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UHV PHOTOMETRY OF' ASTEROID 4;3 EROS ^ Ur wM U ^ w m ww^-+ N v uiU :n .^ :A U w R. L. Millis, E. Bowell, and D. T. Thompson N w r' Planetary Research Center u ^+ ti Q Lowall Observatory b Flagstaff, Arizona, 86-001 W D w P. w w w a ^ V
r Q1 m s -7 o4 - -^ 456^e9 qj I
u, w °; SKEIV-DCF Co -' • T1F ACIUjYrN V x ^; ti NASA s 1NPUi v
Four copies of manuscript submitted.
Man,..s ''pt totals 43 pages, including - 2 -
t
RLWIYG HEAD: UBV PHVIIQ1*:TRY Or ERGS
Send proofs to: Dr. Robert L. Millis Lowell Observatory Post Office Box 1269 Flagstaff, Arizona 86001
r s..r
^ 1 i
- 3 -
ABSTRACT
UBV observations of asteroid 433 Eros were conducted on 17 nights
during the winter of 1.9'(4/75. The peal:-to-peak amplitude of the light
curve varied from about 0.3 mag to nearly 1.4 mag. The absolute V
magnitude, extrapolated to zero phase, is 10.85. Phase coefficients
^.I oi' 0.OP45 mag/degree, 0.0009 mag/degree, and 0.0004 ma,/degree were
derived for V, B-V, and U-B, respectively. The zero-phase color of
Eros (B-u = 0.88, U-B = 0.50) is representative of an S (stlicaceous)
compositional ty pe asteroid. The color does not vary with rotation.
The photometric behavior of Eros can be modeled by a cylinder with
rounded ends having an axial ratio of about 2.3:1. The asteroid is
rotating about a short axis with the north pole at a o = 15 0 S o = 9.°
9Ln
i
- Is -
.I
I. OBSERVATIONS
3 ' UKV observations of Eros were conducted or, 17 nights during the
winter of 1974/75. On mo--t nights the coverage spanned one complete
r(_tation of the asteroid. All measurements were made using a conven-
tiona l_ single-channel photometer equipped with standard UBV filters on
the 42-inch (107-cm) telescope at Lowell Observatory's Anderson ;Iesa
site. A do recording system which produces both an analog record (strip
chart) and a digital output via a teletype printer was employed. The
photomultiplier was an EMI 6256 S cooled to -15°C.
Geocentric positions of Eros are given in Table I for each riight
of observation. This ephemeris was calculated using a method developed
at Lowell Observatory for use in a survey progra.^: of asteroid photometry
and is refezreci to as the method of "quasi-osculating elements." These
are the elements which lead to a geocentric ephemeris in best agreement
with positions given by a rigorous numerical integration that includes
planetary perturbations. The quasi-osculating elements therefore differ
from the true osculating elements in two important respects: they
are applicable over an extended interval of time rather than at ar.
"instantaneous' epoch only, and they contain implicitly the effects
of planetary perturbations and light time.
The quasi-osculating elements for Eros were derived from the
I% positions published in Ephemerides of Minor Planets for 1974, Leningrad
1973, and are as follows: - 5 -
M 35602581 e 0.222484
w 17804367 n 2016.76 aresec/day 0 n 303.8233 a 1.45736 A.U. 1 10.8230
The four spherical elements are referred to the mean ecliptic and
equinox of 1950.0. The accuracy of the ephemeris over the interval
August 1974 through July 1975 is probaLly better than 30 aresec in
a and d, and 0.001 A.U. in r and A.
Each night, observations of Eros were interspersed with observa-
1 .. tions of ine or two comparison stars. An effort was made to select
stars which were near the asteroid's path on the sky and which were
similar to Eros in brightness and color. However, it was not always
possible to satisfy all three criteria simultaneously. The UhV
magnitudes and color indices of the comparison stars as determined
from observations on subsequent nights are given in the last three
columns of Table II. These values are based on from one to four
nights' observations as indicated in column six. The uncertainty in
the magnitudes and color indices as 'udged from the agreement of results
from different nights is estimated to be on the order of 0.01 mag.
Column one contains the dated on which the objects were used as
comparison stars, while column two gives the catalogue numbers of those
stars bright enough to be included in the Bonner Durchmusterung or
Schonield's Southern Durchmusterung. The stars' coordinates are listed
1 U.T. dates and times are used throughout this paper.
LI.. IL " in columns four avid five.
Typically a single measureme:t of the asteroid or a comparison
star consisted of three ten-sc_• onl integrations on the object ane one
ten-second integration on the sky through e .uch of the three filters.
The observations of Faros were reduced relative to those of the l comparison stars using mean values for the extinction and *rancforma-
tion coefficients.
Ii. VPLRJ k1 ION IN BRIGHTNESS a The observed V magnitudes of Eros corrected to unit diste.nce from
the Sun and Earth are listed alone with the Universal Times of the mea-
surements (uncorrected for light time) in Table III. These datF are
plotted as crosses in Figures 1, 2, 3, and 4. The solid curves, which
are shown for visual clarity, wer-_ drawn freehand through thc- same
points shifted to the left and right by amounts equal to Eros' mean
synodic period. The ligh t curves in Figures 1, 2, 3, and 4 hav: been.
aligned so that the times of primary maxima (as defined below) coincide
with the midpoint of the abscissa.
Maxima and Minima ; n the Light Cu rve
Table IV lists epochs of light-curve maxima and minima together
%pith their absolute V magnitudes. Like most asteroids, the light curve
of Eros passes through two maxima and two minima during each rotation.
We define primary maximum as the brighter of the two maxima on the
light curve of 18 October 1974, and primary minimum as th^ fainter of
rt._Y_ a n
- 7 .- 1 `^ v c - .
^ 1 the two minima on that date. Further, in order to identify subsequent
primary maxima without con.°union, we suppose that they succeed each
other after an interval corresponding to one synodic axial rotation of i Eros. Primary minima, seco:dary ma.xima, and secondary minima are
identified in a similar way. From this convention it follows that
maxima and minima succeed each other cyclically in a fixed order,
namely: primary maximum, primary minimum, secondary maximum, secondary r- minimum. In this way maxima and minima may always be related to a
given rotational phase of Eros even though, as examination of Figures
,a 1, 2, 3, and 4 End Table IV shows, primary maximum is not always the
brighter of the two maxima or primary minimum the fainter of the two
minima. 1 Times of maxima and minima were calculated from the chart record
of the photoelectric signal. This analog record is at a conveniently
large scale, 2 minutes per inch in time and 10 inches full-scale M deflection, so that the timing of events may easily be made to ±2s. I Timing :narks were established by identifying events on the chart with
the clock time recorded on the teletype-writer output and are accurate
to •_-l s . Hand-drawn curves were used to determine times of maximum and
tc1nimum light for each of the three filters, and this method wa:
preferred to analytical curve fitting because decisions regarding
oc,)r data could be more easily made. The epochs listed in Table IV
have been corrected for light tine: J.D. (c) = J.D. observed-light
ti;ie. The error e is estimated from the scatter in the epoch
_^ 1 - 8 -
determinations for the three filters, the curvature and regularity of
the light curve, and the number of integrations used to define it; e
should be comparable to the standard deviation. The V magnitudes at
maximur;i and minimum light should contain no significant errors d e
to interpolation.
From the epochs listed in Table IV it is clear that tae intervals
between successive maxima and minima va-ied considerably and in a
complex manner as t1:e apparition progressed. For example, the interval
between primary maximum and primary minimum increased from 1.h19m
(0.250 synodic periods) on 18 C ,_tober 1974 to 1 h 35m (0.301) on
4 January 1975, decreased to a minimum of about 1h 20m (0.25) near
12 February, and increased again to 1h25m (0.2(8) on 19 March. The
intervals between the other maxima and minima likewise varied in a
complex manner. A possible explanation for these variations is given
in section IV.
Absolute Magnitude and Phase Coefficient
Veverka (1971) has discussed the pitfalls which are attendant to
the determination and interpretation of asteroid phase curves. It
appears to us that a meaningful. phase coefficient can be derived for
Eros and other asteroids with large rotational brightness variation
if their shapes can be approximated by a two-axis surface of revolution
such as a prolate spheroid or a cylinder. Such an asteroid, rotating
about a short axis, will always present the same figure and total
projected area (illuminated and in shad-w) near times of maximum light,
k 1s
tr ^._^......
_ n _
regardless of aspect. In this case, changes in the brightness of the
maxima correctel to unit distance ca.n be attributed to phase e,fects.
In Figure 5 we have plotted the observed brightness of Evros at
primary and secondary mYxlm,-, corrected to unit distance from the Sun 1 I and Earth, against solar phase angle. The straight lines, whose equa-
tions are given below, were fitted to the data by least squares.
V(l,a) = lo-85 + 0.023 •( Ial (primary maxim'lm)
;.02 ±.0006
V(l,a) = 10.79 + 0.0255 lal (secondary maximum)
±.02 -.0006 ra Extranolation to zero phase of the brightness data for the secondary
maximum may be unreliable in view of the a pparent curvature. For the
''I absolute magnitude of Eros at photometric maximum, extrapolated to
zero phase, we therefore adopt V0 (1,0) = 10.85. The mean phase coeffi-
cient at the V wavelength is S V = 0.0245 n.ag deg- 1 . Eros is considerably
brighter than most previously published results suggest. Taylor (1971)
gives V0 (1,0) = 11.54.
If Eros were not symmetrical about its long axis, then its pro-
jected area at maximum light--and therefore brightness--would vary with
aspect. The variation in brightness due to aspect alone would be
symmetrical about an aspect of 90 0 (equator-on), while the variation
in brightness due to solar phase angle would be symmetrical about
opposition. We will show later in this paper that the aspect of Eros
was 90 0 on about December 29, 1974, at which time the solar phase angle - 10 -
war 30',30°, while oppo3ition occu , red m, ich later on January 21, 1975.
Hence, if there were any subst}Litia l variation with aspect in the
projected area of Eros at m .Amum light, the drs r.a in Figure 5 could
not possibly be fitted by -.ratght lines. Since the data--particularly
for the primary maxima--are well fitted by straight lines, we conclude
that Eros' figure can be closely approximated by a two-axis surface
of revolution. We further conclude that the ph=:,o coefficient which r - 1 we derived is indeed a measure of `.he roughness of Eros' surface. Ampl itude of the Ligh t Curve
Figure 6 shows the peak-to-peak amplitude in the light curve
plotted against Julian date. The data were calculated from the V
magnitudes in Table IV. We define two measures of amplitude: magnitude
at. primary minimum minus magnitude at l,rimary maximum, and magnitude
at secondary minimum minus magnitude at primary minimum. We refer to
these as primary and secondary amplitudes, respectively. A maximum
amplitude of about IT14 near J.D. 2 1142410 (29 December 1974) is indi-
cated.
Posi tion of the Po le of Rotati on
Many methods have been used to c.etermine the orientation of the
rotation axis of Eros, and most of these have been described by Vesely
(1971). We present here a new method based on the dependence of the
light-curve amplitude on the aspect angle ^ (the angle between the
rotation axis and the line of sight).
Wf: assume: (1) that the maximum amplitude in the light curve
G
• - 11 -
occurs when th sub-Firth point is on the rotational equator of F.rus
(i.e., y = 9U°), (2) that Eros is bisymmetrical alout its equator,
(3) that there is no large-zcale ve.riegation of surface texture or albedo, and (4) that changes in the ph , -,e angle or the asterocent.ric declinations of the Sun and the Earth affect the ma gnitudes at, m,,.:{imurr. and minimum equally, and therefore -o not affect -he amplitude. Clearly it is unlikely that these conditions are precisely met, and so the derived position of the pole may be only approximate.
It follows from our model that the light-curve amplitude depends only or. the asterocentrie declination of the Earth d i; (= 90 0-0 and that a given amplitude occurs twice during the apparition, when the aspect is 90°±dE . Hence, if (a 1 ,6 1 ), (a2 ,6 2 ) are the right ascensions and declinations of Eros at aspects 900 -dE and 900+dE respectively, and if (ao,6,) is the right ascension and declination of the (northern hemisphere) pole of rotatiov of Eros, then
tan 6 _ -co! 6 1 cos (a l-ao ) - cos 6 2 cos (a2-a0) . sin 6 , + sin 62
This equation is to be solved for a a , 6o by optimization techniques.
Separate solutions were attempted for primary and secondary amplitudes,
and we assumed that 1P > 90 0 (dE < 00 ) for dates prior to J.D. 2442410.
Five amplitudes were selected (0.4, 0.6, 0.8, 1.0, and 1.2 magnitudes),
and pairs of dates were computed from Figure 6 using linear interpola-
tion. The corresponding geocentric coordinates (a 1 ,6 1 ), (a2 ,6 2 ) were - 1^ - s
used in the equ%tion above. Trial varies of a 0 for each pair of geo-
centric positions then led to values for 6 0 . We supp ose that if ao is
correctly chosen, then the computed 6 0 will not vary with a,%Aitude,
in which case a plot of 6 0 versus, amplitude sho,lld rEault in a func- AI tiona l. relationship with a gradient or correlation coefficient of
zero. In pra^_tiee it w a found that fairly highly correlated linear
relationships exist be!.ween 6 0 and amplitude for all a 0 anal that a
determinate solution for (u o ,%) exists. 0 The solutions ar: a o = 0 42m8, 6 0 = + 14 .9 from the primary
amplitudes, and ao = 1 h 10.6, 6 0 = + 10.3 from she secondary amplitudes
(1950.0 coordin%ites are used). The difference betwee^ t:te two pole
determinations is manifest in Figure 6 as a time displacement between
the two curves: in general the primary amplitude is first to attain
a given amplitude. The solution for the position of the pole derived
from the secondary amplitudes is ill-conditioned because these vary
with time in a somewhat irregular way after J.D. 2442410. We therefore
reject the solution from the secondary amplitudes and adopt:
a 0 = Oh 42T8 ± 4m0 6o = +14 0.9 t 3.4 (1950.0)
ao = 1504 ± 2°2 so = + 903 ± 308 (1950.0)
The probable errors are estimated from the r.m.s. scatter about the
least-squares line in the 6 0 , amplitude plane. - 13 -
III. UbV COLOR INDICE::
In order to derive accurate color indices, it was necessary to
1 correct for the substantial change in Faros' brightnF^ss which occurred during the time required to obtain a complete thr«-color st_:, of 1 mea3uren% nts. The correction wus mane in the present work by fitting
parabolas through ea—h group of three successive observations in a
g!veri f ]ter aril interpol Fit i.ic the observed V a y .! U intensities to
the time of the R-filter measurement.
Rotational C olor Variation
No evidence of rotational color variation was found on any of the
16 nigh ts ] that multi-filter measurements were made. Figures 7 and 8
illustrate the absence of rotational variation in the color indices of
Eros on two nights separated by about seven week:. The standard devia-
t: s ' the color--index measurements on these two nights is between
0.005 mag and 0.00"( map. Certainly any variation in B-V or U-B had
a peas:-to-peak amplitude less than our detection threshold of 0.01 mag.
UBV Colors and Reddening with Phas e
Reddening of certain asteroids with increasing solar phase angle
has been reported in the literature (see, e.g., Gehrels, 1970). In
Figures y and 10 the nig!7t!y mean color indices of Eros from the present
observations (filled circles) are plotted against solar phase angle.
The solid lines were fitted to these points by least squares and are
11 described by the following expressions:
l Only V measurements are available for the night of 8 November.
'if
- ;
B-V (a) - 0. 884 + 0. 000,, I :, I
± .005 ! .0002
U-_B (a) - 0.503 + 0.00043
.Oil ± .0004
w F • is C' _ y s.._.. it t .. P-.y r It:: a ? n 'y
b { nU- B.
F - Te :o (1975) in 1,-.; , while thw circlet: cc,,.% d,,nm-,Lc,•
J. L. Dun lat, (1975) erd W. Wisni.e,;Ai. (19'(>) in T.. _.n. in goof a". .:. t'.. the Lovell ob:.E'r'J:t', r'..... Tno
Fi 'r r-y Ilunikn and Wisn e-w zI,:{. are also in reasonable a6rt: •
d -tta, al tho': r' th ,' :tter 1 E SC'r . wh at ls_tr^;_ I'.
The U-B meal . _ .ts by the Tucson obE: er y .., apt)c to be systecru:t i c-. ly
redd - by about .04 mad; than !e results obtaine? in Fieg_st^. °." and
Le: Cruces. This difference notwithstandi.nv, it is quite cic.r that
Co'or indices art.: representative of as S (silicaccOU:i) cumpo:i-
tiornal ty..- asteroid (Zenner et P1. , 1975).
1V. THE SEA PE OF EROS
We have shown that the color of Eros does not very with rotation,
aril this sugLests that Eros is not mineralogi.cally variegated on a
large scale. Zellner and Gradie (1975) have shown that the polarization
of Eros is constant during a rotation and have argued that both the
albedo and microscale surface roughness are uniform to at least one
ORIGINAL p;ju.. OF POUR QUALITY go
- 1 -
v L-.: a' is d; le' t c, z; 1^•
Be, caus L is qutt('.,
Eros rl-ii t b4L an el oneKtel body' rota l.ine a shor', axts. W ,2 ha,'t
1 *11 a I r, ,t e-- L ----J thi---t, the- variation with phEt.- ,_ eviele of the absolute
o f 1rros ELL r.-Lax'r.lim light ir:plles a figu re which Is mort., or
On -L a , , ., . C t
h !. - 'rith the d i me•nslnns d — ` v .- I by R. --h and Ste 9 In rulf:A
o^i f , because the projec ,f.•-', areEt Or Such an object sr ^n side or . W. "I
V .4 v^-., greatly with aspect.
In F I C-ire I1 we ha-i plotted the light-curve a--iplltude of Eros
I . in a.] a funotio'- Of a - t.s FICl ire C. , we distirv^uish between
pritria-y and secarida-y Eros' a.;pect angle was computed
a^S'Ming the pole der*. - I Wes-; consider the aspect angle so
c,a l culated to be accurate to within about 3 0 , which is q,iite alequ-.Ile
for the purposes of the following discussion.
Computed amplitude-aspect curves for three candidate blaxi.al
figures are also shown in Figure 11. The figures are a prolate
spheroid (PS), a cyl i nder with hemispherical ends (11C), and EL rloht on cylinder (RC). These curves were computed the assumption that the
amplitude of such a body seen at any particular aspect angle is given
simply by the ratio of the maximum to minimum projected areas, expressed
in stellar magnitudes. This assumption is not completely valid because,
as Veverka (1973) has pointed out, the phase coefficient of a non-spherical
ORIGINA!" PAGE, lb OF pooR QUALITY
• . 1 F --
b will be differe_.t w° t? obj- i s end- .
slde -cn. Hence th+:.• e ,,ll bf: 5:..: d oA a.' c,,
phese angle. Ho-. , , , c t}r +_`^ s ar:^ ^,.. n< t veL'3
great.
The three computed curve.; wert- nur: .- i ? to a r. ' e.rr t Fenp l i t^.Of. 1 •
of 1.2 m». by chor,s i.nG ay! al rkLt i o or 3. r)" . ?. 54:1 , and P.35: 1 fur
rigiiL cylinder, r• l:i vely. Althou^ii tt l itu-". a . - . if
ol,s:, rved for H,- 1r+.rGC_r thci' 1 - 0 rr gk:, w•_ tir,ct th=.tdi fi'er-
er. mr-ty be &te to . :Ing ratite t:rc_ r V e 0% shape of Lin.
asteroid, as explfti r • i below. It is immediately t:: . .LrertL from Ficur'e 11
th !tL the form of ti. , for- a prolate shht:roid i:: v^r'y differer-A
thr to that, of Eros. The etc,• ^,2 for thr- ri Eht cyl i rv;. ' iii .- to r .t c-h
Eros well over the range of aspect angles cori6iderctl, and that for a
cylinder with hemispherical ends; matches rather well.less
Wvien the shares of the com p uted rotational light curves for the
three biaxial figures seen equator-or, are compared to the observed
light curve of Eros; near atYxim= w..:pl itude, it is found that all three
curves fit reasonably well , having broad maximtL and narrow sharp
minima. However, the rotational light curve for the right cylinder
has two-peaked maxima, which is not observed. Therefore, the overall
shape of Eros is well matched by a cylinder with rounded ends. I% An estimate of the axial ratio of Eros may be made as follows.
We consider the effect of shadowing by macroscopic irregularities on
ORIGiNAL PAGF; IS OF POOR QUALI1 Y
W r l __f,ri - 17 -
the side and er,d faces. When Eros is side -on to Earth, the total
eruss-nectionfil ar-a Is at or near maxims, ? when std — on to the
Sun, the area of visible from Fu is ne :r minimum. It is
possible that miLxtmum light occurs Letween there twu positions because,
when viewed side-on to Earth, a sma11 axial rutati.on could result in
a greater change in the area or visible s?iadows than the change in
the total cro:::••scctional area. The opposite ar t;, r-iont holds at
minimun light, where the minirnum cress-sect•iorlal area and the maximum
shadowino hav, to be considered. Thus the fraction or the total a visible area which is due to shadowing by macroscopic irregularities
is greater at minimum light than a*. maxim-un, and the amplitude of
the light curve is thereby increased. Therefore, in order to match
the observations well, we require that the amplitude due to an approxi-
mating figure be less than that observed. Now, since the calculated
curves for either of the cylinders mentioned above can be scaled up or
down by increasing or decreasing the axial ratio, an upper limit may
be set to the axial ratio. We find that the overall shape of Eros is
well matched by a cylinder with rounded ends having an axial ratio
which probably does not exceed 2.3:1.• This result contrasts with
the deductions of previous workers (e.g., Cai.11iatte,1949) who con-
sidered that the 1.5-magnitude maximum amplitude frequently observed
implies that the figure of Eros has ai axial ratio of 4.0:1.
Obviously, the photometric behavior of Eros cannot be precisely
modeled by any completely symmetrical geometrical figure. The primary
• - 16 --
and secondary mftxima are not equally bright, ar4d their relative bright- ness changes throughout the apptirition. The sfv%. is true of the minima. Furthermore, a star-1 earl ±,_ ^ , t17- tim- interval between successive :aaxima and minima changes with time in a complicated mariner.
Undoubtedly, thee idiosyncracies of the observed light curve are the result of irregularities on the surface of Faros. Collisional processes are believed to havo_ been imnortWrnt in the formation an ,i evolution
of asteroids, so a heavily cratered and otherwise irregular surface would not be unexpected for Eros. Such features will cast shadows
and therefore have a significant impact on the observed light curve.
It is possible, by invoking strategically located craters, to account
for most of the departures of the observel a:plItude-aspect curves in
Figure 11 from the selected model curve. Flow:!vcr, it is very doubtful
that a unique picture of Faros can be derived in this way.
APPENDIX
Magnitude at the occultation of K Geminorum A
On 2 14 January 1975. Eros occulted the 14th-magnitude star K Gem A.
This unique naked-eye event was widely observed in the northeastern
United States at about 0 h21m U.T., and timings of its duration have
led to an estimate of the projected size and shape of Faros. According
to O'Leary et al. (1975), the data are best fitted by an ellipse measuring
19 x 7 km 2 (preliminary values).
We have determined by interpolation thr- appare p t 'V' nai-nitL'de at - 19 -
I
the time of the occultation, using datn from the five licit, curves of
1'( January through 2 February 1975. The epoch of the secondary minimum
immediately preceding the occultation was estimated to be 2). Janiviry,
0h 08m 35s U.T. (not corrected for light time). The occultation therefore
occurred on a steeply rising part of the light curve, somr: 12 m after
secondary minimum. A)lowin„ for the variation in thf , interval between
successive secondary minima and taking this interval to be 5h16m02s
on 22 January, we find that the occultation took place at a rotational
phase 0.0393 synodic periods after secondary minimum. V magnitudes
were then calculated for the same rotational phase on the five light
curves mentioned above, and these were interpolated to the occultation
time. As an internal. check this procedure: was repeated using rotational
phaE; , ^l measured with respect to the primary minimum and both maxima.
result is :
1975 Jan 211, 0h 21 m U.T. V = 8.009 ± 0.012 - 0.020/minute;
V(l,a) = 11.8 113 ± 0.012 - 0.020/minute;
V(1,0) = 11.63 ± 0.03 - 0.020/minute.
The last term indicates the instantaneous rate at which Eros was
increasing in brightness. The uncertainty in V and V(l,a) incorporates
estima .;ed errors due to rotational phase determination, interpolation,
and observational scatter in the magnitudes, while the error V(1,0) is
larger because of the uncertainty in extrapolating to zero phase (the
ph p s"; function due to Gehrels, 1970, was used).
%I
' l - 20 -
Geometric Albedo
The geometric albedo p may be calculated using a formula adapted
from Bowel] and 7.ellner 09'00:
log PV = 6.?-4 1, - 0.4 V( 1,0) - 2 log r-0. i The apparent dimensions given by O'Leary et al. (1975) indica`.e a projected
area of 10 1: km 2 at the time of the occultation, which is equivalent
to a circle of diameter Do = 1!.5 kra. This leads to p V = 0.29 { 0.01
where the uncertainty reflects that in V(1,0) only. However, a 1-km
error in the length of the short axis would change p by 0.05, so that
the value of p should be taken as indicative only.
The only other direct estimate of the size of Eros was obtained
visually during a series of mi.crornetric measurements by van den Ros
and Finsen (1931). According to Watson (1937) their estimate implies
a long axis of about 35 kin. If '.;e assume an axial ratio of 2.3:1,
then the short axis measures about 15 km. Consideration of our two
cylindrical models leads to maximum cross-sectional areas of 483 km2
(cylinder with hemispherical ends) e_nd 533 km2 (right cylinder).
Taking the diameters of the spheies of e4ual cross-sectional area to
be D o = 24.8 and 26.0 km and using the absolute magnitude derived in
section TI, we obtain p V = 0.139 and 0.126, respectively. It must
again be stressed that these values are indicat3xc only.
1 1
ACKN OWLEDGEIENTS
We thank Karen Duck for assistance with data reduction. This
research was sunported by NASA grant NGR-03-003-001.
,14
2^
9p . Bos, W. if. , ar:I Finsen, W. S. (1931). Phy: ictUl ob..,.riations
of Er Astron. Na^lir. 241, 329-334.
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Arizor _ pre , Tucson.
Caill.iatte, C. (1949). Sur la fi gure des B101. Astron. 13, 21-°3.
Dun' _,, J. L. (19'(2). Laboratory work on the shape or asteroids. Thr-sis.
University of Arizon,, Tucson.
Dunlap , J. L. ( 19'(5) . Lightcurve ., and the axis of rotation of 433 Frus.
Ica~ us, this issue.
Gehrels, T. (19'(0). Photometry of asteroids. In Surfaces and Interiors
of Planets and Satellites (A. Dollfus, Ed.) , pi). 317-375• Academic
Press, London.
O'Leary, B., Marsden, B., Dragon, R., Hansen, E., and McGrath, M. (1975) .
The occultation of Kappa Geminorum A by 433 Eros or! 1975 January 24.
Bull. Amer. Astron. Son., in press.
Roach, F. E., and Stoddard, L. G. (1938)• A photoelectric .light-curve
of x;,ros. Astro phys. J. 88, 305-312.
TL,ylor, P. C. (1971.). Photometric observations and reductions of
lightcurves of asteroids. In Ph- I cal Studies of Minor Planets
(T. Gehrels, Ed.), p p . 117-131. NASA SP-267.
O ORIGINAL ► OF PO()R QUALITY - 22 -
Tedesco, E. F. ( 1975) . IgMg , this
Vt,3ely, C. (19'(1). Sur..,ury on orie:Ltation or hK .•. In Physical Studies of Minor Pla.,iets (T. Gehrels, Ed.) , pp. 133-1 ]10. NACA S1'-2E'(.
Ve •rerk;^, J. (1971). The physical meaning of phase coefficients. Irk
^P Lsical Studies of M i nor Planets (T. Gchrcls, F.d.) , pp. 79-90. NA;1A Si' 67.
Watson, F. (1937)• Tht• physical natu re of Eros. H g rvurd Colle^ac Obs.
Circ. No. 419.
i s issue. f a Wisniew.:_', W. (1977)• Icarus, th
Zellner, B., and Gradie, J. (1975). Polarization of thr, reflected
light of asteroid 433 Eros. Ic,-i this issu(
Zellner, B., Wisniewski, W., Andersson, L., and Bowel 1, E. (1975). Minor planets and related objects. )CVIII. UHV photor:Qtry and
surface composition. Astron. J., in press.
0R1^1R^ pF P
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►7 r^ M Co C- M CJ r1 OJ In M r N M O C) G)M M^C+ Mr 1 r-iLn ^f % M M %Ci r: In N C^ N M r 1 co V t. rt4 U t» ri n t N CIA r^ r-1 Gl G+f ri r--4 N M 1.4r V V ^f M M M N ri ^I
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Al Table II. Corrq)arison stars
Date R. A. Dec. 197415 B.D. 1950.0 1950.0 N V B-V U-a 18 Oct 5h31m54s +50 0 06'5 4 11.170 0.293 0.225 18 Oct S 31 22 50 01.3 4 10.990 0.367 0.247 19 Oct 5 34 32 50 18.2 3 11.600 0.622 0.052 19 Oct +50° 1208 S 34 47 50 20.4 4 8.422 1.105 0.862
8 Nov 6 3S 12 54 37.4 2 11.033 1.006 0.681 8 Nov +54 0 1054 6 3S 27 54 41.6 2 9.415 1.644 1.959 10 Nov 6 40 32 5S 02.4 2 10.546 1.196 1.173 F a 10 Nov +55° 1112 6 40 18 5S 06.5 2 9.900 0.279 0.078 24 Nov +S6° 1209 7 20 14 56 24.3 1 10.969 1.256 1.136 6 Dec +S6 0 1241 7 47 05 56 31.4 2 R.S43 1.663 1.909 6 Dec +56 0 1242 7 47 32 56 37.3 2 9.405 1.076 0.781 24 Dcc +52 0 1278 8 03 27 52 08.6 2 8.876 0.443 -0.036 4 Jan +46° 1348 7 59 36 45 4S.3 2 7.936 1.048 0.985 12 Jan +38 0 1836 7 51 S9 38 21.0 2 8.093 1.061 0.878 12 Jan +38 0 1834 7 51 20 38 14.5 2 8.374 0.665 0.212 17 Jan 7 47 39 32 44.1 2 10.438 0.639 0.204
19 Jan +30 0 1566 7 44 17 30 13.6 2 8.358 1.051 0.875 23 Jan +26° 1633 7 41 05 25 S4.6 4 5.332 1.551 1.852 27 Jan +20 0 1885 7 40 14 20 14.6 2 8.230 -O.OS4 -0.499 I% 2 Feb +13 0 1725 7 36 51 13 00.5 2 8.929 0.624 0.175 12 Feb 7 36 08 3 00.6 3 10.095 0.885 0.600 27 Feb - 6° 2325 7 48 04 - 6 43.0 3 9.250 0.609 0.083 19 Mar -11 0 2321 8 18 23 -12 16.2 4 9.810 1.246 1.221
4
Tab lh 111. Ob .,crved tlrles iitt1.! reduced tra-nitud,5
U. T. vt11K, AAU.l . v; I Jot, U. I U. L yr I .01 11.1. 3 l+ _ If ^-t .I , 1-4 0 ►h.t . 1 0 gh 30 Ps ll!`u1 0)0% " , I I 0" 111.. 1 0'+ 4, on 56.1 1?.0+11 IFI i;. S 1 ' h . I . O6 I n9 F. 09 11.1 12.049 09 5'.' Ot 1:.0 1' l+i 09 1,30.) 09 46.5 12.185 In 01.! 06 S1.1 I L.1 ') 09 35.9 l: _ 11S 10 On 1 l?.41S ON 51.9 12.50; 10 In. S 1 0' U!. ? 1!. 195 09 Me 1!.0;1 10 11 ' 11.301 01 S5.1 12.3' +4 10 14.+ 1 0' 1;.! l?.IR: (Y) S% : 11.941 in i,+ 1?.144 010 91.1 12.SIN 10 !.` q 1 07 :1.3 1.,-IS) 1!t : + 17.077 09 97.1 12.674 110 :' 1 01 3S.9 1:.061 10 `o.. ` ;r 1974 In u 11.9110 09 11.9 12.74i 10 I' 07 41.1 l:. (NI ; In 35. 11.926 00 10.6 12.845 to 07 S1.4 11.911 Ot :6.9 1:.139 In 4t.n 11.4,q 09 .165 In t i 4 09 09 0 11.11%; 06 3, .' 1'.011: in S! t 11.{11 09 !,,.;I 11.12 In J :. S I On 4: ON 0 1 . S 11.11,11 11.916 M S • . ` ► 1.81N 09 S,I I:.4") h l9. S 1 On 11.4 Il-VI 06 S, -.1 11.995 l m,. S 0" t'..5 11 245 10 $4, l 1 Oa 1!.2 11.140 On 9).4 11.116) ll 11 Z 0' . 1.1.1 12.0•+? 10 ;^. 1 04 31.S 11.$19 07 Ot, 1 11.879 ll 1 q '^ II.Bt^+ Ov 41..1 11.9.'.1 11 t l 09 IJ.4 11.144 0' It 11. 90,j 11.,12 Ov 52.4 11.1;1! ll ^• I Od 111.6 11.911 0' ? 11.965 11 t' . 11.1251 O+ S1.S 11.125 Il I I ON S +. J 11.961 n 11.991 11 3 it. 9A In 0! 6 11.651 11 I' I 09 0'.! 12.0+6 0 1 t, t1t It 4• 12.0•' In 0'.1 II.S,N It I 01) 15.4 1:. In i i + i In it.? 11 1'6 I! t I 09 31.2 1:.14 7 1 it 5^ 17.718 10 IS.4 11.;?q It c 01 ) 11.9 1:.277 O h ` 1 P. til 10 IR.$ 11.521 ll t' I 09 S0.0 11.2S7 of W 1 1 In 21.4 I .SOS 11 4 1^ 09 S).2 12.199 09 1' + l 6 n r 1974 10 26.4 11. SOS ll 1 In 10.1 12.12S 01 2'.4 1' 1:1 In 311 . 4 II.SO4 11 5' i 1 1 11 19.7 1:.041 08 3 7 .1 11.111 O7 2 ! 1 , R 11.789 10 $4.3 II.SII 12 01 9 I 10 2 7 .1 11.966 ON 43.; 111.396 07 28.9 11.750 lO 39.4 II.SSO 1? no . ! 1 10 34.7 11.951 09 $: 11.272 07 40.3 11.724 10 72.5 11.571 111 11.1 1' ' in 4S.1 11.9)15 09 nt.' 1:.125 07 48.1 11.746 111 46.1 11.607 1? 116. l 1 i 10 S;.O 11.901 09 1 0 .1 1?.031 07 55.9 11.788 In SO.? 11.6SR 12 11 O:.S 11.9),d 09 19.4 11.955 ON 01.3 it. oil 10 S4.3 11.710 12 24.S I' 111 IO.S 11.941 09 Ml 11.911 OR 16.0 11.953 I n 58.9 11.414 11 29.? 11 11 :1.0 11.981 01+ 28.7 11.491 D4 15.6 l 2.04 11 03.0 11.890 12 34.0 11.3: 111 35.9 12.041 09 38.2 11.861 08 31.1 12.16' 11 (18.9 12.039 12 38.8 11.3 - 09 4,.6 11.649 O q St,-2 12. 241 11 14.5 12.10S 12 45.6 11.30, 19 150h"1* r 1974 09 51.9 IIASS OR 45.1 I? 391 11 1X.9 12.360 12 48.3 11.4"•, In n 7 .; 11.113 ON 4^ 11 15.0 12.511 12 S4.8 11.43! W. 46.S 12.246 10 F"1.948 ON 5 12.646 it 16.9 11.668 06 S6.5 12-271 In 1N., 11.973 01, 0 3 i 12.811 11 31.0 11.771 12 J..: ::: . 19'5 0' 14.5 12.125 110 27.6 12.069 09 "IN. l 1!.898 u 3S.3 11.112 07 14.4 10 40.0 09 15.9 12.090 12.215 12.714 11 39.9 12.712 07 11.4 11.250 07 1:.5 12.047 10 49.$ 1?. 361 09 23.1 12.49! 11 44.3 11.708 07 19.6 11 'I1 0 7 31.3 11.995 11 04.3 11376 09 31.1 12.240 11 48.4 11.611 07 29.1 11.1'1 07 41.S 11.909 It 13.8 12.539 09 38.6 11 S1.7 12.S63 07 34.0 11.160 07 50.1 11.397 12.541 11 20 J 09 45.8 1, 876 11 S5.6 11.131 07 38.4 11.161 OR 08.4 11.9:7 11 C9.: l'. t'% 09 so., 11-778 it S9.7 12.40S 07 45.2 11.1X3 08 13.9 11.958 11 37.9 1.'. X17 In 06.9 11.707 12 03.7 12.31n 07 49.6 it. 20i 08 :6.9 11.98,1 11 41.3 P.114 In 14.1 11.686 11 07.6 111225 0' 55.0 11.229 08 36.5 11.034 11 53.3 11.99! In 1 0 . 3 11.680 12 MSS 11.056 07 S6.a 11.261 ON 49.2 12.079 11 59.3 11.913 10 26.9 11.704 12 17.8 11.960 ON 06.1 11.376 08 56.9 111133 12 08.0 11.889 10 31.1 11.747 1? 22.3 11.872 08 10.0 11.433 09 00.4 12.131 12 14.6 11-864 10 39. 1 11.819 11 26.4 11.105 08 13.2 11.488 09 iS.O 12.185 12 23.3 11.857 10 46.4 11.922 12 29.4 11.767 09 16.9 11 SSA 09 25.8 12.198 12 29.8 11.871 10 St.S 12.047 Do ?9.9 11. gab 09 33.3 12.250 12 34.3 11.916 10 SR.S 1:.153 4 Ja..wry 1975 09 t;.9 12.000 09 39.6 12.179 12.321 12.087 11 05.7 08 56.9 09 47.3 12.117 24 Noy' d-a t 1974 11 12.6 12.496 07 37.2 11.436 08 41.0 11.184 09 5417 12.047 Il 20.0 U. 6S4 07 41.6 11.471 08 4S.0 12.299 10 OS. 4 11-974 06 3S.9 12.134 11 21.7 11.701 07 46.3 11.519 08 49.4 12.331 10 12.8 11.925 06 4S.1 12.276 11 32.2 11.693 07 $0.7 11.595 08 5:.6 12.307 10 21.1 11.871 06 S6.6 12.496 11 3Q.S 11.629 07 S7.9 11.716 08 57.1 12.211 10 29.0 11.843 11.155 07 04. S 12.653 11 47.0 12.541 08 01.4 11.787 09 01.3 10 39.8 11.8001 07 07.7 11.711 11 57.2 12.407 08 07.7 11.850 09 05.4 12.o6e In 54.6 11.829 11.921 09 0'+.6 11.972 07 16.0 12.79: 12 04.5 12. Ms 08 12.0 11. 91:4 11 01.4 11.1159 07 21.4 12.714 12 16.4 11.9')1 OR 16.6 12.014 09 11.7 11 08.9 11.889 07 30.2 09 17.4 11.769 12.S16 12 21.8 11.891 08 11.1 12.116 11.706 11 19.5 11.950 07 33. 7 12.421 12 31.0 11.816 09 2s.6 12.124 09 10.4 11 26.8 12.000 09 /4.S 11.618 07 41.1 11.119 12 39.0 11.773 09 18.9 11. 318 11 33.4 12.066 07 46.9 09 26.3 11.541 12. 105 ON 33.3 12.430 11 43.S 12.179 07 S2. 3 i?.0I1 24 Deccr&• r 1974 ON 37.7 12.523 09 31.7 11.495 09 35.5 11.441 11 SO.4 11.192 08 00.s 11.904 OR 42.2 12.567 09 40.6 11.379 08 08.7 11.827 07 12. 3 11.782 OR 46.5 11.613 11 Yovr Fee 1974 08 14.S 11.798 07 16.9 11.723 08 50.9 12.427 09 44.s 11.338 09 57.1 11.241 08 12.1 11.794 07 21.3 11.677 08 SS.O 12.25E 07 11.5 11.973 10 01.2 11.2?4 08 30.0 11.790 07 26.5 11.634 on SR.9 12.111 08 07 35.625.9 11.879 11.at1 07 37. 4 11.580 09 03.0 11.979 10 OS. 2 11.209 10 08.4 07 30.4 11.865 08 41.1 11.870 07 42.5 11.559 09 06.3 11.392 11.204 07 44.7 08 48.9 11.784 10 12.4 11.201 11.879 11.935 07 49.7 11.S59 09 10.7 11 16.2 11.203 07 51.0 11.891 08 S6.4 12.026 11, S73 09 IS.1 11.0593 07 59.5 11.95? 09 00.5 I1.09S `0. 3 11.593 09 19.4 11.613 110 20.3 11.211 ON 13.5 12.084 09 08.4 11.233 S.4 11.612 09 :4.2 11.543 10 23.6 11.222 11.476 10 27.S 11.240 08 21.6 112. 179 09 11.7 12.297 UJ -.;.4 11.657 09 23.4 11.266 08 29.1 12.249 09 19.S 12.438 08 IS.I 11.721 09 35.0 11.109 10 31.3 11.199 03 36.5 12. 110 09 2s.1 12.529 08 10.7 11.793 09 41.7 11.340 10 35.6 08 S0.2 12.399 09 33. 2 12.590 08 27.0 11.873 09 45.9 11.318 10 39. 1 11.330
t
'Taft m , {.'3 e 1 01 3 lablt_ Ili contlio.A%
U.1. 3'(I") U. C. Y^lr.) U. i 1..11, 1) U. T. 1..11, 1) U. 11 IS l'h!3It7 11713 - ;h4 1 ^ Oy6 Ih 0,^, l• ..,.3 . t0! l ► n5 4 I V, 11 OS S ; In^4 I' !1.957 0; J) 1 1 t .. I: 05 3 ' n l0 46. l I 1. 1:.060 05 4'.1 1.grit) 013 i • I t Oh I 1. t0 $0. 7 11 I 1 1 .0 1:.201 OS 44.8 11.964 n'• t - ;I 1111 0 , 1 l0 $3.8 t' Sd.6 ► ' 12.114 OS $n.O 11.937 0. 11.0,; O6 c , 1 In $8.1 t1 l? S?.1 1!.043 at SI.3 11.0011 0' t 11.ga• 00, 1 ll 01.1 l OS S2.7 I I r 0 11.111 0' 1 I' ll Oi. t l: 17 J'ut,11r, :17$ 05 $J.2 1 I 0 11. i 0• ! 1 ll 119.9 l l 05 5115 l l . • I' 11. hl n• j 11 1:.9 1' 03 3 1 .9 Il•?'t' 0. .., ; 11•'" I ll.!+: r 1 11 1 7 .6 1 0•• Ci.L 1:•.`-• 0, t'.I 11.6?' 1 11 t 11 n.t.; 1 20.8 1: 0► 11. I on P- , 11,601 1 I. I' r. 1 ll 25 2 I: & 10 .9 11.1•• 06 0-.1 11.1ti1 l II ry 1 ll 29 5 1 06 25.6 II.SJI 06 11.0 11 Ina In I 1 n 1 I U 31.6 1: 06 3,1 .1 11.611 06 it.1 11.419 In II n t 1 It 17,S 1' On I 11.0:4 0, I'.4 11.36' Ut .': 1` t n' I I fry ' I' 0,. 3. • 11.- t [', n 11 11 4 lit 1 f 0 1 Il t I C• J'.J ll.v 11 1 ` I' 0 I 1 •• 1. J l 0• t .1 11.•:, i• I'.' I 1 n' 1 1• ,t ; 11 S: li 0•• ^I.t 1'.q , r 11. L•', I ll 0 i 1 .0 :. l l 5 l l . ' 06 5 ' . 1 V. 11 i n. ) 1 l . Iw: ' 0' 1 11.010 l2 C' 11 070$.3 11.9.'4 Or .8 11.140 in 4 , .7 11.8' 07 1 ,+.1 11.9.'6 it 0 11 •. 01 07.6 11. WO Ot 1' 1 11.081.) 10 S0.8 11./11. 07 21 3 11.949 12 U I! 0" 11.6 11.687 Or, 1- 2 11.061) 10 S!.S 11.9:6 07 2 • 11.853 1? I' II t 0' 1; ' II396 O0, 4:.? IL OSS 10 $3.8 11.OSI 0' St 11.731 1' l' O- !'.: 11.1112 Of ;1.5 11 .14! 10 S5.1 11.978 0' 3: l' I. 0" 11.0.1 Of, 14.8 1' 10 56.9 11..006 07 3 1' o - Sn.l 11.2,67 O6 S-A 1, '' In SR.I 1?.011 07 40.S 11.204 07 0,. •7 II ' In 5').5 a 11 11.016 2 F, 07 44.9 11.154 07 03.9 ''' 11 00.8 1..013 I. 0' 47.6 11.110 0' 06.9 11.01; 11 0..0 11.001 03 31.3 l t . 0" $3.9 1!.OR1 07 09.8 11.041 11 03.; 11.976 OS 35.1 1 1 07 43. r, ll v 0' 58.? ILOS7 07 11.7 11.054 11 0. 11.95? OS 37.4 1i. 41'1 t 0' 48.1 11 06 0 1 .4 II.O34 07 15.9 11.073 11 0, 11.939 03 35 .4 II." 07 56.1 11. ;t: ON O,;.S 11.0160 07 IS.R Il. m t 11 0'.9 1!.+. 03 4:.6 It. 371 OR 00.9 11 t• On 11.1 11.0.'4 0- 11.8 11.11 2 1 OS Jt.3 11.34; at 01.6 11 0, 1;.7 11.0 29 07 24 11.14.) 11 1 0 .9 11.+ ? 03 4;..3 11.326 08 09.1 11 Or ".; 11.0.11 07 !'.7 11.1'1 11 14.6 11.T43 03 4').'a 11.304 08 11.6 11 0, '' . 1 11.0111 0' 3( • .6 11.2r!v 03 54. 1 11.281 O8 19.5 ll ! as .' .5 1.1.19 07 35.7 11..'45 27 J L 1't"., 03 S7.1 11.263 08 26.8 11.1 Si 08 38.6 :.in.' 0' 36.6 it.Zwh 03 5 1).3 11.263 08 5:.3 11.074 08 4S.6 11.31x, 07 3).6 11.356 03 39.7 11.3+' 04 0 L 3 11.259 OR lo.i 11.071 08 $4.4 1'.4?: 0' 4:.7 11.391 O3 41.1 I1.tt 04 03.2 11.261 Oi 11.3 11.06) OR S 11 .3 11.S;t O' 4;.7 11.445 03 50.3 11.1 04 oi.l 11.259 ON 15.4 11.05; 0-+ 04.1 11 b-tu 07 4;.6 11.5117 03 $3.6 H. t 04 07.6 11.253 ON 4j.9 11.003 09 08, 1 IL 7!8 07 S1.8 I1.'•," 03 St'.6 11.511 04 11.3 11.267 ON 54.S 11.0'3 09 13.3 11.819 07 5;.0 11 03 59.6 11.55n 04 15.3 11.277 06 5x•9 111093 09 17.7 11.897 07 SN.5 11 0.1 Oi.3 11.64? 04 19.3 11.287 01) 03.4 11.119 09 22.3 11.961 08 0119 it."'-, 04 08.2 11.694 04 20.3 11.298 09 08.9 11.166 09 17.0 11.995 J8 0;.4 11.81' 04 It.4 11.744 04 21.3 11.313 09 14.2 11.215 09 31.6 11.99? 08 09.9 11.813 04 14.5 11.808 04 24.3 11.324 09 20.S 11.315 09 36.7 :1.9511 08 10.8 11.8`35 04 17.6 11.853 04 26.4 11.33; 09 25.1 11.389 09 41.4 11.865 08 11.1 11.913 04 20.3 11.8')9 04 28.3 11.362 09 30.5 11.486 09 46.0 11.753 08 13.6 11.94: 04 23.1 11.946 04 33.3 11.410 09 35.3 11.597 09 $4.9 13.553 08 1419 11.948 04 2S.1 11.919 04 36.3 11.451 09 40.1 11.715 013 59.4 11.469 08 16.1 11.959 04 27.0 12.017 04 39.2 11.481) 03 44.2 11.798 In 04.5 11.385 08 17.4 11.974 04 1R.9 12.040 04 41.1 I1.S19 09 48.S 11.895 In 0).4 11.317 08 14.7 11.978 04 30.9 12.051 04 43.1 11.546 09 53.5 11.959 10) 20.0 11.198 OR 20.3 11.980 04 31.8 12.063 Of 44.9 11.579 09 57.7 11.017 In 25.3 11.159 08 21.S 11.979 04 34.8 12.06? 04 47.1 11.6?1 10 01.5 12.0.0 to 31.3 11.114 68 21.7 11.980 04 36.7 12.050 04 49.3 11.662 10 06.8 12.058 10 35.5 11.097 08 14.0 11.961 04 38.6 12.019 04 51.3 11.700 10 11.3 12.000 IO 39.9 11.081 O8 25.7 11.914 04 40.5 11.987 04 55.9 11.783 10 15.9 11.927 10 44.4 11.072 08 26.9 11.914 04 41.4 11.943 04 59.! 11.857 10 20.0 11.833 In 48.8 11.067 08 28.2 11.907 04 44.3 11.903 OS 01.1 11.906 10 38.4 :x.443 In S3.2 11.076 08 29.5 11.880 04 47.6 11.850 05 04.1 11.960 10 41. 7 11.376 In $7.9 II.OBS 08 30.8 11.855 04 Sn.6 11.778 05 06.5 12.002 10 4 7 .7 11.312 11 01.2 11.107 08 3.'.3 1I.8.'9 04 53.6 11.717 05 U..# 12.060 10 $2.8 11.248 11 10.4 11.155 OR 35.8 11.746 04 S6.6 11.669 05 10.8 12.093 10 58.8 11.200 11 14.4 111188 08 39.3 11.660 04 59.6 11.610 OS 13.1 12.131 11 03.S 11.169 08 42.4 11.591 OS 02.6 IL S54 05 15.5 12.170 11 01).3 11.115 23 Jwiw ry 1975 08 45.8 11.526 05 OS.7 11.506 05 17.5 12.181 11 14.7 11.076 08 49.0 11.469 OS 08.S 11.456 05 19.5 12.203 It 19.6 11.081 OS 12.8 11.495 08 S1.3 11.413 OS 11.4 11.419 05 21.4 12.208 11 24.5 11.079 OS 18.1 11.579 08 55.3 11.364 05 14.7 11.362 OS 13.3 12.208 11 30.2 11.081) 05 21.1 11.645 08 So- 11.322 05 17.8 11.328 05 25.3 12.195 11 32.4 11.097 OS 17.0 11.738 09 01.7 11.278 OS 2n.8 11.291 OS 27.3 12.175 It 38.7 11.125 OS 31.S 11.821 09 04.8 11.247 05 13.7 11.258 OS 29.2 12.151 11 49.0 11.213 05 33.4 11.861 09 07.7 11.214 05 26.8 11.227 05 31.3 12.118 11 S5.8 11.283 05 34.7 11.890 09 11.0 11.191 OS 30.0 11.208 OS 33.6 12.095 12 01.S 11.3S7 OS 36.3 11.913 09 14.0 11.158 OS 32.9 11.179 05 35.9 12.059 12 06.5 :1.424 05 37.8 11.951 09 17.4 11.135 OS 38.2 11.156 OS 38.6 12.014 12 11.1 11.486 OS 39.3 11.996 09 ZO.4 11.114 OS 41.1 1:.142 05 41.Z 11.971 12 15.0 11.549 OS 40.7 12.n04 09 23.3 11.101 OS 43.9 11.135 05 47.4 11.640 12 19.9 11.630 OS 41.2 12.023 09 26.3 11.094 OS 46.7 11.129 05 49.9 11.794
ORIGINAL PAGE`; IS OF POOR QUALITY
4 Millis et of Toble Tl, gaje 1 of 3 Table 7 1 1 c)411t ft,t:ed.
U.3. Y,1,:) U.1. Yll,.) U. 1. V(i,.I U.T. Y(I,1) U.T. 5(1,•) 6. 21 (v.. )e'd.) Of ' Ir" IT4)."J O,, .f,, 11^ 45, osh irs 11,17. aiI`IM4 1?" ,): 04 I1. S it11.9')') pr. 1,,? 11.457 05 55.2 (2.416 01 15.1 11.81)' Oh;4 ) 1 1^7li Om t'i.7 9, 7- U1) f" 4 11.49: as SJ.O 12.451 of ln.n 11.11%' 0i S6.6 11.6111 04 !!.6 11.4 0o 1 11316 0. 01.7 11.44n 04 19.' It.#)' OS $7.9 11.63% as '4 .5 11.Ae; Of. ;'.5 11.55` Of. 06.S 12.4!4 01 ?s n It 4't OS 19.4 11.6!1 01 2n .S It. 11;s pr. 5 it .61 Of. 10.3 12.4111) 0: + 11 4, On 0:. 7 11. 119 as :4. S 11. 794 07 0. .9 11. -n: Or. 11.9 11.174 01 :. 1 11 . 0 - 06 O;.S II. Si! 04 51.4 11.'111, 0' 01,4 .1 )1.'A1 Or, 17.7 11.IS4 n 1'.4 ► 1.117" On 04.0 11.596 04 S;.O 11.717 07 ii.4 11.4 1 1 On 21.6 12.183 0 S".n 11.96' On 10. 7 11.470 ad 3:.6 11.6'1 07 1,).? 11.nk, W1 2S.2 12.245 a4 S4.2 11.914 06 1.1 .5 11.457 04 Se.I 11. el 07 2t.4 1'.111• 06 29.0 12.181 O4 4?.6 11. 9,11 O6 14.4 I1.4Sn 04 t".6 It. S"o 0' 17.1 1.'.'1, a, 52.8 1..11' 0' 1 t 111.044 On I1.3 11.411 04 4! 4 ll.St4 07 1;. 11 1' Or. 56.6 1!.0.11 04 1 I1 In'
On 18.5 11.3)7 03 11.7 11. S:5 0' t4. • 1 1` t,. M, 4a.S 12.114' 04 y'.7 11.9.0 06 20.7 It. SA7 04 U . ' 1t. ' t 0' 4_ 4 1' ) • Or 4:.1 11.01 , 04 S'.4 11.9;' On 13.1 11.571 04 t • .` 11.5 - (I' 4 , . r 1 Or tv.') 11.4 1? IV 1 Of $4.) 0615.1 ll.,,, 04 $•'.n 11.1 07 $ .n 0, 51 7 11.11 t- 0.'11 1`.no 06 21.1 11.1 , Od ;-' S It.1 0' 5! ' 1'.' ! 0• 5'1.1 II A l 0, 011 .3 l: 071 On 29.1 11.345 08 it. S Ill 0' S + l' ": an S).! 11.8).+ as nq. n 1.. 1011 On 31.6 11. Sin Oa S%.1 11 % ': ! 1'.11 ) 07 02.9 11. Stn Oi II % 1-'.114 06 5A . 2 11.311 04 +,. ' 11. S4% 04 l :. n l I. !: • 0- (,..') I1. 8113 OS 1! 11. 144 On 17.0 11. 321 09 0 i. 3 11 l:: 0,5 1 - '• l l . v• . 07 10. 4 11. 741 0', 1 • l' 177 Or, 39• n 11. 11 - 0• i ,.. l l t u I t w 07 14.6 I I 7 70 0; . 1 0 1' 71 t On 41.0 I1. 0 • 1 . S ll 0 11 0: 14. i 11.75' 0, 2 , 1 1.. ?t t n. 01. 4;.6 ll 11 -, n, ;, 1!.^', 0 1 11.7511 0. 1' •'.. 00 4S . 7 It. c, n- l l. t; 0' s 11. 7112 0-. On 47.7 II. S t • h :. 1'%:, o. 1:.1) 11.5.. 0 so l 11.772 0'• 1:.! l ?1,v 06 49.3 11. 3t1 as 51.7 ll.S'6 07 3.,.9 11,774 OS 34.3 1:.28: On S3.S 11. 1:a OS 11.5 11.6!7 07 3:.7 11.79S 05 41 6 l: 291) O6 S;.5 11.14` as ', 4 11.58; 27 F!Urwry 1975 07 41.i It. Ill OS 4:.11 1l. M t 011 SA. 11. t,). OS 5.1 , 1 11.559 0" 4$.4 11.614 0; 4°.4 1.+.? 54 0° 94.4 11.5'1 0.1 1k.S 11.528 OS 34.8 12.324 G7 49.1 11.81); 05 51.1 1!.211'+ P.! 0' 03.1 11. 03 40.7 It.Sl6 03 34.7 12.276 07 $3.? 11.89% 05 ;4.7 1 ?1' 07 0a.2 11. 40 i OS 4S. 1 11-510 03 4 t. 7 11.143 07 $7. 1 11.937 05 -A. ! 1:. 197 0' 07.0 11.4'" 03 49.S 11.511 03 4'.3 1?.!1)q OA 01.? 11.94? Or. 0:.0 12. In: 07 0v.! 11.41,5 03 Ss.7 11.5:0 03 St.I 11. I T S 04 05.5 12.0.',) O6 01.4 11.11! 0' 111 11.450 OS 58.3 11.S17 03 se,. 1 12. 115 08 51.6 11.301 1 On 07.6 1? N% 0' I3.' 11.475 04 0:.3 11.551 04 01.A Mae! 08 37.2 12.326 on 10.3 12.105 07 16.1 11.498 04 0 7 .7 11.5811 04 01.6 I!.0t1. 08 43.8 12.334 1,k. 13.0 1:.082 07 18.9 11.537 04 1!.0 I1.d56 04 - .4 11.q')) OK 47.2 11.322 On 16.S 11.05) 0 7 20.8 11.556 04 1.'.0 11.715 04 1t.6 11.94.1 08 $0.5 12 294 On 19.9 11.031 0' 11.7 1I.SA6 04 1i.n 1 1 0163 04 1h.G 11.904 as Ss.9 11.271 On 2119 12.00" 07 24.6 r,4 11.607 38.S 11.910 04 21.1 11.if,1 08 5 7 .1 1?. 24A 06 16.8 11.9811 07 16.7 11.617 04 42.7 11.996 04 :1.! 1I.Ati 01) nn.3 11.254 Of, 21 f. 11.973 0' 19.9 11.680 04 46.6 12.049 04 18.0 11.796 pr• VA 11.953 07 30.11 11.704 04 $1.4 12.117 04 31.7 11.770 19 %111 1975 00 5,.1 11.9118 07 31.4 11 7 31 04 ;•.! 12.19! 04 3;.1 11.750 Or. 39.7 11.9.57 07 3 y .9 11.742 05 01.5 11.152 04 34 .2 11.752 0! 4S.3 11.1011 On 42.1 11.91? 0 7 38.0 it. BI' 05 05.9 11-243 04 43.2 11.7:0 0! 49.6 12.216 06 45.6 11.90x, 07 39.9 11.845 05 10.2 12.276 04 4'.0 11.710 02 51.7 12.220 On 19.4 11.89; 07 41.8 11.87' 05 14.5 t?. US 04 S0.7 11.716 02 $11.5 12.215 on 52.2 I1.88n 07 44.3 11.920 OS 18.9 1?. 187 04 54.8 11.711 02 S9.4 17.210 On S4.9 11.8 °1 07 46.6 11.951 0$ 14.1 11.1_'1 05 02.6 11.75A 03 10.5 12.193 On 58.7 11.8 '. 07 49.5 11.999 05 18.6 12.062 05 01'.1 11.781 01 2S.2 12.131 O' 01_9 11.8+ 07 S1.4 12.035 05 31.7 11.981 OS 10.1 11.815 OS 27.3 12.107 07 0(.4 11.8')') 07 53.4 12.063 05 34.5 11.920 05 11.9 11.850 01 30.7 12.085 07 09.2 11.904 07 S5.4 12.089 OS 45.5 11.818 05 17.6 11.895 03 33.6 12.067 07 11.1 11.904 07 SA.2 11.120 05 48.2 11.'73 05 21.4 11.935 01 36.i 12.066 07 14.8 11.9!5 09 00.1 12.139 05 56.8 11.648 OS 15.1 11.980 01 46.8 12.013 07 18.5 11.94! OA 02.0 12.158 06 01.2 11.601 0$ 29.7 12.033 03 50.7 12.005 07 U.1 11.951 08 03.9 12.167 06 05.6 11.561 05 U. 4 121059 OS 53.6 11.989 07 26.7 11.981 08 05.7 12.161 Or, 10.5 11.520 AS 36.2 12.163 01 S6.4 11.9114 07 293 11.990 OK 07.8 12.140 Or, 15.5 11.486 40.) 12.220 OS $9.? 11.948 07 32.8 12.0118 08 09.8 12.111 On 20.0 11.462 OS 43.8 12.274 04 02.9 11.957 08 1I.S 12.082 O6 14.9 11.4SS 05 47.8 12.336 04 06.4 11.912
ORIGINAL PAGE IS OF POUR QUALITY
r.ble LU 3 6 KiINs c 7 .1. Q°9e 11 3
-:V --- . , V Ln Ci C) N C. N C. N C- Cn co Ln Gi Ci C) r/ In Ci C) r. U K. n Ct n ri r1 r/ V V ^D n Cr n M C) C, C. ri ' f riN Nr-J NH r/N rN 1 NH Nr/ Nr-i Nr i rC'J 1 r-1ri f-1r-/ rN 1
o C: ri cC C7 r 1 n 00 G7 M It N n M V r-t' (N 4 C) H N C-J M r1 %C U) ch tfi ,r O +I +I +I +1 +I +I +I +I +I +1 +I +I +1 N r-1 1 N M M OC N, to N PJ Gl 00 00 m Or, Y, Ln H Ln to Lr, U) n Ln ri H 7, )D C. C) %G N 00 G. W ri C) kci or L') tG 1z U W C: n CC "D ^G r-1 C, V C) LL n Or, ror,- 00 Ci C. Q) 07 O C) CID c- +1 CYJ Ct1 C) H Lf n Lr 11^ v Ci) r1 Ln C1 C1 M tom) Ln "C, or, G H N N M M M M t, M tn n V V ~7
*,,' I i N n Ln G, V o M v o Ln v Ln N L7 O G. )J' \.D co or.) O O %D Ln N N N GI or) m co n ^c Ln M r-+ O C) H ri ^-} rrl i rr--i 1 Hr1 Hr 1 r1r--1 r-1 riH r1H riH r--iH r1ri r-1r1 r-ir-1 I. HI Y C) C4' Cd CO Ci c. )D C-. \D c: i C) O M H M tt N Ln ct V t I n (14 U CIS iV %C H H r 1 %0 H -r Ln K r-i a7' cr Ln -A ^ -zt G FI +1 +I +I +I +I +I +I +1 +I +I +I +I +I
• C^ 1 V N C: V %D N Ln %G In M C) Cl H Ln Y Y. -t c n tr ^o n n n rn r i C) .0 o, Ln OrJ 00 M O C) %D n M N 1D 1D O C) N U W V N H C) O V N M r1 r 1 ,.O M O) V r W ^^ C) 00 an n C) m v) C, m a) co m n n Or C, C) r-1 N Ln r^ Ln G1 r1 Ln CT tS3 Ca M M Ln \0 C;, n or:) C r-1 N N M M M ^^• t M M M M M M V V V S V V V X C; C) i O M M Of) O t r) r--i O V M i'S n C1 G^ C) %C N OO C) N N nH %0 O N Lr) n C1 00 )D M N H U O O U r-1 ^t ^ ^ Nr-i HN NH Nr-i HN HN NH HN r-iN HN r/N Nr1
•r1 ^ i O ri ^F C) V CU CC 4--1 O O or, C) O V 4--+ /. N ri N V 00 to Ch co \.p n C) -1 Ln O V U-) V C) +I +1 +I +I +1 +I +I +1 +I +I +I +1 In CJ r-1 '+ I N 0e) It r1 Ln M N Ln O %O r^ M U j }( N N O Lr) 07 H Ln Lr) O r-1 M 00 O 1 O M C) C) \r) V M O n 1- n 00 ¢. R' U LI O Ol n 00 'D 00 M 00 M Ln 00 W A. I C^ Cn m m 00 m o n r- T %D t-: 00 r1 Ln n Ln 1O 4 O H Ln Ln Qt Q M tD n O 1-1 N M M M M M M M M M c1 'I'T V V V V V V O H .J C^ E-' .--1 cri Cr) (14 00 C) r1 H Ch n C) LS M O V r-i N Ln V O n \C n U; 00 00 00 n Ln M N O C. O r1 r-1 r1H r1 Hr1 r-1 r-1H r-i r-4H H H Hr1 Hr1
I 1 H O CIS C13 O Q) n O n r1 O M V %D M C) C) O V O N rA M n 11 -1 'A \.D 00 N r-i r-i •ct u) }+ t? O +I +I +I +I +I +1 +I +1 +I +I +1 R^ N ri t N Q) %O r--i Ln (7) 00 rt V Q) Ln }( ¢t C1t O O O Ln Lr1 r1 n O O Ln H Ln (7) n M n M 11 ^D C1) 0Y U W V 17 O Ln r-+ N 1-1 N n cr C) a. 00 rn rn C) 00 00 CD rn (M C) 00 +I 00 CJ) r-1 L!n n Lr1 r^ V 0; 14 LA Q M M tD n OU O 1-1 N N M M M M M M M V V •c* V zr V ti
H
O U) O O 7 Cv '7
? 00 Cr) 00 C) v t0 V V N t\ C) M n n I r 1 r 1 r-1 N N r 1 .--1 r-1 N N CT a H lr • ^, C 3 C'-^ C 7 C ^ r ^ r^ r• t• r l
^' rJ ►n f^: N C
Y. f
^, { ^nr Ln n c v :Zr
r .I M C) Ci a` ►n ► n N V" n C!.' rl • r-1 r1 ri it r. r{ r 1 r1 ^j C ^ ^..^ N M r i l!1 t G.; +1 +I +; +I r n (1J ^J U N C) t - tJ c^ +, C; v Lnn n Cl ^t v v v J
Ln r i C Z5 7J O ^l^ N ^^ N
y r--I ri r{ r'
} Ln O 1./7 ^ H f• J Qi 01 r{ +i +1 ^ V C +I tl N r / (^^ M u'1 V OM r, ^ N a oo [, +1 o ^j v ^ n rn r1 ti O
"C3 c, ^, n v OU ri r 1 Ll1 aJ M I^ n 00 O
ri r-i r-i Ly r-^1
r. r-Iri G w O n . I G1
r O +I +I +I +I V -4 I N r) Lf) K O W r ^ M n o 00 R: U w n Ln 7:1 +I LA U^ o 0 rl .^^ inv nv vCM ^ I a^ a^ N c. U O U-)
^ N N ^"'^ c0 nr--1 Cl r-1 • - 30 -
FIGUEEs CAP i0.
Figure 1. `1 light curv,.a or 433 Eru:;. The crosses are the actue.l
observed points. The curvea were drawn freehand throi.igh the same
points shifted to the left and right by amounts equal to Eros'
mean synodic time: primary maximum coirncidej with a: period. The of i t
the midpoint of the abscissa. Magnitudes are corrected to unit r.
heliocentric and geocer,trlc distance:;.
POI ' Figure 2. Caption as Figure 1.
Figure 3. Caption as Figure 1.
Figure 4. Calution as Figure 1.
Figure 5. Brightness of Eros at the primary maximum (P.M) a.nd secondary
maximum (SM) of the• light curve plotted as a function of solar
phase angle. Filled circles denote points obtained prior to
opposition; open circles are observations after opposition. The
straight lines were fitted to the data by least squares.
Figure 6. Primary (filled circles) a.d secondary (filled squares)
amplitude of Eros' light curve plotted against Julian date.
1
r - 31 -
Figure 7. Observed V maZni t ulE:; and color i n li ct:s of P;ros from
December A, 19(4, p l otted a. a function of Ur i versat Time.
w The observed V mq-nitudes of the cor:parlson st ,^r• ar also given
as an indication of th .! photon .• tric qurtlity or the night. Note
that the measurements of Ero:;' brightness are plotted on a i compressed scale.
l). Figure 8. Observed V magnitudes and color indices of Eros from
February 12, 1975, plotted W; a function of Universal Time. The
observed V magnitude: of the comparison star are also given as an indication of the photor.-'Lric quality c" the night. Note that. the
measurements of Fruo' brightness are plottt^rl on a compressed scale.
Figure 9. The I)-V color index of Eros as a function of solar prase
angle. The filled circles denote the present observations from
Lowell. The circled crosses are observations by Dunlap (1975)
and Wisneiwski (1975) from Tucson, while the barred circles refer
to measurements by Tedesco (1975) from Las Cruces. The straight
line was fitted by least squares to the Lowell data.
Figure 10. The U-B color index of Eros as a function of solar phase
angle. The filled circles denote the present observations from
Lowell. The circled crosses are observations by Dunlap (1975)
and Wisneiwski (1975) from Tucson, while the barred circles refer
to measurements by Tedesco (1975) from Las Cruces. The straight
line was fitted by least squares to the Lowell data. - P -
Figure 1 t . Prim ary (ci rcles) anI secondary (squares) &-mpl i tude of the light c-_irve of Pros plotted as a function of aspect ^ (lo,;tcr
ordinate) and Julian &- t e (upper ordinate). Filled symbols per-
tain to y > 90°, and open symbols to ^ < 90°. Computed eJrplitude-
a:.pect curves are identified as follows: PS prolate spheroiri,
CH cylinder with hemi.spheri.cal ends, and RC right cylinder.
r ,a
lb
0.1 - M A.G
TIME ^I OUR I+
r
+ ♦ ♦ +
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+ ♦ +
+ ♦ + f ♦ ♦ f f
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+ ,
1.4_ TIME 'I OUR l TIME -^I OUR I^-
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11 1
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moo 11.6 11.8
♦ p 11.7 11.9
O 11.8 • 1.+ • 0 11.9
20° 30° 40° Sl
SOLAR PHASE ANGLE Ll
Mill%$ et al. k6mn 5 '---~--~---r---V--~--~~--'---.---~---r---r---T--~ g 0 VI 0 o N • .q o r; ~ ci h
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9.3 • 9.4 •
9.5
9.6
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9.8.—•
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0.49 •e Inca " e e e " " " e ° e 0.50 ee e e " e ° e I ° e e eee "e" •ee e • W = 0.51 ° e " e " " " e e e e • s 0.52
7 8 9 10 11 12 13 UNIVERSAL TIME (HOURS)
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Amplitude, magnitudes 0 0 0 Or js P ^^ O N A
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