration time ∆ tSNR ~ R tar–4 D tar3/2 A 2 P tx P 1/2   ∆ t 1/2 (1)The integration time needed to achieve any given signal-to-noise ratio for a given target increases as R tar8 A –4 . This iswhy the 305-m Arecibo telescope and the 70-m Goldstoneantenna (DSS-14) are almost entirely responsible for thehistory of asteroid radar, why we try to observe asteroidsat their closest approaches to Earth, and why observationsof extremely close NEAs are especially lucrative.A major structural upgrading of the Arecibo telescopeand modernization of its computer hardware and softwarehave made it an order of magnitude more sensitive andmuch more versatile than it was a decade ago. Transmitterupgrades and installation of a quasioptical transmit/receiveswitch on DSS-14 have increased its effectiveness for NEAradar astronomy by reducing the switching time from ~20 sto ~1 s. Arecibo can see almost twice as far as Goldstone,but Goldstone’s greater steerability gives it access to twiceas much sky and lets it track objects at least 3× longer thanArecibo. For very close targets, transmit/receive switchingand transmitter on/off cycling has been avoided by transmit-ting continuously from DSS-14 and receiving continuouslywith DSS-13, a 34-m antenna 22 km from DSS-14 and con-nected to it by a fiber-optics cable. The complementarity of Arecibo and Goldstone has been exploited frequently.Given unlimited echo strength, the delay resolution islimited by the rate at which signals produced by availabletransmitter amplifier tubes (klystrons) can be modulated,currently about 20 MHz, which corresponds to 0.05 µs(7.5 m of range), compared to 2 µs (300 m) when  Aster-oids II  was written. The transmitted signal travels the round-trip distance to the target and the echo is measured usingwhat is effectively an extremely sensitive voltmeter, theoutput of which is sampled and digitized. The received volt-age is optionally divided into time-delay cells, and then aT coh -long coherent time series of voltage samples within agiven time-delay cell is Fourier-transformed to produce aspectrum of the echo power within that cell with a resolu-tion of  ∆ f = T coh–1 . Because of the intrinsically noiselikenature of the voltage samples (  Jenkins and Watts, 1968), theSNR of a single-power spectrum will generally be <3 foreven the strongest radar echo. The fractional noise (domi-nated by thermal noise for weak echoes or by “self-noise”for strong ones) in a sum of N   such “looks” is N –1/2 , so it isdesirable to sum many looks. Even when the echo strengthoverwhelms the thermal noise of the receiver, one some-times chooses to increase N in order to reduce the self-noise,consequently sacrificing frequency resolution. Thus, a delay-Doppler image is intrinsically a time exposure, combiningcoherent integration in the Fourier analysis with incoherentintegration in the sum of independent looks. The optimum ∆ f for an image with a given tolerable level of noise willdepend in part on the echo bandwidth, and hence on the tar-get’s size and spin state (see section 2.3).At radio frequencies, the phase of the electromagneticfield is maintained all the way to the samplers, so the Fourieranalysis and summing of looks can be done in software afterthe fact, allowing SNR to be traded for frequency resolutionin the data reduction rather than during the data acquisition.However, measurement of range information requires cod-ing of the transmitted signal, so the range resolution must bechosen before beginning the experiment.During an observation, one can remove the Doppler fre-quency shift  ν introduced by the radial motion of the targetby tuning the frequency of either the transmitter or the re-ceiver according to a Doppler-prediction ephemeris, withthe goal of ensuring that the frequency corresponding toechoes from the target’s center of mass (COM) is zero inthe coordinate system of the acquired data. The Dopplershift varies as the target moves and as the Earth rotates, andit must be adjusted many times per second. One also usesthe prediction ephemerides to slew the time base for sam-pling the echoes in order to register sequential samples of echoes from any given range cell on the target. In practice,there will always be a nonzero error ∆ν eph in the Doppler-prediction ephemeris, which is equivalent to a nonzero rateof change in the delay-ephemeris’ error ∆τ eph and hence inthe rate of image smearing in delayd ∆τ eph (t)/dt = – ∆ν eph (t)/F tx (2)where F tx is the transmitter carrier frequency (2380 MHz forArecibo; srcinally 8495 MHz for Goldstone but changedto 8510 MHz in September 1991 and then to 8560 MHz inMarch 1999). Thus a reasonably accurate Doppler ephem-eris is a prerequisite for imaging with fine range resolution.Main-belt asteroids that enter the current radar detect-ability windows usually have many decades of accumulatedoptical astrometry, so preradar pointing uncertainties typi-cally are on the order of 1 arcsec, Doppler uncertainties aresmall compared to the intrinsic frequency dispersion of theechoes, and delay uncertainties are typically of the sameorder as the object’s diameter. For MBA experiments to date,echo strength has been the only factor that has limited ob-tainable delay-Doppler resolution.For NEAs, the accuracy of the ephemerides is often amajor concern, and for newly discovered objects it is critical,because ephemeris accuracy decays away from the intervalspanned by astrometric data. Often, unless follow-up opticalastrometry is obtained between the date of a discovery an-nouncement and the date when an initial radar observation is  Ostro et al.:Asteroid Radar Astronomy 153attempted, the pointing uncertainty will be large comparedto the ~2-arcmin widths of the Arecibo and Goldstone radarbeams. In practice, to avoid an intolerable sacrifice of sensi-tivity, pointing should be good to at least 15 arcsec. Onceechoes have been detected, even coarse Doppler astrometry isadequate to shrink the orbit uncertainties enough to ensure suf-ficient pointing accuracy throughout the discovery apparition. 2.2.Radar Astrometry Radar reconnaissance of a new NEA generally proceedsfrom detection and Doppler-ephemeris refinement using acontinuous-wave (cw, or monochromatic) waveform to delay-ephemeris refinement using a time-modulated waveform(generally a binary-phase-coded waveform; J. K. Harmon,in preparation, 2002) with a fairly coarse delay-resolutioncell (called a baud), to the finest-baud and finest- ∆ f imag-ing supported by the echo strength. In optimizing a setup’stradeoffs between time resolution, spatial resolution, andnoise level, one must consider the accuracy of the delay-Doppler ephemeris and whatever is known about the target’ssize and spin state. Since NEA radar windows are short andtelescope time is precious and difficult to obtain on shortnotice, rapid refinement of orbits and ephemerides usingradar astrometry is critical. Installation of onsite softwareat Goldstone and Arecibo has permitted radar detection of several newly found NEAs within 12 h of the discovery an-nouncement (1999 TY2, 2001 AV43, and 2001 FR85, all atArecibo) and has dramatically sped up the progression fromcw detection to high-resolution imaging (only 15 min for2001 FR85).Almost all radar astrometry ( Giorgini, 2002; see also Ostro et al., 1991a, and Yeomans et al., 1992) reports thetime delay and/or Doppler frequency (at a given transmit-ter frequency) corresponding to echoes from the target’scenter of mass received at a specific UTC epoch and at aparticular telescope reference point; the transmitting tele-scope’s reference point also is specified. For most anten-nas, the reference point is the intersection of the elevationand azimuth axes.As an example of radar astrometry, imaging of Toutatis( Ostro et al., 1995a) using transmissions from DSS-14 andreception at DSS-13 yielded estimates of the 8510-MHzDoppler frequency, 248335.943 ± 0.04 Hz, and time delay,26.056497203 s ± 0.23 µs, corresponding to echoes from theasteroid’s center of mass received at December 6, 1992,16:40:00 UTC. These points’ residuals with respect to themost recent Toutatis orbit are –0.098 Hz and 0.268 µs, sotheir fractional precision is 10 –8 for the delay and 10 –6 forthe Doppler.The fine fractional precision of radar astrometry plus itsorthogonality to optical angle measurements make it pow-erful for refining orbits. A single radar detection secures theorbit well enough to prevent “loss” of a newly discoveredasteroid ( Yeomans et al., 1987). Table 1 lists residuals at thefirst post-discovery-apparition recovery of several NEAs, foran orbit using just optical data and also for an orbit usingboth radar and optical data. Table 2 demonstrates how ra-dar shrinks the sky area that must be searched for a givenprobability of recovering several NEAs observed only dur-ing their discovery apparition.With radar astrometry, the length of the interval overwhich an asteroid’s orbit can be calculated with a given levelof accuracy can be increased by decades or centuries evenfor multiapparition NEAs. Let us give two examples, de-fining a “reliable” prediction interval as one that encom-passes all those approaches to within 0.1 AU from Earth forwhich the 3 σ uncertainty in the date of closest approach isless than 10 d. Then for Toutatis, observed with radar dur-ing the last three of its five optically observed apparitions,the optical-only interval is 1353–2262 and the radar + op-tical interval is 1353–2532; uncertainty associated with thevery close Earth approach in 1353 precludes reliable iden-tification of earlier close Earth approaches. For the single-apparition object 2001 CP36, the optical-only interval is1989–2004 and the radar + optical interval is 1718–2225.Ephemeris uncertainties are strategically important atevery stage of an asteroid radar experiment and normallyare calculated whenever new radar or optical astrometrywarrants orbit refinement. Thus, every astrometric measure-ment lets one assess the accuracy of both the observingephemeris and the uncertainties that had been calculated forit. Similarly, postfit residuals (observations minus the val-ues calculated from the orbit solution) let one assess theaccuracy both of the astrometry and the uncertainty quotedfor it (Table 3). TABLE1.Residuals for past near-Earth-asteroid recoveries.ObjectRecovery DateORO/R1989 PB (4769 Castalia)May 199024 0.4 601991 AQSeptember 199457°0.1°3801986 DA (6178)October 199456 0.9 601991 JX (6489 Golevka)March 19953600 4.6 7801986 JK (14827)April 2000114°0.1°910Here O represents the residual (i.e., the observed position minus the predictedposition) for an orbit solution incorporating only optical astrometry. R representsthe residual for an orbit solution using radar as well as optical. O/R is the ratio of residuals for the two cases.  154  Asteroids III  When ephemeris uncertainties become smaller than theintrinsic delay-Doppler dispersion of a target’s echoes, thechallenge becomes to locate the target’s COM in the delay-Doppler image plane. The accuracy of this process rests onhow well one knows the target’s size and shape. Thus, orbitrefinement is tightly coupled to determination of physicalproperties:Radar measurements that produce new infor-mation about a target’s size, shape, rotation, or surface prop-erties generally have astrometric value, and vice versa. 2.3.Radar Estimation of Shapes and Spin States Interpretation of radar images is complicated by the ge-ometry of the delay-Doppler projection (Fig. 1). Constant- TABLE2.Search areas for future near-Earth-asteroid recoveries.Most FavorableEarth-basedAstrometry3 σ Search Area (arcsec 2 )ObjectRecovery DateData Span (d)OpticalDopplerDelayGap (yr)ORO/R1990 OSNovember 2003132620134.8E84.5E61062000 EH26July 20051404942425772675381998 ML14August 201322523466151.9E73.8E5492001 AV43November 2013384210128.9E71.8E6491998 KY26May 202411207222614568168871999 TY2October 2064511010652.3E71.0E6232001 FR85March 208173631801.6E71.7E4956Each of these objects was observed optically over a short timespan and also was a radar target of opportunity, resulting in the listednumbers of optical (RA + DEC), Doppler, and delay measurements. On the right, we give the total sky area for the 3 σ orbit-determi-nation uncertainties mapped onto the sky at the next favorable Earth-based recovery date (which we define as the next time when theapparent visual magnitude exceeds 20 during reasonable sky-brightness conditions) for both an optical-data-only (O) orbit solutionand a radar + optical-data (R) orbit solution. The O/R ratio conveys how a handful of radar measurements can reduce sky search areasfor an object with minimal optical followup astrometry. Dynamical peculiarities unique to each object, such as the number of plan-etary close approaches, affect these results. For example, 1999 TY2 is unusual in that its 23° inclination to the ecliptic reduces theeffects of in-plane gravitational perturbations, which shrinks mapped uncertainties.TABLE3.Radar astrometry residuals.AntennasNormalized Doppler ResidualsTXRCVmean σ RMSNAreciboArecibo–0.1190.45470.467994DSS 14DSS 14–0.1600.79150.8041113DSS 14DSS 13–0.4551.0951.14412HaystackHaystack–0.4520.15520.46542DSS 14Evpatoria0.16290.59980.605218Sites combined (Doppler):0.014150.69910.6978239AntennasNormalized Delay ResidualsTXRCVmean σ RMSNAreciboArecibo0.000440.69190.686868DSS 14DSS 14–0.25100.69490.735188DSS 14DSS 13–0.46352.1542.12714Sites combined (delay):–0.16790.90410.9170170Doppler/delay combined:–0.061530.79490.7963409Statistics for normalized Doppler and delay postfit residuals (r i , the measurement minusthat predicted by a weighted-least-squares estimate of the orbit from all optical and ra-dar astrometry, normalized by the measurement uncertainty assigned by the observer)obtained from 1968 through March 2001. Here RMS = [ Σ (r i2 )/N] 1/2 and the standard de-viation ( σ ) equals { Σ [(r i –  r 2 ]/(N – 1)} 1/2 , with N the number of observations and  r themean residual. Arecibo has historically produced the lowest-noise, least-biased astrometry,followed by DSS-14 (Goldstone). Most of the DSS-13 (Goldstone) astrometry is from theDecember 1996 Toutatis campaign. Evpatoria results are from the Golevka experimentin 1995. Haystack results are from observations published of asteroid 1566 Icarus in 1968.
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