- Email: [email protected]
Asteroid rotation
ICARUS 43, 20--32 (1980)
Asteroid Rotation III. 1978 O b s e r v a t i o n s A. W. H A R R I S AND J. W. Y O U N G Jet Propulsion Laboratory, Pasadena, California 91103 Received F e b r u a r y 19, 1980; revised April 14, 1980 Photoelectric observations of 32 asteroids o b s e r v e d from Table Mountain O b s e r v a t o r y during the second half of 1978 are reported. Rotation periods were obtained for most objects. Absolute magnitudes and phase functions were not determined for any of these asteroids. The geometric m e a n rotation period of the 32 asteroids o b s e r v e d is 14.2 _+ 1.6 hr, as compared to 9.38 _+ 0.35 hr for 182 asteroids analyzed in Paper I (A. W. Harris and J. A. Burns, 1979, Icarus 40, 115-144). We attribute this difference to an observational selection effect which favors detection of fast rotation, as d i s c u s s e d in Paper I. If this is true, then the present sample contains the reverse bias, since it is complete in that a period (in some c a s e s very approximate) was obtained for each object observed, but fast rotators are u n d e r r e p r e s e n t e d due to prior discovery of their rotation properties.
The asteroids to be o b s e r v e d are selected primarily on the basis of opposition magnitude (B <~ 13) from a m o n g those for which no period determinations have been reported in the literature. In cases where more asteroids are available than can be a c c o m m o d a t e d , preference is given to unusual t a x o n o m i c classes (particularly M class) and to smaller asteroids, since f e w e r data are available on these objects. In a few cases, asteroids have been included for which periods have previously been reported, but which in our judgment are of low reliability (Paper I). The instrumental details of the observations are discussed by Harris and Young (1979). The results are s u m m a r i z e d in Table I. in that table, the t a x o n o m i c class and diameter of each asteroid are listed as given in T R I A D (Bowell et al., 1979). The position and phase angle of each asteroid are tabulated for one date only. In constructing composite lightcurves, corrections were made for day-to-day variations in solar phase angle and distances; however, since only relative p h o t o m e t r y was attempted, these small aspect variations are of no future value and are therefore not tabu-
INTRODUCTION
In the course of analyzing existing data on asteroid rotation rates, it has b e c o m e clear that the available data set is inadequate for testing certain h y p o t h e s e s (e.g., Harris, 1979), and contains significant biases due to observational selection effects (Harris and Burns, 1979, hereafter referred to as P a p e r I). T h e s e limitations have resulted in considerable confusion in interpretations of rotation data (Burns and Tedesco, 1979). In the hope of improving this situation, a program of lightcurve observations was initiated at Table Mountain Observatory. In order to avoid a selection effect against discovery of long periods, we o b s e r v e several asteroids sequentially throughout the night, and continue observations of each asteroid for as m a n y nights as necessary to obtain a period. This method has resulted in reliable period determinations for 80-90% of asteroids observed, and at least some indication of the periods of most of the others. At the same time, the method is quite productive: we obtain an average of one period determination per night of observation. 20 0019-1035/80/070020-13502.00/0 Copyright © 1980by Academic Press, Inc. All rights of reproduction in any form reserved.
ASTEROID ROTATION
21
TABLE I ASPECT Figure No.
-
Asteroid
T ax onomic
18 M e l p o m e n e 30 U r a n i a 36 Atalante 48 Doris 50 Virginia 67 Asia 68 L e t • 74Galatea 87 Sylvia 91 Aegina 116 Sirona 135 H e r t h a 140 Siwa 182 Elsa 221 E o s 224 O c e a n a 230 Athamatis 247 Eukrate 270 Anahita 304 Olga 356 Liguria 362 Havnia 405 T h i a 441 Bathilda 505 Cava 516 Amherstia 660 Crescantia 674 Rachele 709 Fringilla 737 Arequipa 747 Winchester 952 Caia
-
1 2 3 4 5 6 7 8 9 10, 11 12 13 -14 15 16 17 18 -19 20 21 22 23 24 25 26 27 28 29 30
DATA
Date
class
Diam eter (km)
S S C U C S S C CMEU C S M C S U M S C S CMEU C C C M U M S S C S C C?
164 95 124 149 88 66 128 113 251 106 80 79 105 46 98 57 116 143 52 68 157 97 126 66 59 65 45 96 96 45 208 91?
12t04/78 10/29/78 9/02/78 9/02/78 12/04/78 7/28/78 8/27/78 10/29/78 8/30/78 8/25/78 1/01/79 12/04/78 11/08/78 12/05/78 7/29/78 8/30/78 10/23/78 9/02/78 7/28/78 8/28/78 8/28/78 12/04/78 7/31/78 12/04/78 1/01/79 10/29/78 7/29/78 10/29/78 8/28/78 7/28/78 8/01/78 10/29/78
AND
SUMMARY
a (1950) ~i
6h41.m3 23 3 5 . 2 23 52.1 23 4 8 . 0 3 41.9 18 0 1 . 8 22 21.1 I 16.5 23 2 6 . 2 21 5 7 . 7 6 23.6 5 55.9 2 41.5 5 12.3 19 4 8 . 4 23 5 7 . 7 2 56.2 23 11.3 21 0 6 . 3 ~2 1 6 . 0 22 23.2 3 56.4 19 5 2 . 7 5 17.8 8 01.3 2 02.6 20 13.7 7 01.8 22 10.0 19 10.4 20 4 1 . 5 1 38.4
lated. The final two columns list the rotation period and lightcurve amplitude determined from the observations.
18 Melpomene. The results for this asteri
I
i
I
I
+ 6038 ' + 0 52 8 05 + 0 51 + 14 32 12 17 24 55 + 644 20 55 - 14 52 +26 31 +27 02 + 10 56 +20 55 14 26 0 40 +22 40 22 13 12 16 - 7 22 15 26 +2904 6 06 +22 23 +26 18 + 3 0 39 5 03 - 0 09 7 04 + 0 17 17 I1 + 14 20
,~
fl
Phase angle
1000.7 354. "T 355.11 357.6 56.6 270.4 328.0 20.2. 343.8 326.4 95.3 89.1 41.z~ 78.9 296.L. 359S 48.2 340.11 315.4 333.2 332.11 63.0 299.0 80.3 117.] 39.3 304.5 106.~I 331.9 289.] 308.2. 28.11
-16°.4 + 3.2 6.6 + 2.0 5.0 +11.2 -13.6 - 1.3 - 15.8 2.3 + 3.2 + 3.6 4.5 2. I + 6.6 - 0.4 + 5.6 15.6 + 4.1 + 3.2 5.0 + 8.5 + 14.5 0.7 + 5.7 + 17.0
15° 18 8 6 7 17 6 7 6 2 2 7 2 4 4 9 9 6 6 2 2 5 7 3 8 5 6 5 2 13 0 3
+ 14.5
22.7 + 4.0 +22.6 + I.I + 3.8
P (hr)
11.572 13.686 9.93 ll.89 >24. 15.89 14.85 9.0 5.1826 6.025 13.7 16.805 22 o r 32'? 80. 10.45 18.933 24.0 ? 12.10 15.06 18.36 31.82 18. 10.08 10.35 7. 7. 7.92 >30. 52.4 14.13 8. 7.50
Am
±0.002 ±0.004 ±0.02 ±0.01 -+0.03 ±0.05 ±0.5 ±0.0010 ±0.003 ±0. I ±0.010 ±2. ±0.01 ±0.006 ±0.01 ±0.01 -+0.02 _+0.05 ±1. ±0.07 ±0.05 ±1. ± I. ±0.01 ±0.2 _+0.08 +_2. ±0.01
I
i
T
i
I
i
r
i
15
16
©
0.0
©
o
+000 0.1
2 5 o
+ +
0~ 10/23/78
•
0.3
oo
•+
0 1o/2,;/~
o
o
+
1
I/0,'3/78
0.4
I
I 4
l 5
I 6
/ 7
I 8
I 9
0.30 0.45 0.17 0.35 >0.15 0.23 0.15 0.14 0.42 0.15 0.3 0.15 >0.005 0.7 0.05 0.10 >0.15 0.11 0.32 0.20 0.22 0.1 0.15 0.13 0.1 0.15 0.33 >0.15 0.18 0.15 0.13 0.12
oid are given by Binzel and Harris (1980). They are included in Table I for statistical completeness. 30 Urania (Fig. 1). A period of 14 hr was reported by Bailey (1913), and of 13.68 hr by Rigol]et (1950). Both of these were
OBSERVATIONS
I
OF RESULTS
I()
U T 29 O C T O B E R
111
I 12
1978
FIG. 1. Composite lightcurve of 30 Urania.
I 13
I 14
I
22
HARRIS AND YOUNG I
{
0.00 - 0
i
i
i
I
1
I
I
I
•
00
I
•
(~
Q + 0.05
0
O <
0.10
O
0
0
•
0
+o
~ c~ ~qP
0
O 8/~/~ • 9/2/78 + 9/3/~
O O
5
II o.15
0.20
• •
0
J 3
i
l
l 4
L 5
,
I
I
6
7
,
l
I
8
9
,
I
I
10
11
,
I 12
,
i 13
,
I 14
UT 30 AUGUST 1978 FIG.
2. Composite
lightcurve
based on visual observations. Gehrels and Owings (1962) reported a period of 13.668 hr based on photoelectric observations. The latter value was based on two widely spaced nights of observations and was very dependent on the correctness of the previous visual observations. Because of the generally low reliability of such observations, 30 Urania was included in our program. Three nights of observations sufficed to yield an unambiguous period of 13.686 ± 0.004 hr, thus confirming the previously reported values. 36 Atalante (Fig. 2). No period has been previously reported for this asteroid. The composite lightcurve based on three nights of data yields an unambiguous period of 9.93 _+ 0.02 hr. 48 Doris (Fig. 3). T w o successive nights of data (9/2 and 9/3) plus one previous night established that the period is almost exactly a submultiple of 24 hr. Since coverage spans 9 hr with very different end points, 8 hr is ruled out. The only reasonable value is thus 11.89 _+ 0.01 hr. Three hours of the lightcurve remained unobserved. R. Austin (private communication, 1979) observed 48 Doris in 1977. His data, while somewhat noisier than ours, appear remarkably similar and confirm the period approximately. 50 Virginia (Fig. 4). Three nights of observations failed to yield a satisfactory period. The night of 4 D e c e m b e r was of poor quality. If the first point o f that night is not
of
36 Atalante.
included, a very long period of - 4 days appears to be suggested. In any case, a period ~1 day seems to be indicated. We r e c o m m e n d this asteroid for further observations. 67 Asia (Fig. 5). Data were obtained on a total of eight nights; however, coverage was still incomplete due to the near-twothirds commensurability of the period to one day. The period is uniquely determined, though, at 15.89 _ 0.03 hr. 68 Leto (Fig. 6). Five full nights of data were required to determine the period of this asteroid, primarily due to the unusual shape of the lightcurve. Three distinct maxima and minima occur each cycle. The period of 14.85 ± 0.05 hr and the triple maxima and minima are confirmed by Schober and Surdej (1980). 74 Galatea (Fig. 7). Only two nights of observations were obtained which were
0.O
x
i
,
+•
i
,
i
,
i
,
i
n
n
,
n
,
I
(~)
ooO000 •
0
ok 0
o•
75
o •
~oo
•
o
o
• 8/50/78 0 9/2/?'8
oo
++-
+ 9/3/78
0.5
x 9/4/7"8 I
5
FiG.
1
6
I
7
I
I
]
,
ill
112
of 48
Doris.
B 9 I0 U T 3 0 AUGUST 1978
3. Composite
lightcurve
L
ASTEROID ROTATION I
0.0
I
I
I
I
•
23
J
I
•"
I
(~)
I
0.1
•
••
•0
•0
-1...
•
0.2
I
I
6
I
12
I
18
I
0
UT 3 DECEMBER 1978
[ i
,
i
,
4
i
,
i
,
i
6
i
~
i
L
8
t
Ci
~X
~-i
I
~0
F i G . 5.
UT 5 DECEMBER 1978
"
i
i
,
+ 7/29/78 [] 7 / 5 0 / 7 8 • 7/31/78 i,
i,
t ]
" 8/11/7"~ Q I
,
,
12 14 16 UT 51 JULY 1978
t
I
,
18
I
,
L
i
,
20
i
I
~
,
22
Jq/
i
24
Composite lightcurve of 67 Asia.
x
x
+ 8/24178
•
•
• 8/27•78
d 0.2= [
I
6
o,
j-
F
I
0
. . . . . . . . . . . . . . . . . . . . . . . . . .
7/25/78 • 7126178 07/27/78 Z~7 / 2 8 / 7 8
/
E O ' 3 , ,
18
Lightcurves of 50 Virginia.
.
0.2lJ-
~J
I
12
UT 4 DECEMBER 1978 FIG. 4.
~J
[
6
~-
9. ~ -
/
• •
*8/28/78
I
,
I
19
,
I
i
I
i
21
I
i
23
I
I
I
,
0
z~8 / 2 9 / 7 8 I , i , i , i , i , 2 4 6 UT 27 AUGUST 1978
I
1 i
,
i
.
I
i
8
I
i
r
r
I0
I
I
I
i
12
I
14
FIG. 6. Composite lightcurve of 68 Leto. UT 29 OCTOBER 1978 2
3
4
5
6
7
8
9
10
II
I
I
I
I
I
I
I
I
1
I
0.0
+ 10/29/78 • 11/o8/78
•
•
•
+•
+
ID
(~)
+0
+
•
+ •
12
+ + +
0.1-
Otp i
+
+
I
I
I
I
I
I
I
I
I
I
4
5
6
7
8
9
10
11
12
13
ur a NOVEMBER1978 F I G . 7. C o m p o s i t e
lightcurve
widely separated in time. Luckily, it was possible to combine the two uniquely, due to the difference between the two minima. The resulting lightcurve covers all rotational phases. In spite o f this, it is not possible to determine uniquely the n u m b e r of rotations which occurred between the
of 74 Galatea.
two nights. The rotation period is thus somewhat poorly determined at 9.0 -+ 0.5 hr. 87 Sylvia (Fig. 8). The short period and large amplitude facilitated a precise determination with only two nights o f data. By combining our results with those o f Scho-
24
HARRIS AND YOUNG i
0.0
,
I
,
i
,
2o
,
i
,
o'
i
&
L+L ~
I
'
•
]
•
,
I
Z 0
/ ~<~ I L O. 51
0
o
g
I
+ o~
~
'~
I
+
*+~'k+
o o+
~
'
I
'J
(~)
. . ,,+~.
• +
%
+ . . . .
,
4
6
5
I
•
+
0
I
. e"x ~ I
• 8/24/78 • 0 8/25/78 zx 8 / 2 7 / 7 8 + 8/28178
+ I
7 8 9 UT 2 4 AUGUST 1978
I0
itl
it
FIG. 9. Composite lightcuve of 91 Aegina.
O
g
0.~
I
~.~+~
0
0.2
I
o+
~,
0.'0~" 0
'
oO
0.05I-
2
I
2 lO ,~ 000 tx
O
g
(3-I
I
0
• 8/50/78 o 9/2/78
(1913) observed 116 Sirona visually over a period of 7 days and reported a period of 0.4 °° L° 19.3 hr. A Fourier analysis (Paper I) of ' ; ' ~ ' ,b' ,', ',~ Bailey's data revealed equally probable peUT 5 0 AUGUST 1978 riods of 13.7, 10.7, 6.5, and 6.3 hr, in FIG. 8. Composite lightcurve of 87 Sylvia. addition to his proposed 19.3 hr, all of which fit his data. We obtained only one ber and Surdej (1979), a period of 5. 1826 _+ night of data, indicating a period of - 1 3 hr. 0.0010 hr was obtained. 87 Sylvia is listed The only value which is compatible with as class " C M E U " in TRIAD (Boweli et al., both Bailey's observations and ours is 13.7 1979) with the diameter of 251 km based on _+ 0.1 hr. A composite lightcurve of a " C " class aibedo. Chapman (private Bailey's visual observations based on that communication, 1979), based on his spec- value is given in Fig. 11. The error estimate trophotometric data, suggests it may in- of the period is the half power width of the stead be " M " class. The diameter corre- spectral peak at 13.7 hr in Bailey's 1913 sponding to a mean " M " albedo for 87 data. Sylvia would be only 130 km. This same technique was used to analyze 91 Aegina (Fig. 9). A period of 6.025 ___ Bailey's observations of 30 Urania. The 0.003 hr was uniquely determined from four most prominent spectral peak was at a nights observations. No other lightcurves period of 13.68 hr, which was correctly noted by Bailey and verified by our more appear in the literature to date. 116 Sirona (Figs. 10 and 11). Bailey recent measurements (Fig. l). •
I
0
I
'
I
,
I
I
,
I
,
I
I
I
1
0.0
Z O
"~
0.I
0.2
•
•
0.3 ,
I 6
,
I 7
,
8
I
,
9
UT I J A N U A R Y 1979
FIG. 10. Photoelectric lightcurve of 116 Sirona.
I
I
10
71
,
I
12
ASTEROID ROTATION
25
O.0 ~r- OI ]
.....
,
°
,
,
I II
. . . .
I
0
*
I
5
0.5
•
•
I
1
•
I I 1/08/78
UT
/
•
•
•
~' 1
II
ill
J2
FIG. 13. L i g h t c u r v e o f 140 S i w a .
ROTATION PHASE
FIG. 11. C o m p o s i t e l i g h t c u r v e of 116 S i r o n a c o n s t r u c t e d f r o m B a i l e y ' s (1913) v i s u a l o b s e r v a t i o n s .
will be presented in a future publication.) The 1978 observations, composited with the 1979 period, are presented in Fig. 14. This lightcurve's smaller amplitude and more irregular form than those of the lightcurve observed in 1979 suggest that 221 Eos was observed at a nearly polar aspect in 1978. 224 Oceana (Fig. 15). Observations were taken during two observing runs a month apart. A very precise synodic period of 18.933 _+ 0.006 hr was thus obtained. The two sets of observations are presented separately in Fig. 14, aligned one atop the other rather than as a single composite, because the amplitude of variation appears to have changed somewhat in the time between observations. We are somewhat dissatisfied with the results for this object in that we cannot rule out a period of one-half the stated value. The points in the range 11-14 hr on the composite appear to suggest a very slight secondary maximum, but on the other hand the two periods of rapid brightening, between 6-7 hr and 15-16 hr, are not exactly separated by 9.5 hr. A single lightcurve 4 hr in duration obtained in 1980 appears to support the longer period. 230 Athamatis (Fig. 16). Yang et al. (1965) report a period of 7.996 hr based on several nights of photometry showing almost exact repetition on each night. Our
135 Hertha (Fig. 12). The data on 135 Hertha are rather noisy, but seem to allow only one possible solution, P = 16.805 --0.010 hr. We attribute the noise primarily to the fact that the asteroid was within 2° of the galactic plane during the course of observations, resulting in considerable interference from faint field stars. 140 Siwa (Fig. 13). Only one night of observations was obtained. Schober and Stanzel (1979) obtained one night o f data only - 3 0 hr earlier. The two lightcurves are remarkably similar in appearance, suggesting a period of - 3 2 hr if the two curves c o v e r the same rotation phase, or - 2 2 hr if they c o v e r rotation phases one-half cycle apart from one another. Additional observations are needed. 182 Elsa. The results for this asteroid are presented elsewhere (Harris et al., 1980). It is included in the table for statistical completeness. 182 Elsa has the longest rotation period yet discovered. 221 Eos (Fig. 14). Six nights of data indicate a low amplitude (-0.m05). This asteroid was reobserved during 1979, and showed a larger amplitude of --0.ml0 with a period of 10.h45. (The lightcurves from 1979
I /tx o
I
0.0
I ' I
I
I
]
J ++
I
I •
IA' •
I
IO(~] '1
z~O © 0
~" 0.1
!"+ O r.~ + ~1~
•O 12/3/7812/4/78 •+ 12/11/781/1/79
A
Z~C) A
] 2./5/78 ~0.2
I
2
,
I
3
t
I
4
I
I
5
i
I
6
i
I
7
i
I
i
I
i
[
8 9 10 UT 4 DECEMBER1978
i
I
11
FIG. 12. C o m p o s i t e l i g h t c u r v e o f 135 H e r t h a .
i
I
12
L
I
13
i
I
14
i
[
15
O~
26
HARRIS AND YOUNG
o.0
-,<'o . <~',.
~-0.1 ~ I ;3
I 4
o.o
~ t....
• ,:.i"-+,
o 7/27 • 7/28
x 7/30 • 7/31
+ 7/29
~. 8/01
I 6
;
F~
I 7
•
I B UT
~.~ ++
I I0
~t
Ill
II
13
7/2817B
Fir;. 14. Composite lightcurve of 221 Eos. U T 29 O C T O B E R
'
+ 8/28/78 A 9/3/78 • 8/'29/78 * 10/23/78 o 8/3o17B • io/~/7B x 9/2/78 Z 0 <
:E
6 I
7 I
'
'
8 I
'
9 '
~
1978
10 11 ' I ' I **wIj~*
'
12 13 I ' I
14 '
0.0
Z 0
*
*** , • •
•
mmI 0.0
_AA
Ii
0
x
+ ,
I 0
,
I I
,
1 2
,
I 3
,
i 4
++,P',, x,,, ,
i 5
t
I 6
,
I 7
,
[ 8
~
0
A
AA
"°° o ] 9
,
i , I , I , i , I , L , t , I , 1 , I 10 11 12 13 14 15 16 17 18 19
UT 29 A U G U S T
~ I 20
1978
FIG. 15. Composite lightcurve of 224 Oceana. Data from l m o n t h later are plotted above the s a m e rotation phase of the earlier data, since the amplitude of variation appears to have c h a n g e d s o m e w h a t in the interim.
two widely spaced nights confirm this behavior: however, our longer lightcurves appear to rule out a period as short as 8 hr, or even 12 hr. We therefore propose a period of 24 hr. Young (private communication, 1980) confirms the 24-hr period on the basis of observations taken in 1974 and 1979/80. These observations will be published shortly. 247 Eukrate (Fig. 17). Our observations of 247 Eukrate indicated a probable period of - 1 2 hr, but we were unable to uniquely determine the number of cycles between our two dates of observation. Fortunately, the observations of Schober and Surdej (1979), taken a week after ours, were
0.1
• lq/2 Is3 o ll/0~'Tb I C
[ 7
••
o l~ o
I ~
]
9
x0~ x
iii
i off [ _~
i2
FIG. 16. Composite lightcurve of 230 Athamatis.
sufficient to revolve the ambiguity as well as extend the phase coverage considerably. The resulting period is 12.10 + 0.01 hr. 270 Anahita (Fig. 18). Porter and Wallentine (1976) report a rotation period of 17.6 hr based on visual observations. Scaltriti and Zappalh (1978) obtained one short photoelectric lightcurve confirming the large amplitude claimed by visual observers. Our observations on five nights unambiguously yield a period of 15.06 _+ 0.01 hr. 304 Olga. The results for this asteroid are reported by Harris et al. (1980) and are summarized in Table I for completeness. 356 Liguria (Fig. 19). Phase coverage of this object is somewhat incomplete owing to the very long period; however, an unambiguous period of 31.82 + 0.05 hr was determined. 362 Havnia (Fig. 20). The data for this object are somewhat problematical. The period we obtain is 18 + 1 hr. We can only comment that the photometric quality of the three nights was poor, possibly explain-
ASTEROID ROTATION I
i 0.0
o
Z 0
o
I
•
a/ao/78 (TMO)
0
9/2/78 (TMO)
~
I
I
9 / 8 / 7 8 (ESO)
X
9/9/78(ESO)
I
+ill
x
+
+ +O
+
X
c~O
o
5
x X
X
+ • X
b-
+
o •
x + +X
+ X x
+ +
o Q
o •
+
+
o
'~ o.~
I
'
X 0 xl
+
27
+
Q
o ,
I $
L 7
I 9
I
~
I 10
L
I 11
,
t 12
L
[ 13
,
1 14
J
[ 15
UT 2 SEPTEMBER 1978
FIG. 17. Composite lightcurve of 247 Eukrate.
ing the discordant points on 3 December, and that no other choice of period seems to be acceptable at all. 405 Thia (Fig. 21). The period o f 10.08 _+ 0.07 hr was unambiguously determined from three nights of data. 441 Bathilda (Fig. 22). The period of 10.35 + 0.05 hr is uniquely determined. Note the difference in depth of the two minima. Repeated points from the same night are plotted with different symbols in order to clarify the actual duration of individual lightcurves. 505 Cava (Fig. 23). With the exception of the first data point near 4 hr UT, one would conclude that the period of 505 Cava is very near 7 hr and that one full rotation has been covered. The first point is totally discordant with such a period, and is in fact lower than any point in the minimum near 9 hr, assuming a shorter period. While we can find no reason for discounting the first point (the quality of the night was excellent), we must conclude that it is somehow incorrect and therefore take 7 _+ 1 hr to be the correct period. Lagerkvist (1978) obtained a short
~ ° ° Ii. . . . . . . . . . . .t...~. . . . . .~. . . . . . . . o~
o~ o ' 1 - . ua 0.21-
~0
-> I-
t~ J
07/27/78
oo
xT/28/v8
~ ~'~. . . . .(. ~. .
~'t
,,
o4
-.~
~ ~
~
~
Oa
~
o3L " • +7/29/v8 ~ " L. . . . . . . . . . . . . . .A. .7./ 3. .1./ 7. .8. . . . . . . . . x. . . . . . 2
4
6
8
I0 12 UT JULY 1978
" 14
16
18
o~ j
.
20
FIG. 18. Composite lightcurve of 270 Anahita.
J ,-J
photographic lightcurve which suggests a similar period. 516 Amherstia (Fig. 24). This asteroid was observed on only one night of excellent quality (it was too faint to be found on nights of poorer quality). Fortunately the one night sufficed to obtain an approximate period of 7 + 1 hr. 660 Crescentia (Fig. 25). A period of 7.92 - 0.01 hr was determined from three nights o f observations. Note the differing minima and maxima. 674 Rachele (Fig. 26). No period determination was possible from three nights of observations. One cannot help but suspect that a star may have been mistakenly observed rather than the asteroid on 11/08/78. Even discounting this night, the period must be at least - 3 0 hr, based on the lightcurve of 10/29/78. Several lightcurves by Scaltriti and Zappala (private communication, 1979) confirm that the period must be long, but likewise fail to yield a unique value. 709 Fringilla (Fig. 27). The phase coverage of this asteroid is still incomplete in spite of eight nights of observations, due to the extremely long period o f 52.4 + 0.2 hr. The lightcurves are sufficient, however, to show two distinctly different maxima and minima and therefore a period one-half as long is clearly ruled out. 737 Arequipa (Fig. 28). A period of 14.13 -+ 0.08 hr seems fairly secure; however, the small secondary peaks flanking
28
HARRIS AND YOUNG I
'
'
i
i
,
I
i
r
i
i
i
j
i
q
r
,
i
I
i
i
,
i
,
I
i
,
i
,
i
0.0
+++
Ix 0.U
x
•~
-8/24/7~ + a/25/ra
•
IO
I
l
I
•
i
•
•
O
i
I
I
L 6
I
I
I
I
AA
8/29/78
× AA A
[] 9/2/78
A ~
•
x 9/3/78
~,~
0
•
• 8/30/78
0~
08/28/78 I
&
oo
•
A8/27/78 0.2
•
I
I
I
,
i
i
,
i
12
I
,
i
i
i
i
18
LIT 2 9 A U G U S T
I
i
i
i
i
0
1978
FuG. 19. Composite lightcurve of 356 Liguria.
I w
i
•
•
0.0
•
I
I
i
I
'
I
+
i
I
+
0
9
I
• 0
•
•
•
•
r
0 12/'3/~ +
+
12/4/78
+ ]2/%/~
Z 0 < +
•
00 .~
•
O
0.1
• •
+
•
+ o
,
I
r
1
4
I
t
6
O+
•
+
r
•
I
8
O
,
10
O
+
o I
J
I
12 LIT 4 D E C E M B E R
14
r
I 16
t
o
I 18
2O
22
1978
FIG. 20. Composite lightcurve of 362 Havnia.
the maximum at 7 hr U T are suggestive of a period one-half as long. We consider the shorter period unlikely, but not impossible. 747 Winchester (Fig. 29). Only two nights of data were obtained, and these could not be combined uniquely to obtain a period. One possible composite is presented, although the 7/30/78 points could just as well repeat the coverage from 8 to l0 hr UT. A period not much different from 8 hr is evident from the August I lightcurve alone. The composite given in Fig. 29 allows almost no correction for decreasing phase angle betwen the two nights. This in turn suggests that the opposition brightening be-
o
W°ff
o
o
< ,~
o o
+7/3o,vo +%1
ee ~,
i
5
,
i
,
i
?
i
i
0 8/1178 ,
i
,
i
,
9 UT
i
,
i
II 51 J U L Y
,
i
,
13
i
i
i
i
i
,
15
1978
FIG. 21. Composite lightcurve of 405 Thia.
i
17
i
t
tween V.0 phase angle (7/30) and 0.35 phase angle (8/1) was much less than expected, particularly for a dark asteroid surface. Since an exact period was not obtained, it was not possible to quantify this result. 952 Caia (Fig. 30). This asteroid was observed on three widely spaced nights at Table Mountain, and fortunately was also observed at the Observatoire de Haute Provence in France on five nights during the same interval (Stanzel and Schober, 1980). A composite lightcurve of all of the observations is presented in Fig. 30. The composite fit appears to yield differences several times larger than the scatter of points within individual curves. The end of the lightcurve on 10/26/78 is particularly discordant. This difficulty suggests the possibility that the period may be approximately twice as long as the 7.50 +__ 0.01-hr period upon which we base our composite. Nevertheless, we favor the shorter value, since the longer period would require a very unusually structured lightcurve.
ASTEROID ROTATION ,~ II z 0.0
'
K
I
I
I
A
I
i
• z~x+/',
•
o
•¢
.A+O+~÷
o+ OA +
3
lit
I
~•+
+•
_~ o., Oe°°e 2
I
29
6
5
4
O jUt,.
+ x IZ/3/~ • 0 I//4/7B • A 12,/5/'78
•+
7
9
8
•O~
I0
11
F i G . 22. C o m p o s i t e
I
I
I
lightcurve
I
I
I
I
I
• •
I
I
I
5
4
13
o f 441 B a t h i l d a .
:-' 0.0
0.1
12
UT 4 DECEMBER1978
•
I
,
I
,
7
6
•
I
(~)
• I
,
8
,
•
I
,
9
I
,
I 12
,
11
l0
,
I
13
UT I JANUARY 1979 FIG.
23. Lightcurve
I
I
i
of 505 Cava.
I
I
I
I
I
0.0
0.1 •
0.2
9
I 5
•
O 0
I
I
I
I
I
I
7
8
9
I0
11
12
UT 29 OCTOBER 1978 Fno.
n
24. Lightcurve
i
i
0.(3
of 516 Amherstia.
' i i • 7128/78
i
i
i
i
i
+ 8/I/78 +•
•L-'_ O.t
o
+
o ~
~++
o
o
o U- 0.2
3
g
•
+
e+o
+O
• °+
+
o÷ o*+ o
°
0.3 i
3
,
i
~
1
i
s
% i
6
;
i
a
;
,;
,
,',
,'2
UT 28 ,JULY 1978 FIG.
25. Composite
light
952 C a i a is n o t p r e s e n t l y i n c l u d e d in t h e T R I A D file ( B o w e l l et al., 1979): h e n c e , its c o m p o s i t i o n a l c l a s s is n o t k n o w n . W e h a v e a s s u m e d a " C " c l a s s b a s e d o n its l o c a t i o n
curve
of 660 Crescentia.
in t h e o u t e r a s t e r o i d b e l t (a = 3.0 A U ) , a n d c o m p u t e a d i a m e t e r o f 91 k m b a s e d o n a n a s s u m e d a l b e d o o f 0.037 as a p p r o p r i a t e f o r a C-class object.
30
HARRIS A N D Y O U N G I
0.1
n
•
0,0
[
I
I
. . . .
• •
I
•.
I
m~
at least s o m e e s t i m a t e o f p e r i o d s e v e n for t h e s e . T h u s our s a m p l e d o e s not suffer significantly f r o m inability to m e a s u r e long rotation periods. In fact, s i n c e w e did not r e o b s e r v e o b j e c t s with rotation rates already w e l l k n o w n , our s a m p l e will carry a bias w h i c h is the r e v e r s e o f any that e x i s t s in the set o f already k n o w n periods. T o illustrate this point, w e c o m p a r e our s a m p l e o f 32 rotation rates w i t h the s a m p l e o f
I
<:~Tb
10223178
+0.1 y
0.1
10129/78
0,0
? +0,1!
•
OD
0.1
0,0
•
•
t
loll
•
•
!11208/78
•
Harris and Burns (Paper I). Since most of
DISCUSSION
our p r e s e n t p e r i o d s w e r e included as unpublished data in Paper I, w e r e c o m p u t e the g e o m e t r i c m e a n period' with t h o s e v a l u e s r e m o v e d ( h o w e v e r , retaining earlier values of objects which we reobserved). W e find
O f the 32 a s t e r o i d s reported here, o n l y 3 (50, 140, and 674) h a v e significant uncertainties in the p e r i o d s d e t e r m i n e d . W e h a v e
; In Paper I, we used the term "logarithmic mean" period, which is the same as the geometric mean.
+0,]
q
B
0
7
8
9
10
11
12
OT
FIG. 26. Lightcurves of 674 Rachele.
0.0[_ I
I
I
o.,F '~A
'
××
"
0
6
12
I
i
18
0
'
6
12
÷ 8/27/m •
-'~0.2
'
I
I
6
8/28' i v
12
UT 27 AUGUST 1978
18
0
UT 28 AUGUST 1978
UT 29 AUGUST 1978
FIG. 27. Composite lightcurve of 709 Fringilla. ,
i
,
r
,
i
,
)L
i
,
i
~:
,
i
,
I
I
I
I
0
I
I
2
,
r
,
i
,
I
,
I
,
I
oI
4
,
I
,
I
,
i
~{]~)
,
t
,
O0110Ollo0++++ I
,
I
I
I
,
I
6 8 UT 2 8 JULY 1978
,
t
o
+ ,
I
I0
,
I
,
I
12
,
I
14
I
'
I
'
I
,
i
I
I
I
I
I
I
I
l
..-'.
I r
,¢-,
.
+ + i t
/
• 8/I/78
4-
~-
+ ++
•
+
ci:: 0.151_+ i
_
*o .
•
+1 i
i
i
i
i
i
i
i
i
UT ' A U G U S T 1978
FIG. 29. Composite lightcurve of 747 Winchester.
I
}
I 16
FIG. 28. Composite lightcurve of 737 Arequipa. --0.051 '
]
,1
I
+++o+ +
i
~
"0 ,
,
i ° t
000000 I
i
,7/28,'78
o+
OJ II Ii
,
+ 7127170
"7 °c / ++o+
I
...I
ASTEROID ROTATION 1 [ | 0.0[~ l
• + o x
/
t~
I
|
-
-I o ~ • •
I
x
I
10/29[TM0) 10/29(OHP) IO/50(OHP) 11/08(TMO)
o ,, . .
o
I
I
10/~'5 (TMO) 10/24(OHP) 10/26(OHP) 10/28(OHP)
,~ ~ ~(: ~ e
I ~ o-P~
v~
31
.a
, , 'o~ a
I
I
I
I
xa" x ' 8 , , -a x o e k,
o
a~t'..,".
.
J.
d2"~X
.'do
o
~
x
,,.
x
o ~ltE
t~
I
4
I
5
I
6
I
I
7
8 UT
29
I
I
9 OCTOBER
I0
I
II
I
12
I
13
1978
FIG. 30. Composite lightcurve of 952 Caia.
of 160 objects. The present sample of 32 NASA under Contract NAS 7-100 to the Jet Propulrotation rates yields a geometric mean pe- sion Laboratory of the California Institute of Technolriod (P) = 14.2 ___ 1.6 hr. We believe that ogy. this dramatic difference proves without a doubt that a considerable bias exists in the REFERENCES available data set. Unfortunately, it is BINZEL, R. P., AND HARRIS, A. W. (1980). Photodifficult to estimate quantitatively the exelectric lightcurves of asteroid 18 Melpomene. Icarus 42, 43-45. tent of the bias. A lower limit to the bias might be estimated by simply including our BOWELL, E., GEHRELS, T., AND ZELLNER, B. (1979). Magnitudes, colors, types and adopted diameters of sample with the rest; this yields essentially the asteroids. In AsteroMs (T. Gehrels, Ed.), pp. the Harris and Burns result, (P) = 9.38 _+ 1108-1129. Univ. of Arizona Press, Tucson. 0.35 hr. We expect that the unbiased (P) BURNS, J. A., AND TEDESCO, E. F. (1979). Lightcurve variations of asteroids: Results for asteroid rotations must be at least this long because our and shapes. In Asteroids (T. Gehrels, Ed.), pp. 494sample cannot-be expected to completely 527. Univ. of Arizona Press, Tucson. cure the bias of the prior sample, only to GEHRELS, T., AND OWmGS, D. (1962). Photometric reduce it. An upper limit to the unbiased studies of asteroids. IX. Additional lightcurves. (P) might be obtained by simply taking Astrophys. J, 135, 906-924. the geometric mean of the two values of HARRIS, A. W. (1979). Asteroid rotation rates. II. A theory for the collisional evolution of rotation rates. (P), to obtain (P) ~ 11.17 hr. This in Icarus 40, 145-153. effect declares that all of the previous HARRIS, A. W., AND BURNS, J. A. (1979). Asteroid sample carries the same bias. We expect Rotation I. Tabulation and analysis of rates, pole that this is too extreme, since the prior positions and shapes, h'arus 40, 115-144. [Paper I] sample is complete through the first 32 HARRIS, A. W., AND YOUNG, J. (1979). Photoelectric lightcurves of asteroids 42 Isis, 45 Eugenia, 56 numbered asteroids, and many other obMelete, 103 Hera, 532 Herculina, and 558 Carmen. jects have attracted special interest resultIcarus 38, 100-105. ing in periods being determined in spite HARRIS, A. W., BOWELL, E., AND YOUNG, J. W. of all difficulties. We therefore conclude (1980). The lightcurve and phase function of the asteroid 304 Olga. Icarus, in press. that a bias-corrected value of (P) is probably - 1 0 hr with an uncertainty of nearly HARRIS, A. W., YOUNG, J. W., SCALTRITI, F., AND ZAPPALA, V. (1980). Photoelectric lightcurve and __+ l h r . ACKNOWLEDGMENTS We thank E. Bowell for providing ephemerides of the asteroids observed, and H. J. Schober, F. Scaltriti, and V. Zappalh for providing plans and results of their observations in advance of publication. This work was supported by the Lunar and Planetary Program of
period of rotation of the asteroid 182 Elsa. Icarus 41, 316-317. LAGERKVlST, C.-I. (1978). Photographic photometry of 110 main-belt asteroids. Astron. Astrophys. Suppl. 31, 361-38l. PORTER, A. C., AND WALLENTINE, D. (1976). Minor planet rotation studies: 1976 January-June. Minor Planet Bull. 4, 14-15.
32
HARRIS AND YOUNG
RIGOLLET, R. (1950). Sur les changements d'6clat ft.
courte p6riode des petites planetes et sur la variabilit6 de (63) Ausonia. C. R. Acad. Sci. Paris 230, 2077-2078. SCALTRITI, F., AND ZAPPALA,V. (1978). Photoelectric photometry of asteroids: 37, 80, 97, 216, 270, 313 and 471. Icarus 34, 428-435. SCHOaER, H. J., AND STANZEL, R. (1979). On the lightvariations of the C-type asteroids 140 Siwa and 790 Pretoria. Astron. Astrophys. Suppl. 38, 265-268. SCHOBER, H. J., AND SURDEJ, J. (1979). UBV photometry of the asteroids 9 Metis, 87 Sylvia and 247 Eukrate during their oppositions in 1978 with re-
spect to lightcurves. Astron. Astrohys. Suppl. 38, 269-274. S'rANZEL, R., AND SCHOaER, H. J. (1980). The asteroids 118 Peitho and 952 Caia: Rotation periods and lightcurves from photoelectric observations. Astron. Astrophys. Suppl. Ser. 39, 3-5. StJROEJ, J. AND SCHOBER, H. J. (1980). Rotation period and photoelectric lightcurves of asteroids 68 Leto and 563 Suleika. Astron. Astrophys. Suppl. Ser., in press. YANG, X.-Y., ZHANG, Y. Y., AND LI, X.-Q. (1965). Photometric observations of variable asteroids, III. Acta Astron. Sinica 13, 66-74.
Asteroid Rotation III. 1978 O b s e r v a t i o n s A. W. H A R R I S AND J. W. Y O U N G Jet Propulsion Laboratory, Pasadena, California 91103 Received F e b r u a r y 19, 1980; revised April 14, 1980 Photoelectric observations of 32 asteroids o b s e r v e d from Table Mountain O b s e r v a t o r y during the second half of 1978 are reported. Rotation periods were obtained for most objects. Absolute magnitudes and phase functions were not determined for any of these asteroids. The geometric m e a n rotation period of the 32 asteroids o b s e r v e d is 14.2 _+ 1.6 hr, as compared to 9.38 _+ 0.35 hr for 182 asteroids analyzed in Paper I (A. W. Harris and J. A. Burns, 1979, Icarus 40, 115-144). We attribute this difference to an observational selection effect which favors detection of fast rotation, as d i s c u s s e d in Paper I. If this is true, then the present sample contains the reverse bias, since it is complete in that a period (in some c a s e s very approximate) was obtained for each object observed, but fast rotators are u n d e r r e p r e s e n t e d due to prior discovery of their rotation properties.
The asteroids to be o b s e r v e d are selected primarily on the basis of opposition magnitude (B <~ 13) from a m o n g those for which no period determinations have been reported in the literature. In cases where more asteroids are available than can be a c c o m m o d a t e d , preference is given to unusual t a x o n o m i c classes (particularly M class) and to smaller asteroids, since f e w e r data are available on these objects. In a few cases, asteroids have been included for which periods have previously been reported, but which in our judgment are of low reliability (Paper I). The instrumental details of the observations are discussed by Harris and Young (1979). The results are s u m m a r i z e d in Table I. in that table, the t a x o n o m i c class and diameter of each asteroid are listed as given in T R I A D (Bowell et al., 1979). The position and phase angle of each asteroid are tabulated for one date only. In constructing composite lightcurves, corrections were made for day-to-day variations in solar phase angle and distances; however, since only relative p h o t o m e t r y was attempted, these small aspect variations are of no future value and are therefore not tabu-
INTRODUCTION
In the course of analyzing existing data on asteroid rotation rates, it has b e c o m e clear that the available data set is inadequate for testing certain h y p o t h e s e s (e.g., Harris, 1979), and contains significant biases due to observational selection effects (Harris and Burns, 1979, hereafter referred to as P a p e r I). T h e s e limitations have resulted in considerable confusion in interpretations of rotation data (Burns and Tedesco, 1979). In the hope of improving this situation, a program of lightcurve observations was initiated at Table Mountain Observatory. In order to avoid a selection effect against discovery of long periods, we o b s e r v e several asteroids sequentially throughout the night, and continue observations of each asteroid for as m a n y nights as necessary to obtain a period. This method has resulted in reliable period determinations for 80-90% of asteroids observed, and at least some indication of the periods of most of the others. At the same time, the method is quite productive: we obtain an average of one period determination per night of observation. 20 0019-1035/80/070020-13502.00/0 Copyright © 1980by Academic Press, Inc. All rights of reproduction in any form reserved.
ASTEROID ROTATION
21
TABLE I ASPECT Figure No.
-
Asteroid
T ax onomic
18 M e l p o m e n e 30 U r a n i a 36 Atalante 48 Doris 50 Virginia 67 Asia 68 L e t • 74Galatea 87 Sylvia 91 Aegina 116 Sirona 135 H e r t h a 140 Siwa 182 Elsa 221 E o s 224 O c e a n a 230 Athamatis 247 Eukrate 270 Anahita 304 Olga 356 Liguria 362 Havnia 405 T h i a 441 Bathilda 505 Cava 516 Amherstia 660 Crescantia 674 Rachele 709 Fringilla 737 Arequipa 747 Winchester 952 Caia
-
1 2 3 4 5 6 7 8 9 10, 11 12 13 -14 15 16 17 18 -19 20 21 22 23 24 25 26 27 28 29 30
DATA
Date
class
Diam eter (km)
S S C U C S S C CMEU C S M C S U M S C S CMEU C C C M U M S S C S C C?
164 95 124 149 88 66 128 113 251 106 80 79 105 46 98 57 116 143 52 68 157 97 126 66 59 65 45 96 96 45 208 91?
12t04/78 10/29/78 9/02/78 9/02/78 12/04/78 7/28/78 8/27/78 10/29/78 8/30/78 8/25/78 1/01/79 12/04/78 11/08/78 12/05/78 7/29/78 8/30/78 10/23/78 9/02/78 7/28/78 8/28/78 8/28/78 12/04/78 7/31/78 12/04/78 1/01/79 10/29/78 7/29/78 10/29/78 8/28/78 7/28/78 8/01/78 10/29/78
AND
SUMMARY
a (1950) ~i
6h41.m3 23 3 5 . 2 23 52.1 23 4 8 . 0 3 41.9 18 0 1 . 8 22 21.1 I 16.5 23 2 6 . 2 21 5 7 . 7 6 23.6 5 55.9 2 41.5 5 12.3 19 4 8 . 4 23 5 7 . 7 2 56.2 23 11.3 21 0 6 . 3 ~2 1 6 . 0 22 23.2 3 56.4 19 5 2 . 7 5 17.8 8 01.3 2 02.6 20 13.7 7 01.8 22 10.0 19 10.4 20 4 1 . 5 1 38.4
lated. The final two columns list the rotation period and lightcurve amplitude determined from the observations.
18 Melpomene. The results for this asteri
I
i
I
I
+ 6038 ' + 0 52 8 05 + 0 51 + 14 32 12 17 24 55 + 644 20 55 - 14 52 +26 31 +27 02 + 10 56 +20 55 14 26 0 40 +22 40 22 13 12 16 - 7 22 15 26 +2904 6 06 +22 23 +26 18 + 3 0 39 5 03 - 0 09 7 04 + 0 17 17 I1 + 14 20
,~
fl
Phase angle
1000.7 354. "T 355.11 357.6 56.6 270.4 328.0 20.2. 343.8 326.4 95.3 89.1 41.z~ 78.9 296.L. 359S 48.2 340.11 315.4 333.2 332.11 63.0 299.0 80.3 117.] 39.3 304.5 106.~I 331.9 289.] 308.2. 28.11
-16°.4 + 3.2 6.6 + 2.0 5.0 +11.2 -13.6 - 1.3 - 15.8 2.3 + 3.2 + 3.6 4.5 2. I + 6.6 - 0.4 + 5.6 15.6 + 4.1 + 3.2 5.0 + 8.5 + 14.5 0.7 + 5.7 + 17.0
15° 18 8 6 7 17 6 7 6 2 2 7 2 4 4 9 9 6 6 2 2 5 7 3 8 5 6 5 2 13 0 3
+ 14.5
22.7 + 4.0 +22.6 + I.I + 3.8
P (hr)
11.572 13.686 9.93 ll.89 >24. 15.89 14.85 9.0 5.1826 6.025 13.7 16.805 22 o r 32'? 80. 10.45 18.933 24.0 ? 12.10 15.06 18.36 31.82 18. 10.08 10.35 7. 7. 7.92 >30. 52.4 14.13 8. 7.50
Am
±0.002 ±0.004 ±0.02 ±0.01 -+0.03 ±0.05 ±0.5 ±0.0010 ±0.003 ±0. I ±0.010 ±2. ±0.01 ±0.006 ±0.01 ±0.01 -+0.02 _+0.05 ±1. ±0.07 ±0.05 ±1. ± I. ±0.01 ±0.2 _+0.08 +_2. ±0.01
I
i
T
i
I
i
r
i
15
16
©
0.0
©
o
+000 0.1
2 5 o
+ +
0~ 10/23/78
•
0.3
oo
•+
0 1o/2,;/~
o
o
+
1
I/0,'3/78
0.4
I
I 4
l 5
I 6
/ 7
I 8
I 9
0.30 0.45 0.17 0.35 >0.15 0.23 0.15 0.14 0.42 0.15 0.3 0.15 >0.005 0.7 0.05 0.10 >0.15 0.11 0.32 0.20 0.22 0.1 0.15 0.13 0.1 0.15 0.33 >0.15 0.18 0.15 0.13 0.12
oid are given by Binzel and Harris (1980). They are included in Table I for statistical completeness. 30 Urania (Fig. 1). A period of 14 hr was reported by Bailey (1913), and of 13.68 hr by Rigol]et (1950). Both of these were
OBSERVATIONS
I
OF RESULTS
I()
U T 29 O C T O B E R
111
I 12
1978
FIG. 1. Composite lightcurve of 30 Urania.
I 13
I 14
I
22
HARRIS AND YOUNG I
{
0.00 - 0
i
i
i
I
1
I
I
I
•
00
I
•
(~
Q + 0.05
0
O <
0.10
O
0
0
•
0
+o
~ c~ ~qP
0
O 8/~/~ • 9/2/78 + 9/3/~
O O
5
II o.15
0.20
• •
0
J 3
i
l
l 4
L 5
,
I
I
6
7
,
l
I
8
9
,
I
I
10
11
,
I 12
,
i 13
,
I 14
UT 30 AUGUST 1978 FIG.
2. Composite
lightcurve
based on visual observations. Gehrels and Owings (1962) reported a period of 13.668 hr based on photoelectric observations. The latter value was based on two widely spaced nights of observations and was very dependent on the correctness of the previous visual observations. Because of the generally low reliability of such observations, 30 Urania was included in our program. Three nights of observations sufficed to yield an unambiguous period of 13.686 ± 0.004 hr, thus confirming the previously reported values. 36 Atalante (Fig. 2). No period has been previously reported for this asteroid. The composite lightcurve based on three nights of data yields an unambiguous period of 9.93 _+ 0.02 hr. 48 Doris (Fig. 3). T w o successive nights of data (9/2 and 9/3) plus one previous night established that the period is almost exactly a submultiple of 24 hr. Since coverage spans 9 hr with very different end points, 8 hr is ruled out. The only reasonable value is thus 11.89 _+ 0.01 hr. Three hours of the lightcurve remained unobserved. R. Austin (private communication, 1979) observed 48 Doris in 1977. His data, while somewhat noisier than ours, appear remarkably similar and confirm the period approximately. 50 Virginia (Fig. 4). Three nights of observations failed to yield a satisfactory period. The night of 4 D e c e m b e r was of poor quality. If the first point o f that night is not
of
36 Atalante.
included, a very long period of - 4 days appears to be suggested. In any case, a period ~1 day seems to be indicated. We r e c o m m e n d this asteroid for further observations. 67 Asia (Fig. 5). Data were obtained on a total of eight nights; however, coverage was still incomplete due to the near-twothirds commensurability of the period to one day. The period is uniquely determined, though, at 15.89 _ 0.03 hr. 68 Leto (Fig. 6). Five full nights of data were required to determine the period of this asteroid, primarily due to the unusual shape of the lightcurve. Three distinct maxima and minima occur each cycle. The period of 14.85 ± 0.05 hr and the triple maxima and minima are confirmed by Schober and Surdej (1980). 74 Galatea (Fig. 7). Only two nights of observations were obtained which were
0.O
x
i
,
+•
i
,
i
,
i
,
i
n
n
,
n
,
I
(~)
ooO000 •
0
ok 0
o•
75
o •
~oo
•
o
o
• 8/50/78 0 9/2/?'8
oo
++-
+ 9/3/78
0.5
x 9/4/7"8 I
5
FiG.
1
6
I
7
I
I
]
,
ill
112
of 48
Doris.
B 9 I0 U T 3 0 AUGUST 1978
3. Composite
lightcurve
L
ASTEROID ROTATION I
0.0
I
I
I
I
•
23
J
I
•"
I
(~)
I
0.1
•
••
•0
•0
-1...
•
0.2
I
I
6
I
12
I
18
I
0
UT 3 DECEMBER 1978
[ i
,
i
,
4
i
,
i
,
i
6
i
~
i
L
8
t
Ci
~X
~-i
I
~0
F i G . 5.
UT 5 DECEMBER 1978
"
i
i
,
+ 7/29/78 [] 7 / 5 0 / 7 8 • 7/31/78 i,
i,
t ]
" 8/11/7"~ Q I
,
,
12 14 16 UT 51 JULY 1978
t
I
,
18
I
,
L
i
,
20
i
I
~
,
22
Jq/
i
24
Composite lightcurve of 67 Asia.
x
x
+ 8/24178
•
•
• 8/27•78
d 0.2= [
I
6
o,
j-
F
I
0
. . . . . . . . . . . . . . . . . . . . . . . . . .
7/25/78 • 7126178 07/27/78 Z~7 / 2 8 / 7 8
/
E O ' 3 , ,
18
Lightcurves of 50 Virginia.
.
0.2lJ-
~J
I
12
UT 4 DECEMBER 1978 FIG. 4.
~J
[
6
~-
9. ~ -
/
• •
*8/28/78
I
,
I
19
,
I
i
I
i
21
I
i
23
I
I
I
,
0
z~8 / 2 9 / 7 8 I , i , i , i , i , 2 4 6 UT 27 AUGUST 1978
I
1 i
,
i
.
I
i
8
I
i
r
r
I0
I
I
I
i
12
I
14
FIG. 6. Composite lightcurve of 68 Leto. UT 29 OCTOBER 1978 2
3
4
5
6
7
8
9
10
II
I
I
I
I
I
I
I
I
1
I
0.0
+ 10/29/78 • 11/o8/78
•
•
•
+•
+
ID
(~)
+0
+
•
+ •
12
+ + +
0.1-
Otp i
+
+
I
I
I
I
I
I
I
I
I
I
4
5
6
7
8
9
10
11
12
13
ur a NOVEMBER1978 F I G . 7. C o m p o s i t e
lightcurve
widely separated in time. Luckily, it was possible to combine the two uniquely, due to the difference between the two minima. The resulting lightcurve covers all rotational phases. In spite o f this, it is not possible to determine uniquely the n u m b e r of rotations which occurred between the
of 74 Galatea.
two nights. The rotation period is thus somewhat poorly determined at 9.0 -+ 0.5 hr. 87 Sylvia (Fig. 8). The short period and large amplitude facilitated a precise determination with only two nights o f data. By combining our results with those o f Scho-
24
HARRIS AND YOUNG i
0.0
,
I
,
i
,
2o
,
i
,
o'
i
&
L+L ~
I
'
•
]
•
,
I
Z 0
/ ~<~ I L O. 51
0
o
g
I
+ o~
~
'~
I
+
*+~'k+
o o+
~
'
I
'J
(~)
. . ,,+~.
• +
%
+ . . . .
,
4
6
5
I
•
+
0
I
. e"x ~ I
• 8/24/78 • 0 8/25/78 zx 8 / 2 7 / 7 8 + 8/28178
+ I
7 8 9 UT 2 4 AUGUST 1978
I0
itl
it
FIG. 9. Composite lightcuve of 91 Aegina.
O
g
0.~
I
~.~+~
0
0.2
I
o+
~,
0.'0~" 0
'
oO
0.05I-
2
I
2 lO ,~ 000 tx
O
g
(3-I
I
0
• 8/50/78 o 9/2/78
(1913) observed 116 Sirona visually over a period of 7 days and reported a period of 0.4 °° L° 19.3 hr. A Fourier analysis (Paper I) of ' ; ' ~ ' ,b' ,', ',~ Bailey's data revealed equally probable peUT 5 0 AUGUST 1978 riods of 13.7, 10.7, 6.5, and 6.3 hr, in FIG. 8. Composite lightcurve of 87 Sylvia. addition to his proposed 19.3 hr, all of which fit his data. We obtained only one ber and Surdej (1979), a period of 5. 1826 _+ night of data, indicating a period of - 1 3 hr. 0.0010 hr was obtained. 87 Sylvia is listed The only value which is compatible with as class " C M E U " in TRIAD (Boweli et al., both Bailey's observations and ours is 13.7 1979) with the diameter of 251 km based on _+ 0.1 hr. A composite lightcurve of a " C " class aibedo. Chapman (private Bailey's visual observations based on that communication, 1979), based on his spec- value is given in Fig. 11. The error estimate trophotometric data, suggests it may in- of the period is the half power width of the stead be " M " class. The diameter corre- spectral peak at 13.7 hr in Bailey's 1913 sponding to a mean " M " albedo for 87 data. Sylvia would be only 130 km. This same technique was used to analyze 91 Aegina (Fig. 9). A period of 6.025 ___ Bailey's observations of 30 Urania. The 0.003 hr was uniquely determined from four most prominent spectral peak was at a nights observations. No other lightcurves period of 13.68 hr, which was correctly noted by Bailey and verified by our more appear in the literature to date. 116 Sirona (Figs. 10 and 11). Bailey recent measurements (Fig. l). •
I
0
I
'
I
,
I
I
,
I
,
I
I
I
1
0.0
Z O
"~
0.I
0.2
•
•
0.3 ,
I 6
,
I 7
,
8
I
,
9
UT I J A N U A R Y 1979
FIG. 10. Photoelectric lightcurve of 116 Sirona.
I
I
10
71
,
I
12
ASTEROID ROTATION
25
O.0 ~r- OI ]
.....
,
°
,
,
I II
. . . .
I
0
*
I
5
0.5
•
•
I
1
•
I I 1/08/78
UT
/
•
•
•
~' 1
II
ill
J2
FIG. 13. L i g h t c u r v e o f 140 S i w a .
ROTATION PHASE
FIG. 11. C o m p o s i t e l i g h t c u r v e of 116 S i r o n a c o n s t r u c t e d f r o m B a i l e y ' s (1913) v i s u a l o b s e r v a t i o n s .
will be presented in a future publication.) The 1978 observations, composited with the 1979 period, are presented in Fig. 14. This lightcurve's smaller amplitude and more irregular form than those of the lightcurve observed in 1979 suggest that 221 Eos was observed at a nearly polar aspect in 1978. 224 Oceana (Fig. 15). Observations were taken during two observing runs a month apart. A very precise synodic period of 18.933 _+ 0.006 hr was thus obtained. The two sets of observations are presented separately in Fig. 14, aligned one atop the other rather than as a single composite, because the amplitude of variation appears to have changed somewhat in the time between observations. We are somewhat dissatisfied with the results for this object in that we cannot rule out a period of one-half the stated value. The points in the range 11-14 hr on the composite appear to suggest a very slight secondary maximum, but on the other hand the two periods of rapid brightening, between 6-7 hr and 15-16 hr, are not exactly separated by 9.5 hr. A single lightcurve 4 hr in duration obtained in 1980 appears to support the longer period. 230 Athamatis (Fig. 16). Yang et al. (1965) report a period of 7.996 hr based on several nights of photometry showing almost exact repetition on each night. Our
135 Hertha (Fig. 12). The data on 135 Hertha are rather noisy, but seem to allow only one possible solution, P = 16.805 --0.010 hr. We attribute the noise primarily to the fact that the asteroid was within 2° of the galactic plane during the course of observations, resulting in considerable interference from faint field stars. 140 Siwa (Fig. 13). Only one night of observations was obtained. Schober and Stanzel (1979) obtained one night o f data only - 3 0 hr earlier. The two lightcurves are remarkably similar in appearance, suggesting a period of - 3 2 hr if the two curves c o v e r the same rotation phase, or - 2 2 hr if they c o v e r rotation phases one-half cycle apart from one another. Additional observations are needed. 182 Elsa. The results for this asteroid are presented elsewhere (Harris et al., 1980). It is included in the table for statistical completeness. 182 Elsa has the longest rotation period yet discovered. 221 Eos (Fig. 14). Six nights of data indicate a low amplitude (-0.m05). This asteroid was reobserved during 1979, and showed a larger amplitude of --0.ml0 with a period of 10.h45. (The lightcurves from 1979
I /tx o
I
0.0
I ' I
I
I
]
J ++
I
I •
IA' •
I
IO(~] '1
z~O © 0
~" 0.1
!"+ O r.~ + ~1~
•O 12/3/7812/4/78 •+ 12/11/781/1/79
A
Z~C) A
] 2./5/78 ~0.2
I
2
,
I
3
t
I
4
I
I
5
i
I
6
i
I
7
i
I
i
I
i
[
8 9 10 UT 4 DECEMBER1978
i
I
11
FIG. 12. C o m p o s i t e l i g h t c u r v e o f 135 H e r t h a .
i
I
12
L
I
13
i
I
14
i
[
15
O~
26
HARRIS AND YOUNG
o.0
-,<'o . <~',.
~-0.1 ~ I ;3
I 4
o.o
~ t....
• ,:.i"-+,
o 7/27 • 7/28
x 7/30 • 7/31
+ 7/29
~. 8/01
I 6
;
F~
I 7
•
I B UT
~.~ ++
I I0
~t
Ill
II
13
7/2817B
Fir;. 14. Composite lightcurve of 221 Eos. U T 29 O C T O B E R
'
+ 8/28/78 A 9/3/78 • 8/'29/78 * 10/23/78 o 8/3o17B • io/~/7B x 9/2/78 Z 0 <
:E
6 I
7 I
'
'
8 I
'
9 '
~
1978
10 11 ' I ' I **wIj~*
'
12 13 I ' I
14 '
0.0
Z 0
*
*** , • •
•
mmI 0.0
_AA
Ii
0
x
+ ,
I 0
,
I I
,
1 2
,
I 3
,
i 4
++,P',, x,,, ,
i 5
t
I 6
,
I 7
,
[ 8
~
0
A
AA
"°° o ] 9
,
i , I , I , i , I , L , t , I , 1 , I 10 11 12 13 14 15 16 17 18 19
UT 29 A U G U S T
~ I 20
1978
FIG. 15. Composite lightcurve of 224 Oceana. Data from l m o n t h later are plotted above the s a m e rotation phase of the earlier data, since the amplitude of variation appears to have c h a n g e d s o m e w h a t in the interim.
two widely spaced nights confirm this behavior: however, our longer lightcurves appear to rule out a period as short as 8 hr, or even 12 hr. We therefore propose a period of 24 hr. Young (private communication, 1980) confirms the 24-hr period on the basis of observations taken in 1974 and 1979/80. These observations will be published shortly. 247 Eukrate (Fig. 17). Our observations of 247 Eukrate indicated a probable period of - 1 2 hr, but we were unable to uniquely determine the number of cycles between our two dates of observation. Fortunately, the observations of Schober and Surdej (1979), taken a week after ours, were
0.1
• lq/2 Is3 o ll/0~'Tb I C
[ 7
••
o l~ o
I ~
]
9
x0~ x
iii
i off [ _~
i2
FIG. 16. Composite lightcurve of 230 Athamatis.
sufficient to revolve the ambiguity as well as extend the phase coverage considerably. The resulting period is 12.10 + 0.01 hr. 270 Anahita (Fig. 18). Porter and Wallentine (1976) report a rotation period of 17.6 hr based on visual observations. Scaltriti and Zappalh (1978) obtained one short photoelectric lightcurve confirming the large amplitude claimed by visual observers. Our observations on five nights unambiguously yield a period of 15.06 _+ 0.01 hr. 304 Olga. The results for this asteroid are reported by Harris et al. (1980) and are summarized in Table I for completeness. 356 Liguria (Fig. 19). Phase coverage of this object is somewhat incomplete owing to the very long period; however, an unambiguous period of 31.82 + 0.05 hr was determined. 362 Havnia (Fig. 20). The data for this object are somewhat problematical. The period we obtain is 18 + 1 hr. We can only comment that the photometric quality of the three nights was poor, possibly explain-
ASTEROID ROTATION I
i 0.0
o
Z 0
o
I
•
a/ao/78 (TMO)
0
9/2/78 (TMO)
~
I
I
9 / 8 / 7 8 (ESO)
X
9/9/78(ESO)
I
+ill
x
+
+ +O
+
X
c~O
o
5
x X
X
+ • X
b-
+
o •
x + +X
+ X x
+ +
o Q
o •
+
+
o
'~ o.~
I
'
X 0 xl
+
27
+
Q
o ,
I $
L 7
I 9
I
~
I 10
L
I 11
,
t 12
L
[ 13
,
1 14
J
[ 15
UT 2 SEPTEMBER 1978
FIG. 17. Composite lightcurve of 247 Eukrate.
ing the discordant points on 3 December, and that no other choice of period seems to be acceptable at all. 405 Thia (Fig. 21). The period o f 10.08 _+ 0.07 hr was unambiguously determined from three nights of data. 441 Bathilda (Fig. 22). The period of 10.35 + 0.05 hr is uniquely determined. Note the difference in depth of the two minima. Repeated points from the same night are plotted with different symbols in order to clarify the actual duration of individual lightcurves. 505 Cava (Fig. 23). With the exception of the first data point near 4 hr UT, one would conclude that the period of 505 Cava is very near 7 hr and that one full rotation has been covered. The first point is totally discordant with such a period, and is in fact lower than any point in the minimum near 9 hr, assuming a shorter period. While we can find no reason for discounting the first point (the quality of the night was excellent), we must conclude that it is somehow incorrect and therefore take 7 _+ 1 hr to be the correct period. Lagerkvist (1978) obtained a short
~ ° ° Ii. . . . . . . . . . . .t...~. . . . . .~. . . . . . . . o~
o~ o ' 1 - . ua 0.21-
~0
-> I-
t~ J
07/27/78
oo
xT/28/v8
~ ~'~. . . . .(. ~. .
~'t
,,
o4
-.~
~ ~
~
~
Oa
~
o3L " • +7/29/v8 ~ " L. . . . . . . . . . . . . . .A. .7./ 3. .1./ 7. .8. . . . . . . . . x. . . . . . 2
4
6
8
I0 12 UT JULY 1978
" 14
16
18
o~ j
.
20
FIG. 18. Composite lightcurve of 270 Anahita.
J ,-J
photographic lightcurve which suggests a similar period. 516 Amherstia (Fig. 24). This asteroid was observed on only one night of excellent quality (it was too faint to be found on nights of poorer quality). Fortunately the one night sufficed to obtain an approximate period of 7 + 1 hr. 660 Crescentia (Fig. 25). A period of 7.92 - 0.01 hr was determined from three nights o f observations. Note the differing minima and maxima. 674 Rachele (Fig. 26). No period determination was possible from three nights of observations. One cannot help but suspect that a star may have been mistakenly observed rather than the asteroid on 11/08/78. Even discounting this night, the period must be at least - 3 0 hr, based on the lightcurve of 10/29/78. Several lightcurves by Scaltriti and Zappala (private communication, 1979) confirm that the period must be long, but likewise fail to yield a unique value. 709 Fringilla (Fig. 27). The phase coverage of this asteroid is still incomplete in spite of eight nights of observations, due to the extremely long period o f 52.4 + 0.2 hr. The lightcurves are sufficient, however, to show two distinctly different maxima and minima and therefore a period one-half as long is clearly ruled out. 737 Arequipa (Fig. 28). A period of 14.13 -+ 0.08 hr seems fairly secure; however, the small secondary peaks flanking
28
HARRIS AND YOUNG I
'
'
i
i
,
I
i
r
i
i
i
j
i
q
r
,
i
I
i
i
,
i
,
I
i
,
i
,
i
0.0
+++
Ix 0.U
x
•~
-8/24/7~ + a/25/ra
•
IO
I
l
I
•
i
•
•
O
i
I
I
L 6
I
I
I
I
AA
8/29/78
× AA A
[] 9/2/78
A ~
•
x 9/3/78
~,~
0
•
• 8/30/78
0~
08/28/78 I
&
oo
•
A8/27/78 0.2
•
I
I
I
,
i
i
,
i
12
I
,
i
i
i
i
18
LIT 2 9 A U G U S T
I
i
i
i
i
0
1978
FuG. 19. Composite lightcurve of 356 Liguria.
I w
i
•
•
0.0
•
I
I
i
I
'
I
+
i
I
+
0
9
I
• 0
•
•
•
•
r
0 12/'3/~ +
+
12/4/78
+ ]2/%/~
Z 0 < +
•
00 .~
•
O
0.1
• •
+
•
+ o
,
I
r
1
4
I
t
6
O+
•
+
r
•
I
8
O
,
10
O
+
o I
J
I
12 LIT 4 D E C E M B E R
14
r
I 16
t
o
I 18
2O
22
1978
FIG. 20. Composite lightcurve of 362 Havnia.
the maximum at 7 hr U T are suggestive of a period one-half as long. We consider the shorter period unlikely, but not impossible. 747 Winchester (Fig. 29). Only two nights of data were obtained, and these could not be combined uniquely to obtain a period. One possible composite is presented, although the 7/30/78 points could just as well repeat the coverage from 8 to l0 hr UT. A period not much different from 8 hr is evident from the August I lightcurve alone. The composite given in Fig. 29 allows almost no correction for decreasing phase angle betwen the two nights. This in turn suggests that the opposition brightening be-
o
W°ff
o
o
< ,~
o o
+7/3o,vo +%1
ee ~,
i
5
,
i
,
i
?
i
i
0 8/1178 ,
i
,
i
,
9 UT
i
,
i
II 51 J U L Y
,
i
,
13
i
i
i
i
i
,
15
1978
FIG. 21. Composite lightcurve of 405 Thia.
i
17
i
t
tween V.0 phase angle (7/30) and 0.35 phase angle (8/1) was much less than expected, particularly for a dark asteroid surface. Since an exact period was not obtained, it was not possible to quantify this result. 952 Caia (Fig. 30). This asteroid was observed on three widely spaced nights at Table Mountain, and fortunately was also observed at the Observatoire de Haute Provence in France on five nights during the same interval (Stanzel and Schober, 1980). A composite lightcurve of all of the observations is presented in Fig. 30. The composite fit appears to yield differences several times larger than the scatter of points within individual curves. The end of the lightcurve on 10/26/78 is particularly discordant. This difficulty suggests the possibility that the period may be approximately twice as long as the 7.50 +__ 0.01-hr period upon which we base our composite. Nevertheless, we favor the shorter value, since the longer period would require a very unusually structured lightcurve.
ASTEROID ROTATION ,~ II z 0.0
'
K
I
I
I
A
I
i
• z~x+/',
•
o
•¢
.A+O+~÷
o+ OA +
3
lit
I
~•+
+•
_~ o., Oe°°e 2
I
29
6
5
4
O jUt,.
+ x IZ/3/~ • 0 I//4/7B • A 12,/5/'78
•+
7
9
8
•O~
I0
11
F i G . 22. C o m p o s i t e
I
I
I
lightcurve
I
I
I
I
I
• •
I
I
I
5
4
13
o f 441 B a t h i l d a .
:-' 0.0
0.1
12
UT 4 DECEMBER1978
•
I
,
I
,
7
6
•
I
(~)
• I
,
8
,
•
I
,
9
I
,
I 12
,
11
l0
,
I
13
UT I JANUARY 1979 FIG.
23. Lightcurve
I
I
i
of 505 Cava.
I
I
I
I
I
0.0
0.1 •
0.2
9
I 5
•
O 0
I
I
I
I
I
I
7
8
9
I0
11
12
UT 29 OCTOBER 1978 Fno.
n
24. Lightcurve
i
i
0.(3
of 516 Amherstia.
' i i • 7128/78
i
i
i
i
i
+ 8/I/78 +•
•L-'_ O.t
o
+
o ~
~++
o
o
o U- 0.2
3
g
•
+
e+o
+O
• °+
+
o÷ o*+ o
°
0.3 i
3
,
i
~
1
i
s
% i
6
;
i
a
;
,;
,
,',
,'2
UT 28 ,JULY 1978 FIG.
25. Composite
light
952 C a i a is n o t p r e s e n t l y i n c l u d e d in t h e T R I A D file ( B o w e l l et al., 1979): h e n c e , its c o m p o s i t i o n a l c l a s s is n o t k n o w n . W e h a v e a s s u m e d a " C " c l a s s b a s e d o n its l o c a t i o n
curve
of 660 Crescentia.
in t h e o u t e r a s t e r o i d b e l t (a = 3.0 A U ) , a n d c o m p u t e a d i a m e t e r o f 91 k m b a s e d o n a n a s s u m e d a l b e d o o f 0.037 as a p p r o p r i a t e f o r a C-class object.
30
HARRIS A N D Y O U N G I
0.1
n
•
0,0
[
I
I
. . . .
• •
I
•.
I
m~
at least s o m e e s t i m a t e o f p e r i o d s e v e n for t h e s e . T h u s our s a m p l e d o e s not suffer significantly f r o m inability to m e a s u r e long rotation periods. In fact, s i n c e w e did not r e o b s e r v e o b j e c t s with rotation rates already w e l l k n o w n , our s a m p l e will carry a bias w h i c h is the r e v e r s e o f any that e x i s t s in the set o f already k n o w n periods. T o illustrate this point, w e c o m p a r e our s a m p l e o f 32 rotation rates w i t h the s a m p l e o f
I
<:~Tb
10223178
+0.1 y
0.1
10129/78
0,0
? +0,1!
•
OD
0.1
0,0
•
•
t
loll
•
•
!11208/78
•
Harris and Burns (Paper I). Since most of
DISCUSSION
our p r e s e n t p e r i o d s w e r e included as unpublished data in Paper I, w e r e c o m p u t e the g e o m e t r i c m e a n period' with t h o s e v a l u e s r e m o v e d ( h o w e v e r , retaining earlier values of objects which we reobserved). W e find
O f the 32 a s t e r o i d s reported here, o n l y 3 (50, 140, and 674) h a v e significant uncertainties in the p e r i o d s d e t e r m i n e d . W e h a v e
; In Paper I, we used the term "logarithmic mean" period, which is the same as the geometric mean.
+0,]
q
B
0
7
8
9
10
11
12
OT
FIG. 26. Lightcurves of 674 Rachele.
0.0[_ I
I
I
o.,F '~A
'
××
"
0
6
12
I
i
18
0
'
6
12
÷ 8/27/m •
-'~0.2
'
I
I
6
8/28' i v
12
UT 27 AUGUST 1978
18
0
UT 28 AUGUST 1978
UT 29 AUGUST 1978
FIG. 27. Composite lightcurve of 709 Fringilla. ,
i
,
r
,
i
,
)L
i
,
i
~:
,
i
,
I
I
I
I
0
I
I
2
,
r
,
i
,
I
,
I
,
I
oI
4
,
I
,
I
,
i
~{]~)
,
t
,
O0110Ollo0++++ I
,
I
I
I
,
I
6 8 UT 2 8 JULY 1978
,
t
o
+ ,
I
I0
,
I
,
I
12
,
I
14
I
'
I
'
I
,
i
I
I
I
I
I
I
I
l
..-'.
I r
,¢-,
.
+ + i t
/
• 8/I/78
4-
~-
+ ++
•
+
ci:: 0.151_+ i
_
*o .
•
+1 i
i
i
i
i
i
i
i
i
UT ' A U G U S T 1978
FIG. 29. Composite lightcurve of 747 Winchester.
I
}
I 16
FIG. 28. Composite lightcurve of 737 Arequipa. --0.051 '
]
,1
I
+++o+ +
i
~
"0 ,
,
i ° t
000000 I
i
,7/28,'78
o+
OJ II Ii
,
+ 7127170
"7 °c / ++o+
I
...I
ASTEROID ROTATION 1 [ | 0.0[~ l
• + o x
/
t~
I
|
-
-I o ~ • •
I
x
I
10/29[TM0) 10/29(OHP) IO/50(OHP) 11/08(TMO)
o ,, . .
o
I
I
10/~'5 (TMO) 10/24(OHP) 10/26(OHP) 10/28(OHP)
,~ ~ ~(: ~ e
I ~ o-P~
v~
31
.a
, , 'o~ a
I
I
I
I
xa" x ' 8 , , -a x o e k,
o
a~t'..,".
.
J.
d2"~X
.'do
o
~
x
,,.
x
o ~ltE
t~
I
4
I
5
I
6
I
I
7
8 UT
29
I
I
9 OCTOBER
I0
I
II
I
12
I
13
1978
FIG. 30. Composite lightcurve of 952 Caia.
of 160 objects. The present sample of 32 NASA under Contract NAS 7-100 to the Jet Propulrotation rates yields a geometric mean pe- sion Laboratory of the California Institute of Technolriod (P) = 14.2 ___ 1.6 hr. We believe that ogy. this dramatic difference proves without a doubt that a considerable bias exists in the REFERENCES available data set. Unfortunately, it is BINZEL, R. P., AND HARRIS, A. W. (1980). Photodifficult to estimate quantitatively the exelectric lightcurves of asteroid 18 Melpomene. Icarus 42, 43-45. tent of the bias. A lower limit to the bias might be estimated by simply including our BOWELL, E., GEHRELS, T., AND ZELLNER, B. (1979). Magnitudes, colors, types and adopted diameters of sample with the rest; this yields essentially the asteroids. In AsteroMs (T. Gehrels, Ed.), pp. the Harris and Burns result, (P) = 9.38 _+ 1108-1129. Univ. of Arizona Press, Tucson. 0.35 hr. We expect that the unbiased (P) BURNS, J. A., AND TEDESCO, E. F. (1979). Lightcurve variations of asteroids: Results for asteroid rotations must be at least this long because our and shapes. In Asteroids (T. Gehrels, Ed.), pp. 494sample cannot-be expected to completely 527. Univ. of Arizona Press, Tucson. cure the bias of the prior sample, only to GEHRELS, T., AND OWmGS, D. (1962). Photometric reduce it. An upper limit to the unbiased studies of asteroids. IX. Additional lightcurves. (P) might be obtained by simply taking Astrophys. J, 135, 906-924. the geometric mean of the two values of HARRIS, A. W. (1979). Asteroid rotation rates. II. A theory for the collisional evolution of rotation rates. (P), to obtain (P) ~ 11.17 hr. This in Icarus 40, 145-153. effect declares that all of the previous HARRIS, A. W., AND BURNS, J. A. (1979). Asteroid sample carries the same bias. We expect Rotation I. Tabulation and analysis of rates, pole that this is too extreme, since the prior positions and shapes, h'arus 40, 115-144. [Paper I] sample is complete through the first 32 HARRIS, A. W., AND YOUNG, J. (1979). Photoelectric lightcurves of asteroids 42 Isis, 45 Eugenia, 56 numbered asteroids, and many other obMelete, 103 Hera, 532 Herculina, and 558 Carmen. jects have attracted special interest resultIcarus 38, 100-105. ing in periods being determined in spite HARRIS, A. W., BOWELL, E., AND YOUNG, J. W. of all difficulties. We therefore conclude (1980). The lightcurve and phase function of the asteroid 304 Olga. Icarus, in press. that a bias-corrected value of (P) is probably - 1 0 hr with an uncertainty of nearly HARRIS, A. W., YOUNG, J. W., SCALTRITI, F., AND ZAPPALA, V. (1980). Photoelectric lightcurve and __+ l h r . ACKNOWLEDGMENTS We thank E. Bowell for providing ephemerides of the asteroids observed, and H. J. Schober, F. Scaltriti, and V. Zappalh for providing plans and results of their observations in advance of publication. This work was supported by the Lunar and Planetary Program of
period of rotation of the asteroid 182 Elsa. Icarus 41, 316-317. LAGERKVlST, C.-I. (1978). Photographic photometry of 110 main-belt asteroids. Astron. Astrophys. Suppl. 31, 361-38l. PORTER, A. C., AND WALLENTINE, D. (1976). Minor planet rotation studies: 1976 January-June. Minor Planet Bull. 4, 14-15.
32
HARRIS AND YOUNG
RIGOLLET, R. (1950). Sur les changements d'6clat ft.
courte p6riode des petites planetes et sur la variabilit6 de (63) Ausonia. C. R. Acad. Sci. Paris 230, 2077-2078. SCALTRITI, F., AND ZAPPALA,V. (1978). Photoelectric photometry of asteroids: 37, 80, 97, 216, 270, 313 and 471. Icarus 34, 428-435. SCHOaER, H. J., AND STANZEL, R. (1979). On the lightvariations of the C-type asteroids 140 Siwa and 790 Pretoria. Astron. Astrophys. Suppl. 38, 265-268. SCHOBER, H. J., AND SURDEJ, J. (1979). UBV photometry of the asteroids 9 Metis, 87 Sylvia and 247 Eukrate during their oppositions in 1978 with re-
spect to lightcurves. Astron. Astrohys. Suppl. 38, 269-274. S'rANZEL, R., AND SCHOaER, H. J. (1980). The asteroids 118 Peitho and 952 Caia: Rotation periods and lightcurves from photoelectric observations. Astron. Astrophys. Suppl. Ser. 39, 3-5. StJROEJ, J. AND SCHOBER, H. J. (1980). Rotation period and photoelectric lightcurves of asteroids 68 Leto and 563 Suleika. Astron. Astrophys. Suppl. Ser., in press. YANG, X.-Y., ZHANG, Y. Y., AND LI, X.-Q. (1965). Photometric observations of variable asteroids, III. Acta Astron. Sinica 13, 66-74.