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Radar observations of asteroid 1580 Betulia
ICARUS 40, 350--354 (1979)
Radar Observations of Asteroid 1580 Betulia GORDON H. PETTENGILL, STEVEN J. OSTRO,~ AND IRWIN I. SHAPIRO Department o f Earth and Planetary Sciences, Massachusetts Institute o f Technology, Cambridge, Massachusetts 02139
BRIAN G. MARSDEN Smithsonian Astrophysical Observatory, Cambridge, Massachusetts 02138 AND
DONALD B. CA MPBE L L National Astronomy and Ionosphere Center, z Arecibo, Puerto Rico 00613 Received March 15, 1979; revised May 22, 1979 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 km ~ 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.
INTRODUCTION
In May 1976, the Amor asteroid 1580 Betulia passed within 0.14 AU of Earth and provided astronomers with an excellent opportunity to study it. Optical observations disclosed a lightcurve with three maxima and three minima, suggesting the presence of a major surface inhomogeneity on one side (Tedesco et al., 1978); in addition, its visual geometric albedo was found to be ~<0.05 (Lebofsky et al., 1978), surprisingly low compared to that of other Marscrossing asteroids. Here we present results from radar observations of Betulia made at the Arecibo Observatory. OBSERVATIONS
Although the declination of Betulia at opposition on 22 May 1976 placed it outside ~ Present address: National Astronomy and Ionosphere Center, Cornell University, Ithaca, N e w York 14850. 2 Operated by Cornell University under contract with the National Science Foundation and with support from the National Aeronautics and Space Administration.
the antenna coverage of the Arecibo Observatory, its position during the preceding week was ideal for radar investigation. Our observations, at a radar wavelength of 12.6 cm, were made during this period on the early mornings of 18 and 19 May 1976. On these dates, the roundtrip echo time delays were about 150 and 143 sec, respectively. The observations were broken into 5-min cycles, each consisting of a 40-sec set-up time leading into the transmission, for approximately 130 sec, of a 2380-MHz, unmodulated, right-circularly polarized signal, followed immediately by reception for an equal period of the Doppler-shifted echo in the orthogonal circular ( " P C " ) sense of polarization. The PC sense was chosen in the hope of maximizing the echo strength, since coherent reflection favors this polarization sense. The declination of Betulia, coupled with the limited sky coverage of the Arecibo antenna, precluded more than 12 such transmit-receive cycles (runs) per day. Using an ephemeris prepared at MIT and based on orbital elements supplied by the Smithsonian Astrophysical Observa-
350 0019-1035/79/120350-05502.00/0 Copyright © 1979by Academic Press, Inc. All rights of reproduction in any form reserved.
RADAR OBSERVATIONS OF BETULIA tory, we continuously adjusted the receiver frequency to compensate for the anticipated Doppler shift caused by the line-of-sight motion of Betulia relative to the radar. Each run was segmented into 130 successive 1-sec data sets, which were individually Fourier analyzed; the corresponding frequency components from each data set were incoherently summed, yielding an echo power spectrum having approximately l-Hz resolution. A total of 11 and 9 such power-spectra were obtained from the observations on 18 and 19 May, respectively. The spectra obtained from a weighted average of the runs for each day are shown in Fig. 1. Values of the radar cross section corresponding to the total echo power for each run are given in Table I. DISCUSSION
The echo spectra appear quite fiat, with steep edges. From visual inspection of each
2:[
BETULIA
MAY
TABLE I MEASUREMENTS OF RADAR CROSS SECTION O'oc FOR BETULIA FROM INDIVIDUAL, 5-MIN RUNS a
Date (1976)
Mean time of reception (UTC) (hr)(min)(sec)
Radar cross section (kin2)
Rotational phase angle (deg)
May 18
05 22 20 05 34 20 05 40 20 05 46 20 05 52 32 05 58 45 06 04 20 06 10 20 06 16 20 06 25 20 06 31 20
2.50 1.53 0.60 0.50 2.07 2.07 2.34 2.42 2.52 2.58 1.72
314.8 326.5 332.4 338.3 344.3 350.4 355.9 1.7 7.6 16.4 22.2
May 19
05 28 16 05 34 16 05 40 16 05 46 16 05 52 16 05 58 16 06 04 16 06 10 16 06 16 16
3.24 2.86 3.44 2.96 2.11 1.48 2.71 2.80 2.27
288.2 294.1 299.9 305.8 311.7 317.5 323.4 329.3 335.1
a The origin of rotational pha s e is consistent with Fig. 15 of Tedesco et al. (1978).
of the two spectra, we obtain an estimate of the mean limb-to-limb bandwidth: fLL = 26.5 --+ 1.5 HZ (standard error). For a spherical target o f rotation period, P , the radius is given by
A e3 > 18
351
1976
P
R = APfLL/(87r sin 8),
lco
A,~,r~A ,, IV.~_._ L, ...A
v"vv,'V',,'"" ' V l t V ' ~
w
I~. ~A ^^~ v-w'v'~
o (3_
-
{
I 9
MAY
1976
vw " v~, ,,'~,jv,r,-- V "" L -20o
V'V -,,~,v
{ i l l { -150 - I O 0 - 5 0 0 50 DOPPLER FREQUENCY (HZ)
vV~ i 10o
FIG. l. Power s p e c t r a for echoes from the asteroid 1580 Betulia o b s e r v e d on 18 and 19 May 1976. Rec e i v e d power, in units of standard deviations of associated noise, is plotted as a function of Doppler shift. Zero Do ppler shift c o r r e s p o n d s to our least-squares estimate of the center frequency of the echo s p e c t r u m (see text). The sp ectra have been s m o o t h e d to a resolution of 3 Hz.
where h is the length of a radar wave and 8 is the angle between the target's rotation axis and the radar line of sight. Analysis of Betulia's visible-wavelength lightcurve by Tedesco et al. (1978) yielded a value of 6.130 _+ 0.006 hr for the synodic rotation period. H o w e v e r , the shape, scattering law, and pole position of Betulia are poorly known. Thus, we may calculate only a lower limit for the radius of 2.9 _+ 0.2 km from the apparent bandwidth of the echo spectrum. Lebofsky et al. (1978) analyzed broadband visual and 10.6-tzm photometric observations using the "radiometric m e t h o d . " This technique yields estimates for Betulia's radius and visual geometric albedo p
352
PETTENGILL ET AL.
which depend critically on how the thermal response of the surface is modeled. L e b o f s k y et al. investigated the consequences of two models. F r o m the first model, which postulates a low-thermalinertia surface (similar to the lunar regolith), they obtained: R -- 2. l0 _+ 0.40 km and p -- 0.108 _ 0.012. From the second model, which assumes a relatively highthermal-inertia surface (e.g., bare rock), they obtained: R = 3.74 _+ 0.17 km and p -- 0.034 _ 0.004. Pursuing a different route using a well-established empirical relation between visual polarization and albedo, Tedesco estimated values for R of 3.3_+ 0.2 km and for p of 0.04_+ 0.01. Thus, all values for the radius except the smaller of the radiometric values are reasonably consistent with R = 3.5 kin, if a minimum value for 8 of about 55° is invoked. Approximating the angular behavior of the scattering by cos ~ O, where O is the angle of incidence to the mean (spherical) surface, we obtained weighted-leastsquares estimates of three parameters: the scattering law exponent n, an amplitude scale factor tr', and the Doppler shift v referenced to the center of the spectrum for the model. The value of R sin 8 was constrained for reasons discussed by Campbell et al. (1978) in connection with a similar analysis for the Galilean satellites. Estimates of v, valid for 2.0 -< R -< 3.6 km, are given in Table II. The weighted mean of the estimates for n is 1.0 _ 0.2, implying that the asteroid appears uniformly bright under 12.6-cm wavelength illumination. H o w e v e r , if Betulia's actual shape is significantly nonspherical, or the polar aspect is substantially different from normal, the physical meaning to be attached to the estimate of n is less clear and our model becomes merely a convenient tool for the estimation of the center frequency of the echo spectrum. The mean value and standard deviation of the radar cross section troc for Betulia, as determined from the entries in Table I, are
TABLE II DOPPLER SHIFTS AT MHz a DETERMINED FOR BETULIA ON 18 AND 19 MAY 1976 Date (1976)
Mean time of reception (UTC) (hr)(min)(sec)
Doppler shift for transmitted frequency of 2380 MHz
(Hz) 18 May 19 May
05 56 50 05 52 16
225,980.0 _+ 1.0 186,012.5 _+ 1.0
a Estimates of Doppler shifts and their associated standard errors have been rounded to the nearest multiple of 0.5 Hz.
2.2 - 0.8 km". Figure 2 shows the radar cross section plotted as a function of the rotational phase ~ . The large excursion in O-oc may result, in part, from statistical and systematic sources of error. The difference between independent determinations of cross section near = 335° on the two dates may be due to tracking problems associated with the first use of a new feed at Arecibo. But some of the variation in cross section with rotational phase may be physically significant. The visual lightcurve for Betulia exhibited three maxima and three minima and could result, for example, from a prolate object rotating about a minor axis (Tedesco et al. 1978). Figure 2 shows that the radar observations were concentrated around the second minimum (m2) in the visual lightcurve and that no radar data were obtained at phases corresponding to visual maxima. If the model of Tedesco et al. is valid, the long axis of Betulia was not oriented normal to the line o f sight during the radar observations, possibly accounting for the fact that the polarimetric estimate of R is about 14% higher than the radar lower limit. Unfortunately, the spectra from single 130-sec runs do not have sufficiently high signal-to-noise ratios to permit the extraction of individual estimates of R. The 12.6-cm reflectivity of Betulia, expressed as the normalized radar cross section &oc -= troc/zrR 2, is obviously difficult to
RADAR OBSERVATIONS OF BETULIA ~--4( :E
A
z~
A
A
. . . . .
AA A AA AA
~
~ 2.C o 1:3
AA
MI
I 270 °
t
m2
l
300 ° 330 ° ROTATIONAL PHASE
I 0°
50 °
FIG. 2. Measurements of the radar cross section (roe of Betulia from individual 5-min runs (see Table I), plotted as a function of rotational phase @. Results for 18 (19) May 1976 are denoted by solid (open) triangles. The dashed line at 2.2 km2 shows the mean value. The origin o f ~ is based on Fig. 15 of Tedesco et al. (1978). Values of phase corresponding to the first maximum (M1) and second minimum (m2), as reported by Tedesco et al., are indicated.
establish without an accurate estimate of target size a n d shape. S u b s t i t u t i n g the r a d a r result (R -> 2.9 + 0.2 km) yields &oc -< 0.08 _+ 0.03, a n u p p e r limit w h i c h is v e r y close to the a v e r a g e n o r m a l i z e d cross s e c t i o n for the M o o n a n d t e r r e s t r i a l p l a n e t s , a l t h o u g h we note that the r a d a r b a c k s c a t t e r ing for t h e s e targets is m u c h m o r e s h a r p l y p e a k e d (i.e., " q u a s i - s p e c u l a r " ) t h a n for Betulip (Pettengill, 1978). S u b s t i t u t i n g the i n f r a r e d - r a d i o m e t r i c v a l u e (R = 3.7 --- 0.2 kin) gives &oc -- 0.05 _+ 0.02, a v a l u e w h i c h is a l m o s t as l o w as that d e t e r m i n e d for C e r e s (6-oc = 0.04 _ 0.02; O s t r o e t al., 1979). Three other Apollo-Amor asteroids have b e e n d e t e c t e d b y radar: 1566 I c a r u s (Goldstein, 1968, 1969; P e t t e n g i l l e t a l . , 1969), 1685 Toro ( G o l d s t e i n e t al., 1973), a n d 433 E r o s (Jurgens a n d G o l d s t e i n , 1976; C a m p b e l l e t a l . , 1976). B e c a u s e o f the u n c e r t a i n t y in the size, s h a p e , a n d pole p o s i t i o n s of t h e s e obj e c t s , c o m p a r i s o n s in t e r m s of s c a t t e r i n g law a n d reflectivity are difficult. H o w e v e r , I c a r u s , Toro, E r o s , a n d B e t u l i a share the f o l l o w i n g S - b a n d r a d a r p r o p e r t i e s : (1) their n o r m a l i z e d " O C " cross s e c t i o n s are less t h a n 0.20; a n d (2) the d o m i n a n t s c a t t e r i n g m e c h a n i s m a p p e a r s to be diffuse r a t h e r than quasi-specular.
353
U n f o r t u n a t e l y , no o b s e r v a t i o n s o f Bet u l i a in the s a m e s e n s e o f c i r c u l a r polarization as t r a n s m i t t e d (the " S C " sense) c o u l d be m a d e d u r i n g this l i m i t e d o b s e r v i n g opp o r t u n i t y ; thus, the c i r c u l a r p o l a r i z a t i o n r a t i o / z c = crsc/troc r e m a i n s u n k n o w n . Assuming/z~ < 1, we c a n set a n u p p e r limit o f 0.04 ___ 0.01 o n the g e o m e t r i c a l b e d o o f Betulia for h = 12.6 cm. This limit is s i m i l a r to the v a l u e for the v i s u a l g e o m e t r i c a l b e d o d e t e r m i n e d polarimetrically by Tedesco et al. (1978). ACKNOWLEDGMENTS We wish to thank Richard Simpson of Stanford University, Antonia Forni of MIT, and the staff of the Arecibo Observatory for their assistance. This research was supported in part under NASA Grant NGR 22-007-672, and in part under NSF Grant GP 37107. REFERENCES CAMPBELL, D. B., CHANDLER, J. F., O S T R O , S. J . , PE-rTENGILL,G. H., AND SHAPIRO,I. I. (1978). Galilean satellites: 1976 radar results. Icarus 34, 254267. CAMPBELL, D. B., PETTENGILL,G. H., A N D S H A P I R O , I. I. (1976). 70-cm radar observations of 433 Eros. Icarus 28, 17-20. GOLDS-rEIN, R. M. (1968). Radar observations of Icarus. Science 162, 903-904. GOLDS'rEIN, R. M. (1969). Radar observations of Icarus. Icarus 10, 430-431. GOLDSTEIN, R. M., HOLDRIDGE, D. B., AND LIESKE,
J. H. (1973). Minor planets and related objects. XII. Radar observations of 1685 Toro. Astron. J. 78, 508-509. JURGENS, R. F., AND BENDER, D. F. (1977). Radar detectability of asteroids: A survey of opportunities for 1977 through 1987. Icarus 31, 483-497. J U R G E N S , R . F . , A N D G O L D S T E I N , R . M . (1976). Radar observations at 3.5 and 12.6 cm wavelength of asteroid 433 Eros. h'arus 28, 1-15. LEBOFSKY, L. A., VEEDER, G. J., LEBOFSKY, M. J., AND MATSON,D. L. (1978). Visual and radiometric photometry of 1580 Betulia. Icarus 35, 336-343. LAGERKVlST, C. I. (1977). A photographic lightcurve of the Amor asteroid 1580 Betulia. Icarus 32, 233234. O S T R O , S. J., PETTENGILL, G. H., S H A P I R O , I. I., C A M P B E L L , D. B., AND GREEN, R. R. (1979). Radar observations of Asteroid 1 Ceres. Icarus, 40, 355358. PETTENGILL, G. H. (1978). Physical properties of the planets and satellites from radar observations. Ann. Rev. Astron, Astrophys. 16, 265-292.
354
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PETTENGILL, G. H., SHAPIRO, I. I., ASH, M. E., INGALLS, R. P., RAINVILLE, L. P., SMITH, W. B., AND STONE, M. L. (1969). Radar observations of Icarus. Icarus 10, 432-435.
TEDESCO, E., DRUMMOND, J., CANDY, M., BIRCH, P., NIKOLOEE, I., AND ZELLNER, B. (1978). 1580 Betulia: An unusual asteroid with an extraordinary lightcurve. Icarus 35, 344-359.
Radar Observations of Asteroid 1580 Betulia GORDON H. PETTENGILL, STEVEN J. OSTRO,~ AND IRWIN I. SHAPIRO Department o f Earth and Planetary Sciences, Massachusetts Institute o f Technology, Cambridge, Massachusetts 02139
BRIAN G. MARSDEN Smithsonian Astrophysical Observatory, Cambridge, Massachusetts 02138 AND
DONALD B. CA MPBE L L National Astronomy and Ionosphere Center, z Arecibo, Puerto Rico 00613 Received March 15, 1979; revised May 22, 1979 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 km ~ 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.
INTRODUCTION
In May 1976, the Amor asteroid 1580 Betulia passed within 0.14 AU of Earth and provided astronomers with an excellent opportunity to study it. Optical observations disclosed a lightcurve with three maxima and three minima, suggesting the presence of a major surface inhomogeneity on one side (Tedesco et al., 1978); in addition, its visual geometric albedo was found to be ~<0.05 (Lebofsky et al., 1978), surprisingly low compared to that of other Marscrossing asteroids. Here we present results from radar observations of Betulia made at the Arecibo Observatory. OBSERVATIONS
Although the declination of Betulia at opposition on 22 May 1976 placed it outside ~ Present address: National Astronomy and Ionosphere Center, Cornell University, Ithaca, N e w York 14850. 2 Operated by Cornell University under contract with the National Science Foundation and with support from the National Aeronautics and Space Administration.
the antenna coverage of the Arecibo Observatory, its position during the preceding week was ideal for radar investigation. Our observations, at a radar wavelength of 12.6 cm, were made during this period on the early mornings of 18 and 19 May 1976. On these dates, the roundtrip echo time delays were about 150 and 143 sec, respectively. The observations were broken into 5-min cycles, each consisting of a 40-sec set-up time leading into the transmission, for approximately 130 sec, of a 2380-MHz, unmodulated, right-circularly polarized signal, followed immediately by reception for an equal period of the Doppler-shifted echo in the orthogonal circular ( " P C " ) sense of polarization. The PC sense was chosen in the hope of maximizing the echo strength, since coherent reflection favors this polarization sense. The declination of Betulia, coupled with the limited sky coverage of the Arecibo antenna, precluded more than 12 such transmit-receive cycles (runs) per day. Using an ephemeris prepared at MIT and based on orbital elements supplied by the Smithsonian Astrophysical Observa-
350 0019-1035/79/120350-05502.00/0 Copyright © 1979by Academic Press, Inc. All rights of reproduction in any form reserved.
RADAR OBSERVATIONS OF BETULIA tory, we continuously adjusted the receiver frequency to compensate for the anticipated Doppler shift caused by the line-of-sight motion of Betulia relative to the radar. Each run was segmented into 130 successive 1-sec data sets, which were individually Fourier analyzed; the corresponding frequency components from each data set were incoherently summed, yielding an echo power spectrum having approximately l-Hz resolution. A total of 11 and 9 such power-spectra were obtained from the observations on 18 and 19 May, respectively. The spectra obtained from a weighted average of the runs for each day are shown in Fig. 1. Values of the radar cross section corresponding to the total echo power for each run are given in Table I. DISCUSSION
The echo spectra appear quite fiat, with steep edges. From visual inspection of each
2:[
BETULIA
MAY
TABLE I MEASUREMENTS OF RADAR CROSS SECTION O'oc FOR BETULIA FROM INDIVIDUAL, 5-MIN RUNS a
Date (1976)
Mean time of reception (UTC) (hr)(min)(sec)
Radar cross section (kin2)
Rotational phase angle (deg)
May 18
05 22 20 05 34 20 05 40 20 05 46 20 05 52 32 05 58 45 06 04 20 06 10 20 06 16 20 06 25 20 06 31 20
2.50 1.53 0.60 0.50 2.07 2.07 2.34 2.42 2.52 2.58 1.72
314.8 326.5 332.4 338.3 344.3 350.4 355.9 1.7 7.6 16.4 22.2
May 19
05 28 16 05 34 16 05 40 16 05 46 16 05 52 16 05 58 16 06 04 16 06 10 16 06 16 16
3.24 2.86 3.44 2.96 2.11 1.48 2.71 2.80 2.27
288.2 294.1 299.9 305.8 311.7 317.5 323.4 329.3 335.1
a The origin of rotational pha s e is consistent with Fig. 15 of Tedesco et al. (1978).
of the two spectra, we obtain an estimate of the mean limb-to-limb bandwidth: fLL = 26.5 --+ 1.5 HZ (standard error). For a spherical target o f rotation period, P , the radius is given by
A e3 > 18
351
1976
P
R = APfLL/(87r sin 8),
lco
A,~,r~A ,, IV.~_._ L, ...A
v"vv,'V',,'"" ' V l t V ' ~
w
I~. ~A ^^~ v-w'v'~
o (3_
-
{
I 9
MAY
1976
vw " v~, ,,'~,jv,r,-- V "" L -20o
V'V -,,~,v
{ i l l { -150 - I O 0 - 5 0 0 50 DOPPLER FREQUENCY (HZ)
vV~ i 10o
FIG. l. Power s p e c t r a for echoes from the asteroid 1580 Betulia o b s e r v e d on 18 and 19 May 1976. Rec e i v e d power, in units of standard deviations of associated noise, is plotted as a function of Doppler shift. Zero Do ppler shift c o r r e s p o n d s to our least-squares estimate of the center frequency of the echo s p e c t r u m (see text). The sp ectra have been s m o o t h e d to a resolution of 3 Hz.
where h is the length of a radar wave and 8 is the angle between the target's rotation axis and the radar line of sight. Analysis of Betulia's visible-wavelength lightcurve by Tedesco et al. (1978) yielded a value of 6.130 _+ 0.006 hr for the synodic rotation period. H o w e v e r , the shape, scattering law, and pole position of Betulia are poorly known. Thus, we may calculate only a lower limit for the radius of 2.9 _+ 0.2 km from the apparent bandwidth of the echo spectrum. Lebofsky et al. (1978) analyzed broadband visual and 10.6-tzm photometric observations using the "radiometric m e t h o d . " This technique yields estimates for Betulia's radius and visual geometric albedo p
352
PETTENGILL ET AL.
which depend critically on how the thermal response of the surface is modeled. L e b o f s k y et al. investigated the consequences of two models. F r o m the first model, which postulates a low-thermalinertia surface (similar to the lunar regolith), they obtained: R -- 2. l0 _+ 0.40 km and p -- 0.108 _ 0.012. From the second model, which assumes a relatively highthermal-inertia surface (e.g., bare rock), they obtained: R = 3.74 _+ 0.17 km and p -- 0.034 _ 0.004. Pursuing a different route using a well-established empirical relation between visual polarization and albedo, Tedesco estimated values for R of 3.3_+ 0.2 km and for p of 0.04_+ 0.01. Thus, all values for the radius except the smaller of the radiometric values are reasonably consistent with R = 3.5 kin, if a minimum value for 8 of about 55° is invoked. Approximating the angular behavior of the scattering by cos ~ O, where O is the angle of incidence to the mean (spherical) surface, we obtained weighted-leastsquares estimates of three parameters: the scattering law exponent n, an amplitude scale factor tr', and the Doppler shift v referenced to the center of the spectrum for the model. The value of R sin 8 was constrained for reasons discussed by Campbell et al. (1978) in connection with a similar analysis for the Galilean satellites. Estimates of v, valid for 2.0 -< R -< 3.6 km, are given in Table II. The weighted mean of the estimates for n is 1.0 _ 0.2, implying that the asteroid appears uniformly bright under 12.6-cm wavelength illumination. H o w e v e r , if Betulia's actual shape is significantly nonspherical, or the polar aspect is substantially different from normal, the physical meaning to be attached to the estimate of n is less clear and our model becomes merely a convenient tool for the estimation of the center frequency of the echo spectrum. The mean value and standard deviation of the radar cross section troc for Betulia, as determined from the entries in Table I, are
TABLE II DOPPLER SHIFTS AT MHz a DETERMINED FOR BETULIA ON 18 AND 19 MAY 1976 Date (1976)
Mean time of reception (UTC) (hr)(min)(sec)
Doppler shift for transmitted frequency of 2380 MHz
(Hz) 18 May 19 May
05 56 50 05 52 16
225,980.0 _+ 1.0 186,012.5 _+ 1.0
a Estimates of Doppler shifts and their associated standard errors have been rounded to the nearest multiple of 0.5 Hz.
2.2 - 0.8 km". Figure 2 shows the radar cross section plotted as a function of the rotational phase ~ . The large excursion in O-oc may result, in part, from statistical and systematic sources of error. The difference between independent determinations of cross section near = 335° on the two dates may be due to tracking problems associated with the first use of a new feed at Arecibo. But some of the variation in cross section with rotational phase may be physically significant. The visual lightcurve for Betulia exhibited three maxima and three minima and could result, for example, from a prolate object rotating about a minor axis (Tedesco et al. 1978). Figure 2 shows that the radar observations were concentrated around the second minimum (m2) in the visual lightcurve and that no radar data were obtained at phases corresponding to visual maxima. If the model of Tedesco et al. is valid, the long axis of Betulia was not oriented normal to the line o f sight during the radar observations, possibly accounting for the fact that the polarimetric estimate of R is about 14% higher than the radar lower limit. Unfortunately, the spectra from single 130-sec runs do not have sufficiently high signal-to-noise ratios to permit the extraction of individual estimates of R. The 12.6-cm reflectivity of Betulia, expressed as the normalized radar cross section &oc -= troc/zrR 2, is obviously difficult to
RADAR OBSERVATIONS OF BETULIA ~--4( :E
A
z~
A
A
. . . . .
AA A AA AA
~
~ 2.C o 1:3
AA
MI
I 270 °
t
m2
l
300 ° 330 ° ROTATIONAL PHASE
I 0°
50 °
FIG. 2. Measurements of the radar cross section (roe of Betulia from individual 5-min runs (see Table I), plotted as a function of rotational phase @. Results for 18 (19) May 1976 are denoted by solid (open) triangles. The dashed line at 2.2 km2 shows the mean value. The origin o f ~ is based on Fig. 15 of Tedesco et al. (1978). Values of phase corresponding to the first maximum (M1) and second minimum (m2), as reported by Tedesco et al., are indicated.
establish without an accurate estimate of target size a n d shape. S u b s t i t u t i n g the r a d a r result (R -> 2.9 + 0.2 km) yields &oc -< 0.08 _+ 0.03, a n u p p e r limit w h i c h is v e r y close to the a v e r a g e n o r m a l i z e d cross s e c t i o n for the M o o n a n d t e r r e s t r i a l p l a n e t s , a l t h o u g h we note that the r a d a r b a c k s c a t t e r ing for t h e s e targets is m u c h m o r e s h a r p l y p e a k e d (i.e., " q u a s i - s p e c u l a r " ) t h a n for Betulip (Pettengill, 1978). S u b s t i t u t i n g the i n f r a r e d - r a d i o m e t r i c v a l u e (R = 3.7 --- 0.2 kin) gives &oc -- 0.05 _+ 0.02, a v a l u e w h i c h is a l m o s t as l o w as that d e t e r m i n e d for C e r e s (6-oc = 0.04 _ 0.02; O s t r o e t al., 1979). Three other Apollo-Amor asteroids have b e e n d e t e c t e d b y radar: 1566 I c a r u s (Goldstein, 1968, 1969; P e t t e n g i l l e t a l . , 1969), 1685 Toro ( G o l d s t e i n e t al., 1973), a n d 433 E r o s (Jurgens a n d G o l d s t e i n , 1976; C a m p b e l l e t a l . , 1976). B e c a u s e o f the u n c e r t a i n t y in the size, s h a p e , a n d pole p o s i t i o n s of t h e s e obj e c t s , c o m p a r i s o n s in t e r m s of s c a t t e r i n g law a n d reflectivity are difficult. H o w e v e r , I c a r u s , Toro, E r o s , a n d B e t u l i a share the f o l l o w i n g S - b a n d r a d a r p r o p e r t i e s : (1) their n o r m a l i z e d " O C " cross s e c t i o n s are less t h a n 0.20; a n d (2) the d o m i n a n t s c a t t e r i n g m e c h a n i s m a p p e a r s to be diffuse r a t h e r than quasi-specular.
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U n f o r t u n a t e l y , no o b s e r v a t i o n s o f Bet u l i a in the s a m e s e n s e o f c i r c u l a r polarization as t r a n s m i t t e d (the " S C " sense) c o u l d be m a d e d u r i n g this l i m i t e d o b s e r v i n g opp o r t u n i t y ; thus, the c i r c u l a r p o l a r i z a t i o n r a t i o / z c = crsc/troc r e m a i n s u n k n o w n . Assuming/z~ < 1, we c a n set a n u p p e r limit o f 0.04 ___ 0.01 o n the g e o m e t r i c a l b e d o o f Betulia for h = 12.6 cm. This limit is s i m i l a r to the v a l u e for the v i s u a l g e o m e t r i c a l b e d o d e t e r m i n e d polarimetrically by Tedesco et al. (1978). ACKNOWLEDGMENTS We wish to thank Richard Simpson of Stanford University, Antonia Forni of MIT, and the staff of the Arecibo Observatory for their assistance. This research was supported in part under NASA Grant NGR 22-007-672, and in part under NSF Grant GP 37107. REFERENCES CAMPBELL, D. B., CHANDLER, J. F., O S T R O , S. J . , PE-rTENGILL,G. H., AND SHAPIRO,I. I. (1978). Galilean satellites: 1976 radar results. Icarus 34, 254267. CAMPBELL, D. B., PETTENGILL,G. H., A N D S H A P I R O , I. I. (1976). 70-cm radar observations of 433 Eros. Icarus 28, 17-20. GOLDS-rEIN, R. M. (1968). Radar observations of Icarus. Science 162, 903-904. GOLDS'rEIN, R. M. (1969). Radar observations of Icarus. Icarus 10, 430-431. GOLDSTEIN, R. M., HOLDRIDGE, D. B., AND LIESKE,
J. H. (1973). Minor planets and related objects. XII. Radar observations of 1685 Toro. Astron. J. 78, 508-509. JURGENS, R. F., AND BENDER, D. F. (1977). Radar detectability of asteroids: A survey of opportunities for 1977 through 1987. Icarus 31, 483-497. J U R G E N S , R . F . , A N D G O L D S T E I N , R . M . (1976). Radar observations at 3.5 and 12.6 cm wavelength of asteroid 433 Eros. h'arus 28, 1-15. LEBOFSKY, L. A., VEEDER, G. J., LEBOFSKY, M. J., AND MATSON,D. L. (1978). Visual and radiometric photometry of 1580 Betulia. Icarus 35, 336-343. LAGERKVlST, C. I. (1977). A photographic lightcurve of the Amor asteroid 1580 Betulia. Icarus 32, 233234. O S T R O , S. J., PETTENGILL, G. H., S H A P I R O , I. I., C A M P B E L L , D. B., AND GREEN, R. R. (1979). Radar observations of Asteroid 1 Ceres. Icarus, 40, 355358. PETTENGILL, G. H. (1978). Physical properties of the planets and satellites from radar observations. Ann. Rev. Astron, Astrophys. 16, 265-292.
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PETTENGILL, G. H., SHAPIRO, I. I., ASH, M. E., INGALLS, R. P., RAINVILLE, L. P., SMITH, W. B., AND STONE, M. L. (1969). Radar observations of Icarus. Icarus 10, 432-435.
TEDESCO, E., DRUMMOND, J., CANDY, M., BIRCH, P., NIKOLOEE, I., AND ZELLNER, B. (1978). 1580 Betulia: An unusual asteroid with an extraordinary lightcurve. Icarus 35, 344-359.