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Graduate Student Theses, Dissertations, & Professional Papers Graduate School
1976
A dynamical analysis of the observed time residuals for eclipsing binary stars
John Harrington Doolittle The University of Montana
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Recommended Citation Doolittle, John Harrington, "A dynamical analysis of the observed time residuals for eclipsing binary stars" (1976). Graduate Student Theses, Dissertations, & Professional Papers. 8446. https://scholarworks.umt.edu/etd/8446
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RESIDUALS FOR ECLIPSING BINARY STARS
By
John H. Doolittle
B.A. Physics, University of Montana, 1973
Presented in partial fulfillment of the requirements of the degree of
Master of Arts
UNIVERSITY OF MONTANA
1976
Approved by:
Chairman, Board of Examiners & D e a ^ Grdduare>^chool UMI Number: EP39247
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Doolittle, John H., Master of Arts, December, 1976 Physics
A Dynamical Analysis of the Observed Time Residuals for Eclipsing Binary Stars (174 pp.)
Director; Thomas E. Margrave^'^Çj^^/^
This thesis presents a method of analysis for determining the masses and dynamics of unseen companion bodies whose presence about an eclipsing binary star may be inferred from the cyclic variation in residuals of the observed times of eclipse. Applica tion to the eclipsing binary system RZ Cassiopeiae indicates that the observed time residuals may be the result of the motion of two unseen companions of spectral types M3-M5. Included are FORTRAN computer codes which predict future eclipses, create and manipu late 0-C residual data files, and f i t observations with a theoret ical 0-C residual curve generated by a three-body dynamical interaction model. A tabulation of time residuals is given for fourteen eclipsing binary stars. ACKNOWLEDGEMENTS
This study has been supported in part by University of Montana
Small Research Grant 841-3R, which has allowed the author to make eclipsing variable star observations at the Blue Mountain Observatory.
The literature search has been greatly simplified by access to the
University of Pennsylvania's Eclipsing Variable Star card catalog, pro vided through the courtesy of R. S. Koch. Appreciation is also extended to Mrs. E. H. Doolittle for assistance in locating reference material at
Weslyan University, and to H. G. Krogstad for clerical assistance in assembling eclipsing variable star data files.
m TABLE OF CONTENTS
ABSTRACT i i
ACKNOWLEDGEMENTS ü i
ILLUSTRATIONS vi
TABLES V i i
Chapter
T. INTRODUCTION .
An effect of companions on eclipsing binary stars 1 Abundance of multipi e-body systems . . . 2 Binary star classification ...... 3 Eclipsing binary star light curves . 4 Predicting eclipses ...... 6 Variations of eclipse period . 7
Continuous variations . 7 Discontinuous variations . 9
Selection criteria . . . 10 Observed times of minima . 11 Average eclipse period . 14 Visual detectability . 14
II. PHYSICAL ANALYSIS 20
General procedure 20 Circular orbits . 21 Elliptical orbits ... 24 Mutual-interaction model 30 Units 37
I I I . APPLICATION OF MUTUAL-INTERACTION MODEL TO RZ CASSIOPEIAE .... 39
IV. DISCUSSION . 49
Radial velocity residuals 49 Reduced 0-C residuals 51 Osculating orbital elements 51 Error control ...... 53 Minimizing companion interactions 54 Predictions ...... 55
SUMMARY 56
Appendix
1. 0-C RESIDUAL FILES . 58
KO Aquilae . 60 RY Aquar11 . 62 BF Aurigae ...... 64 BF Aurigae (secondary) 66 441 Bootis ...... 68 441 Bootis (secondary) 71 DO Cassiopeiae . . 73 RZ Cassiopeiae ...... 75 RZ Cassiopeiae (abbreviated) 88 TW Cassiopeiae . . . . 92 XX Cephei - * 94 SW Cygni 97 WW Cygni . . 100 TW Draconis 103 TX Herculis ...... 107 IX Herculis (secondary) 109 Z Orionis . . . . 111 AT Pegasi 113
?. FORTRAN CODE LISTINGS 115
Program FILCHG . 116 Program AVEPER , 121 Program DETECT , 124 Program NTERAC . 127 Program BINOBS , 149 Program OCPLOT . 153
1. SPATIAL CONFIGURATION PLOTS 156
Model 67 . 157 Model 127 160
LITERATURE CITED . 172 ILLUSTRATIONS
Light Curve of RZ Cassiopeiae o
2. Evidence of Apsidal Rotation . 8
3. Detectability of Companions 18
4. Epicyclic Model 22
5. Elliptical Orbits 25
6. Inclination of Fundamental Plane . 28
7. 0-C Curve Fit by Elliptical Model 29
8. Three-Body Interaction Forces 31
9. Coordinate Translation . 36
10. Effect of the Longitude of Periapse on the Placement of the 0-C Curve . . . 42
11. 0-C Curve Fit by Interaction Model 67 43
12. 0-C Curve Fit by Interaction Model 127 46
13. Radial Velocity Residuals 50
14. Reduced 0-C Residuals 52
15. Interaction Model Flow Chart , 128
VI TABLES
1. Candidate Program Stars 12
2. Mass-Luminosity Ratio 16
3. Companion Masses and Orbital Parameters Found Using Elliptical Model ----- 30
Companion Masses and Initial Rectangular Parameters Found Using Interaction Model 44
5. Accuracy of Observations 58
6. Typical Model Log 131
7. Eclipsing Variable Schedule of Minima 150
vn CHAPTER I
INTRODUCTION
An effect of companions on eclipsing binary stars
It has long been recognized that the presence of unseen companion bodies in motion about an eclipsing binary pair could result in the ob served deviation from predicted times of occurrence for the binary eclipses. The gravitational reaction of the central pair of stars to moving companions would cause it to wander with respect to the center- of-mass (COM) of the multibody system. This wandering motion of the eclipsing binary will cause its distance from the sun to be variable.
Since the speed of light is a constant, the amount of time required for light to arrive from an eclipsed binary pair is directly proportional to its distance. The variation of light travel-time with distance is ex hibited in the long term variation of the residuals found by subtracting the expected time of eclipse from the observed time of eclipse. The light travel-time effect has the underlying assumption that the period of revolution of the binary pair about each other is constant. Any radial motion toward or away from the sun that the entire multibody system might have will be constant and thus adds a constant amount to the intrinsic period of the eclipsing binary pairs without affecting the amplitude of the period variation.
While the light travel-time effect has often been postulated to explain the historical behavior of certain eclipsing binary systems, no method of analysis has yet been devised which describes the masses and
time-dependent positions and velocities of the possible companions which
would account for the observed residuals. A method of determining these
parameters by applying a technique of fitting the residual curve using
dynamical models is developed in this thesis. The method is then applied
to the eclipsing binary system RZ Cassiopeiae.
Abundance of multipi e-body systems
Before suggesting the existance of companions to explain the time
residuals observed for the light minima of eclipsing binary systems,
it is worth considering whether such systems are likely. Choosing as a
representative sample of the galaxy's spiral arm population, the 253
stars found within 10 parsecs (32.62 light-years) of the sun, 42.3% are
found to be single stars, while the majority (57.7%) are members of
multiple star systems. It seems probable that less massive dark compan
ions would be associated with stellar systems in even greater abundance,
since the greatest gravitational interaction experienced by any one
companion would most likely be due to the central pair, while the other
companions would only offer secondary perturbations, and gravitational
stability of the system could be expected. B. M. Oliver (1972) lists
examples of several stars known to have dark companions, either through
astrometric or spectroscopic studies, and concludes "that a more or
less continuous spectrum of systems exists between symmetrical binaries
at one extreme and single stars with a giant planet, or planets, at the
other." Apparently, multipi e-body systems are the rule rather than the exception, and it is quite plausible to hypothesize low-mass companions about the central pair in eclipsing binary systems.
Binary star classification
Binary star systems can be classified in one or more of several catagories. Stars which appear on nearly the same line of sight yet are separated by such large distances that they are not bound gravitation al ly, are known as optical pairs and are of lit tle interest. Visual binary stars are also resolvable but are indeed bound. Their motion about a common barycenter, or two-body center-of-mass, is usually well described by the laws of Kepler and observations can yield a determina tion of their orbital elements and masses.
For many binary systems only one point of light can be seen due to its particular distance from the earth and spatial separation and the relative luminosities of the component stars. One classification of unresolved pairs Is that of the astrometric binary. Although these systems often are relatively close to the earth and the apparent magni tude of one body is beyond detectability, the presence of the dark companion is seen as a wavy displacement of the visible star rather than the linear proper motion expected for a single star when sky photographs that are taken several years apart are compared. An example of an astrometric binary is Barnard's star. Explanations for the observed motions of this star have been offered which postulate the presence of one (Van de Kamp 1962, 1969a), two (Van de Kamp 1969b), or even three
(Suffolk & Black 1973) unseen companions whose masses are comparable to that of Jupiter. Spectroscopic binaries are those whose spectra show a periodic
doppler effect. Much information about the projected orbit of one or
both stars about the system's COM can be derived by noting the temporal manner in which the spectral lines are shifted towards the red as a star
recedes and towards the blue as it approaches the point of observation.
Binary stars whose motions are in a plane other than the plane of the sky
(i.e. the plane whose normal is the line of sight) will have radial
velocities with respect to the earth and might be expected to exhibit
such a doppler effect. A maximum doppler effect for any system occurs
when the system's orbital plane lies along the line of sight to earth.
These systems are particularly interesting because their orientation
causes each star to periodically eclipse the other and are thus referred
to as eclipsing binaries. Since eclipsing binaries are also spectro
scopic systems, information about the relative orbits and masses of the
stars can be determined through spectroscopic analysis.
Eclipsing binary star light curves
The variation of the brightness of eclipsing binary stars is conven
iently displayed by a graph depicting the system's apparent magnitude
versus time. Usually referred to as a light curve (figure 1; Rossati,
1970), it is characterized by constant brightness except during times
when eclipses cause a reduction in the amount of light reaching the
observer. Since the two stars may be of different absolute magnitudes,
alternate eclipses can differ in depth as measured from the near con
stant brightness seen during times outside of eclipse. The deeper or
primary eclipse occurs when the brighter star is eclipsed by the less OLU 3
O c
0.0 0.5 1.0 PHASE
Fig 1. Light curve of RZ Cassiopeiae D bright star. The secondary eclipse occurs approximately one-half period
later when it is the less bright star which is being blocked from view
by the brighter star. Since the light curve is repetitive, the period can be defined between any two times with the same relative phase.
However, by convention the time of zero phase occurs at the midpoint of
the primary eclipse.
Predicting eclipses
When the period (P) of an eclipsing binary is well defined, the
prediction of times of occurrences of eclipses be made simply
by extrapolating from a known time of occurrence (T^nown) ^ past
eclipse.
Tcalc = Tknown + ^ * P (1-1) The epoch (E) is necessarily an integer indicating the number of events
which have occurred since the known time.
The linear elements of this expression (i.e. P and are
occasionally revised for binary systems which display apparent variations
in eclipse period.
The difference between the observed time of an eclipse (0) and the
time calculated from the linear elements (C) is referred to as an 0-C
time residual. A plot of 0-C residuals against time, in years (appendix
1), or against epoch number, shows a temporal history of the system's
eclipse period. The sign of any particular residual indicates whether
that eclipse occurred earlier (negative) or later (positive) than pre
dicted. The slope of the 0-C curve shows whether the eclipse period at that time tends to be shorter (positive) or longer (negative) than the value of the period chosen for the calculations.
Variations of eclipse period
The period variations exhibited in the 0-C residual curves of eclipsing binary stars may be classified as being either continuous or discontinuous.
Continuous variations. A possible explanation of a continuous variation which is periodic could be apsidal rotation. If the relative orbit of the eclipsing pair of stars is an ellipse of eccentricity greater than zero, then a rotation of the line of apsides is possible. The effect of the variable orbital velocities associated with elliptical orbits com pounded by the rotation of the orbit is to produce a sinusoidal variation in the 0-C curve (figure 2). Observational evidence for apsidal rotation is found when a graph of the time residuals for the secondary minima has the same shape as the graph of primary minima residuals but is of the opposite phase (Wood, 1950). In such cases the secondary minima will oscillate about the 0.5 phase point of the light curve with a period corresponding to the period of apsidal rotation.
It is interesting to note that a light travel-time effect also is associated with these systems. The spatial excursion of the point of eclipse, however, is relatively small. Typically this effect has an 0-C amplitude of less than one minute during the cycle of apsidal rotation and therefore may be considered to be of minor importance.
In other cases in which the 0-C curve shows continuous variation, the secondary minima residual plot again shows the same form as the O)
• HOT • COOL ROTATION OF APSIS
r i M f J L— I J I L O .5 1 0 .5 1 ihrt; 3~
LIGHT CURVES
LATE
0-C
EARLY
PRIMARY RESIDUALS
LATE
0-C
EARLY SECONDARY RESIDUALS
Fig. 2. Evidence of apsidal rotation y primary minima residual plot, but the phases of both curves are the same.
In such cases the secondary minima remain fixed halfway between the pri mary minima, further excluding apsidal rotation as an explanation. The continuous variation exhibited by the 0-C curve may then be attributable to the presence of a third body in motion about the COM of the entire system. The displacement of the eclipsing binary stars with respect to the three-body center-of-mass is observed at earth as a light travel-time effect. Translation of the three-body COM relative to our heliocentric coordinate system will cause a difference between the observed eclipse period and the absolute period. However, since this difference is a constant, it is of lit t le consequence in a study of period variation.
If there is more than one periodicity in the 0-C curve it may be neces sary to postulate the presence of additional bodies to satisfactorily explain the nature of the system.
Discontinuous variations. The second category of eclipsing binary 0-C curves is characterized by abrupt discontinuities attributed to sudden changes in the eclipse period. The explanation for this is mass ejection by either or both of the binary's components. According to Kepler's
Third Law,
(m^+mg)?^ = (1.2) where m^ and mg are the masses of the components, P is the orbital period of revolution, and ^ is the average linear separation between the components, a change in period can be caused by either a change in separation or in either body's mass. F. B. Wood (1950) has shown that while the ejection of mass can only provide an increase in period, the 10 eruptive force of this action working within the gravitational field of the other star can provide either an increase or a decrease in period as a result of a change in the separation, depending on the point on the
star's surface at which the thrust acts. He concludes that the greater
effect is ascribed to the explosion with less importance given to the
effect of mass loss and points out that sometimes the two will reinforce
each other, and at other times they will cancel. Quantitatively, he
finds that a mass loss of about 10"^ solar masses (M^) can cause a period
change of one second in a typical system which has a total mass of 2M1 , o a period of revolution of about 2 days, and a mean separation of 0.039
A.U.
In cases where the mass loss model is applicable, the primary and
secondary 0-C residual curves are effected equally and maintain the same
phase as they do for systems classified under the unseen companion hypo
thesis. Therefore, for systems whose residual periodicity is not well
defined, there remains some ambiguity as to which of these latter two
groups it belongs. It seems likely that perturbing forces of a multiple-
body system acting to change the separation between the eclipsing binary
components could also cause sudden jump discontinuities in an otherwise
periodically varying 0-C curve.
Selection criteria
The intent of this study is to investigate eclipsing binary stars
whose behavior is explained by the unseen companion hypothesis. Select
ing suitable stars for analysis began with a search through the Flower
and Cook Observatory Finding List of Eclipsing Variable Stars (1963). 11
Attention was given only to those entries which are noted as having variable eclipse periods. A further selection criteria imposed was that of observability at latitude 46.8°N from early July until the middle of
November, the operating season of the University of Montana Blue Mountain
Observatory. This allows for continuing investigation at that site of any stars determined to be of interest. An upper limit to apparent magnitude was set at 10?5. Table 1 shows the uneclipsed apparent magni tude (m^), the depth in magnitude of both the primary (Pri.) and secondary (Sec.) eclipses, and the orbital eccentricity (e) of several candidate stars selected.
A literature search was begun with an initial objective of finding the published values of eccentricity of the relative orbits for each candidate star. Systems with an eccentricity greater than 0.10 were considered to be susceptible to apsidal rotation and were excluded from further consideration under the multiple-body hypothesis. It should be noted, however, that a study of the secondary minima behavior and a com parison of the secondary minima 0-C residuals with those of the primary minima might reveal that apsidal rotation is, in fact, not evident. In such a case, a system would warrant further consideration for application of the three-body analysis.
Observed times of minima
In order to determine whether the period variation noted in the
Finding List mentioned above is of a continuous or discontinuous nature, it next became necessary to assemble a lis t of observed times of primary minima to be used in plotting an 0-C curve for each candidate star. 12
TABLE 1
CANDIDATE PROGRAM STARS
Star P ri. Sec. e Ref.
KO Agi 8?5 1?0 0?1 0.02 1. 2 RY Aqr 9.0 1.3 0.1 0.00 1, 3 BF Aur 8.5 0.7 0.7 1, 44i Boo 6.5 0.6 0.5 0.00 1, 4 DO Cas 8.5 0.4 0.1 0.13 1, 5 RZ Cas 6.4 1.5 0.1 0.052 1, 4 TW Cas 8.5 0.6 0.1 0.071 1, 6 U Cep 7.0 2.8 0.1 0.47 1, 7 XX Cep 8.5 1.1 0.1 0.14 1, 8 U CrB 7.5 1.2 0.13 1, 4 SW Cyg 9.5 2.6 0.30 1, 4 WW Cyg 10.0 3.8 0.1 0.00 1, 4 TW Dra 7.5 2.3 0.1 0.027 1, 4 TX Her 8.0 0.7 0.4 0.00 1, 4 Ori A 3.0 0.2 0.016 1, 4 Z Ori 10.0 0.9 0.1 0.23 1, 6 AT Peg 8.5 0.7 0.2 0.024 1, 9 RT Per 10.5 1.4 0.2 0.043 1, 6 U Sge 6.5 3.6 0.035 1, 4 X Tau 4.0 0.5 0.1 0.055 1, 4 TX UMa 7.1 2.2 0.162 1, 10
References : 1. Flower and Cook Ob., Finding List of Eclipsing Variables. 2. Ap.J., Vol. 102, p. 470. 3. A.J., Vol. 56, No. 1, p. 3. 4. Lick Observatory Bulletin. No. 521. 5. A.J■, Vol. 71, No. 1, p. 44. 6. A.J., Vol. 76, No. 6, pp. 547-8. 7. Obs., Vol. 69, p. 203. 8. Var. Stars, Vol. 12, No. 21. 9. P.A.S.P., Vol. 84, p. 432. 10. P.A.S.P., Vol. 52, p. 287. 13
This task was greatly simplified through access to the University of
Pennsylvania's eclipsing variable star card catalog, which is a rather
complete lis t of literature references categorized by star name. More
than 200 journal articles were reviewed in varying degrees of thorough
ness and a total of about 1400 heliocentric times of minima for 14 stars
were compiled chronologically (appendix 1). These lists will remain
archived on magnetic tape at the University of Montana where they will
be accessible for future related investigations. Included in the lists
are two photoelectric minima of RZ Cassiopeiae (Margrave) and one un
published minima of AT Pegasi from observations made at the Blue Mountain
Observatory.
The process of compiling the data lists was accomplished through
the execution of the FORTRAN computer program code FILCHG (appendix 2).
The information is written onto a disk file to facilitate further data
handling. Since the code has been designed with full update capability,
the data files need never be considered closed. As more eclipse times
become available, either through additional journal research or through
observation, these can be added.
The 0-C time residuals corresponding to each observed event are
determined by the linear elements of eq. (1.1). The set of values for
0-C, and thus the shape of the residual curve, will depend on the choice
of both a known time of primary eclipse occurrence (T^nown^ the
assumed eclipse period. The values of the periods used to calculate the
files found in appendix 1 are those recently quoted in the literature.
Although these values closely f i t the current observations, it is not
correct to suggest that they are the genuine orbital periods of one 14 binary component about the other, since the fact that the periods vary
implies that they may include the effects of spatial motion (i.e. apsidal rotation or perturbations caused by unseen companions).
Plots of the 0-C residuals for 14 stars are given in appendix 1.
Also included there are a few plots of secondary minima 0-C residuals.
Average eclipse period
It was found to be advantageous in this study to accept as a useful
value of the eclipse period one which causes the 0-C residuals of the
primary minima to be symmetrically distributed about the line 0-C= 0.0.
This step is accomplished by the FORTRAN code AVEPER (appendix 2).
Admittedly, this method is susceptible to statistical biasing due to
occasional inaccurate data points or intervals of few observations, yet
defining an "average period" has a definite advantage in a study which
is concerned with the entire recorded history of a binary since published
values usually apply only to limited time spans.
Visual Detectability
It is important to consider whether a hypothetical companion will
be visually detectable, since if it proves to be theoretically possible
to observe a companion but such an observation has not been made, then
the validity of the hypothesis will be in doubt. The following analysis
is pursued to insure that in any subsequent postulation of unseen com
panions associated with stellar systems, the hypothetical companions
would indeed be non-visible. 15
In a statistical study on the completeness of binary discovery,
W. D. Heintz (1969) adopts the "measure of difficulty" of discovering a visual binary which was previously introduced by E. Opik in 1924. When the visual binaries discovered over the past decades were plotted in a diagram relating the angular separation (/*) of the two component stars to the difference in their apparent visual magnitudes (Am^), it was found that nearly all are located in a strip bounded by the straight lines
0.22Am^ - log/^= 0.47 and 0.99. Heintz assumes that three ranges of the discoverability index, defined as D = 0.22Am^ - log/*, are delimited by
D = 0.5 and D = 1.0. Binary pairs for which D<0.5 have been discovered
prior to the past decades and are considered to be "completely discov
ered", while those with 0.5 D>1.0 remain "undiscovered". In the present application D>1.0 is con sidered a criteria for non-detectability. An eclipsing binary pair appears visually as one point of light. The detectability index (D), as well as intuition, suggests that a dim companion would be seen more easily if the brightness of the visible point of light was reduced to a minimum. Since this occurs at the time of primary eclipse, it is the published value of apparent visual magni tude for the midpoint of the primary eclipse which is used in the calcu lation of the detectability index. To determine the apparent visual magnitude of the dark companion it is firs t necessary to find its fractional luminosity (L/L^) in solar units through the mass-luminosity relation, L/Lg = (M/Mg)* (1.3) 16 where M/M^ is the companions fractional mass, also in solar units, and the exponent a is found to vary with mass as seen in Table 2 (Allen). TABLE 2 MASS-LUMINOSITY RATIO log M/M log L/L^ a -1.0 -2.9 2.9 -0.8 -2.5 3.125 -0.6 -2.0 3.33 -0.4 -1.5 3.75 -0.2 -0.8 4.0 0.0 0.0 4.0 +0.2 +0.8 4.0 Assuming a value for the companion mass and choosing the appropriate value for a, the luminosity is easily obtained. This is used in eq. (1.4) to determine the magnitude that the companion would have if it were located at a standard distance of 10 parsecs and if radiation of all wavelengths was included. This quality is usually referred to as an absolute bolometric magnitude (M^^^). Mboi = 4.77 - 2.5 log(L/Lg) (1.4) The absolute bolometric magnitude of the sun is +4.77. In order to convert the absolute bolometric magnitude of the com panion into an absoltue visual magnitude (M^), it is necessary to add (eq. 1.5) the appropriate bolometric correction (BC). % = "bol + BC (1.5) As explained by T. L. Swihart (1968), "the BC is a measure of the ratio 17 of the total energy radiated by a star to that which it radiates in the visual region of the spectrum". The apparent visual magnitude (m^) of the companion is calculated according to eq. (1.6), niv = Mv + 5 log(r/10) (1.6) which is dependent on the distance (r) in parsecs of the system from earth. Finally, the difference in apparent visual magnitude between the eclipsing binary at primary minimum and the companion is found by sub traction. Since one parsec is the distance at which one astronomical unit sub tends an angle of one second of arc, a knowledge of the distance (r) to the system in parsecs and the spatial separation (d) in A.U.'s between the companion and the visible star, as measured across the line of sight, will give the angular separation in seconds of arc at that time. /"(") = d(AU)/r(pc) (1.7) The magnitude difference and angular separation are then used to calcu late the index of discoverability. D = 0.22amy - logP (1.8) In application, it is easy to determine detectability of a suggested companion by examining its mass and greatest separation from the visible component of the system. A study has been made using the FORTRAN code DETECT (appendix 2) which incorporates the preceding analysis. The results shown in figure 3 show the curve corresponding to D = 1.0. In the region to the right of the curve,D is less than 1.0, indicating that such stars would be visible, while stars located in the left-hand region are considered non-detectable because D there is greater than 1.0. Since 18 DETECTABILITY 3 C/) H 1.00 \ JZ if) (/) < s r z o 500 < VISIBLE Q_ Z O U NON-VISIBLE 0 50. 0 150. SEPARATION CAU) Fig. 3. Detectability of companions 19 the index D is dependent on distance and apparent visual magnitude, a separate study must be made for each star system considered. Figure 3 is characteristic of RZ Cassiopeiae, whose distance is about 90 pc and mid-eclipse magnitude is about +7?88. CHAPTER II PHYSICAL ANALYSIS General procedure Once it is assumed that one or more unseen companions are causing the observed variation in the eclipse period of a binary, it then becomes desirable to derive the parameters describing the companion(s) and the dynamics of the multi-body system. A method of trial curve-fitting was used wherein a set of initial parameters is assumed and applied to a physical model which describes the relationships among all the bodies involved. Incremental time steps are then taken to simulate the hypothetical motion of the masses. The displacement of the eclipsing binary pair toward or away from the earth is used to determine the light travel-time effect during the time interval covered by eclipse minima observations. This result is super imposed on the empirically-derived 0-C plot and a judgement is made as to how well the theoretical curve fits the actual history of the eclipsing binary. The best-fitting trial then gives the parameters which, based on the assumptions of the model, describe the dynamics of the system. The models evolved with the specific case of RZ Cassiopeiae in mind. It seems evident from the double periodicity seen in the 0-C residual curve of RZ Cassiopeiae (appendix 1) that at least two 20 21 companions are necessary to f i t the past observations. Therefore, for considerations of spatial displacement, all analysis which follows assumes three coplanar point masses; two which represent the companions, and the third which represents the total mass of the binary pair located at the common barycenter. The simplifying assumption that the binary is reduced to a point seems to be justified in a first-order calculation, since the separation of the binary pair is typically less than 1% of the distance to the closest companion. The direction of revolution of all bodies about the system's center-of-mass is arbitrarily chosen to be counterclockwise with increasing time. Circular orbits The simplest model which was considered to explain the behavior of RZ Cassiopeiae is one in which the orbits of the companions are circular. The orbital motion (figure 4) of the closest companion (mg) about the two-body center-of-mass (COM^) causes a simultaneous circular motion of the binary. The total binary mass (m^) is known from published spectro scopic results. Adopting the shorter periodicity exhibited in the 0-C curve as the value for (in years), and deducing a value of the distance (rj) of the binary from COM^ from the amplitude of the 0-C curve (i.e . r^ = 0-C half-amplitude in days times speed of light in A.U./day), then the companion mass (mg) in solar units, and its distance (rg) from COM^ can easily be determined through a simultaneous solution of eq. (2.1), which is the definition of the center of mass, and Kepler's Third Law (2.2). m^r^ = mgrg (2.1) 22 COM COM to Earth Fig. 4. Epicyclic model 23 (m^ + + rg)^ (2.2) Because the angular velocity is constant, the angular displacement ( 0 ) at any time (t) may be found by 0 = 2wi + 0^ (2.3) where 0^ gives the initial longitude. The motion of the outer companion is determined by a similar treat ment. The masses m^ and m^ are combined and assumed to be located at COM^. The values of Pg and r^g ^re again obtained from the 0-C curve and are used to determine r^ and m^ (see figure 4). (m^ + mglr^g = m^r^ (2.4) (m^ + Mg + m^iPg^ = (r^2 + r^)^ The epicyclic displacement of the binary produces the expected superposition of sinusoidally-varying 0-C values once the factor relat ing distance to time delay (i.e. the speed of light) is applied. Through a procedure of making trial fits of the 0-C curve by slightly varying the input parameters, a best f i t was found for the case of RZ Cassiopeiae. The inadequacy of the model was immediately apparent. Since it is based on circular geometry, this model can only generate the sum of two symmetrical sine waves. The periodic variations seen in the 0-C curve of RZ Cassiopeiae (appendix 1) show a definite skewness. Therefore it was decided to pursue the problem further by introducing elliptical orbits. 24 Elliptical Orbits The method used to determine the instantaneous position of a body which is constrained to an elliptical orbit is outlined in most texts on celestial mechanics (e.g. Roy, 1965). It is necessary in this analy sis to specify the following set of parameters (figure 5) which define the relative orbit and the position of the body at a known time: T = Period of revolution a = Semi-major axis e = Eccentricity t^= Time of periapse passage w = Longitude of the periapse where to is measured with respect to the line of sight and in the direc tion of revolution. The calculations begin by determining the mean angular velocity n = 2tt/T (2.6) This is used in finding the mean anomaly M which corresponds to a specific time t through the relation M = n(t-t ) (2.7) Ü The mean anomaly is inserted into Kepler's Equation, E = M + e sin E (2.8) which must be solved through a process of converging iteration. The resulting value of the eccentric anomaly (E) is used to locate the body in terms of the radius vector r measured from the focal point of the ellipse and the angular displacement f measured from.the periapse, using the standard equations " = a(l-e cos E) (2.9) 25 \ \ \ \ COM periapse\ CO / / / to Earth Earth TRUE ORBITS RELATIVE ORBIT Fig. 5. Elliptical Orbits 26 f = 2 arctan tan (2.10) The longitude of the periapse is added to refer the angular displacement to the line of sight, whence G = to + f (2.11) The focal points of both of the orbital ellipses (figure 5) are located at the two-body center-of-mass. Although the two orbits are pro portionate ellipses, the longitude of each periapse differs by 180° with respect to the other. The companion mass and orbital semi-major axis are also found from two-body mechanics. At any time, the center-of-mass expression (eq 2.1) must hold true. At the particular time when the bodies are located at apastron, their distances (r^ and rg) from the COM can be related to the semi-major axes of their orbits by the following expressions: r^ = a^ (1 + e) rg = ag (1 + e) (2.12) Inserting these into eq. (2.1), we obtain.. m^a^ = nigag (2.13) Since the semi-major axis of the relative orbit is the sum ofboth true orbit semi-major axes, Kepler's Third Law may be expressed here as (m^ + mg)P^ =(a^ + ag)^ (2.14) Solving eq. (2.13) for ag and substituting into eq. (2.14) (m^ + mg)P^ = a^^(l + j~)^ (2.15) This may be solved for m« which, in turn, may be used in eq. (2.13) to '2 find ag. In the calculational procedure, it is easiest to write the quartic expression (eq. 2.15) as 27 gCm^) = (mg* + m^mg^)P^ - a^^(mg + (2.16) and then to find the value of mg which causes g(mg) to be equal to zero. By Descartes’ rule of signs, there is, at most, one positive value of mg. At this point the analysis follows the same general sequence as for the circular model. The superposition of ellipses has a greater degree of freedom which allows the skewness displayed in the 0-C curve of RZ Cas siopeiae to be fitted more easily. It was decided to choose as the fundamental plane of the three-body motion that which is defined by the binary itself. From spectroscopy the inclination of this plane (figure 6; X, Y) for RZ Cassiopeiae is known to be about 82° (82?14, Horak, 1951} with respect to the plane of the sky ( V , Z'). Observations of light travel-time effects are due strictly to the component of the eclipsing binary pair's motion which is directed toward or away from the earth, and therefore the sine of the inclination is used to project the x-value of the binary's position onto the line of sight. According to Chambliss (1976), the value of the total binary mass of RZ Cassiopeiae is 2.4 solar masses (m^ = m^ + mj^, where m^ = 1.75MI and m. = 0.61M ). a 0 D 0 The best f it obtained using an elliptical orbit model is shown as a solid curve in figure 7. The rms deviation from the observations is about ±5^15^. The orbital parameters which lead to this result are given in table 3. Also included there are the companion masses expres sed in solar units. While these masses are great enough to be luminous stars, their luminosities are faint enough such that they are not visually detectable at their greatest separation from the central pair (see figure 3). 28 V X' to earth Y=Y Fig. 6. Inclination of fundamental plane 0.09 0.08 0.07 _ 0.06 (/) ■XD cn 0.05 Q #—I LÜCO o: o I o 0.03 0.02 0.01 0.00 100 ro YEARS SINCE DISCOVERY IN 1906 Fig. 7. 0-C curve of RZ Cassiopeiae fit by elliptical model 30 TABLE 3 MASSES AND ORBITAL PARAMETERS OF THE HYPOTHETICAL COMPANIONS Companion M/Ml a(A.U.) P(yr) e w 0 to Outer 0.37 31.25 105 0.85 1973 155° Inner 0.32 11.29 23 0.4 1920 210° The closeness of the f i t gives encouragement that the presence of faint companions can be postulated to explain the historical patterns of the 0-C residuals. Upon closer inspection, however, it is found that the gravitational attraction between the two companions at some time exceeds the attractive force exerted on either by the binary. Therefore, since it is incorrect to neglect the companion interaction, the value of this model is only in suggesting plausibility. A physically realistic con figuration of the multi-body system can only be simulated by a model which incorporates all of the gravitational interactions simultaneously. Mutual interaction model The solution of the three-body problem may be found by the method of special perturbations. This requires a step-by-step numerical inte gration of the differential equations of motion and results in position and velocity information which describes the system at any desired time based on some initial configuration. Reference is made in the following derivation of the equations of motion to figure 8, which shows the coplanar relationship among the three bodies. The origin is chosen at the system's center-of-mass. 31 COM Fig. 8. Three-body interaction forces 32 The total force F^. acting on each body is the vector sum of the individual gravitational forces due to the presence of the other bodies, -> F. = ZF.. (2.17) From Newton's Second Law F. = m.t. = m. ------» (2.18) ^ ^ ^ T d t^ Since the position and velocity of one of the bodies is most easily ob tained through COM considerations once these quantities are known the the other two, the analysis can proceed by concentrating on masses m^ and m^. Equating eqs. (2.17) and (2.18), and resolving into rectangular coordinates, we obtain dfx, mg 2 “ Fg^cos + FggCOS Og (2.19a) 2 d yg ^2“^ = Fg^sin 0^ + FggSin Og (2.19b) ^3 j^2 = Fg^cos Og + FggCOS 0g (2.19c) mg j^2 = Fg^sin 0g + FggSin 0g (2.19d) Now, according to Newton's third law and his law of universal gravitation, Gm.m. ^ ^ = — / ""ij = (Z'ZO) where r.jj = ((xj-x^. + (yj-y^)^)^; r^j = î(Xj-x^) + o(yj.-y^) 33 Applying this to eqs. (2.19), we obtain 2 d x« Gm. Gm^ _ = ^os G- + — ^ o s 0« (2.21a) •'12 '-23 2 d _ Gm- Gm« Ô ’ — V sin 0. + — ^ sin 0« (2.21b) d t' ^23 2 d Gm, Gm^ 9 = ------9 cos 0- _ ir cos 0« (2.21c) ^13 ’"23 2 d yg Gm, Gmp = _ sin 0 Q _ 9 - sin 0 « (2 .21d) From the geometry shown in figure 8 (X9 -X,) (yp-yj cos 0 , = < ■ - sin 0, = —y--- (2.22) 1 r ^2 ^ ^12 (x^-Xp) (yo^yp) cos 09 = ^ ■ -■- sin 09 = - - ^ T23 ^ ^22 (x-5-x, ) (yo“yi) cos 0 . = ■ V - - sin ©2 = - r - ^ '^13 13 Expressing the fractional masses as follows mg m<, 1-2 ■ i f ’ 3 ■ i f '"-“ I and inserting into eqs. (2 .2 1 ), we obtain 34 A (2.24a) dt 12 23 0 0 C (2.24b) 3 ^ 3 ( ^12 '^23 d^x. [-(X 3 -X1 ) y 2 ^ ^3~^2 ^ 2 ” 1 3 - 3 (2.24c) dt \ ’’^13 '"23 /-(y3-y i) _ ^2^^3”'^2^ = Gm. (2.24d) dt ^ 3 „ 3 \ ""13 ’’^23 Al so. dx, "^2 _ , (2.25) dt = dt dXo ^^3 _ , dt - Eqs. (2.24) and (2.25) are the eight equations of motion for masses m^ and m^. Using the Runga-Kutta method of numerical integration, these are solved simultaneously for Xg, y 2 » x^, y^, , Vy , and at each step in time. The values of x., y,, , and V at each step are determined 1 i Xi yj through the defining expression for the center-of-mass. 0 = m^r^ + #2^2 + m^r^ (2.26) In rectangular component form 0 = m^x^ + #2X2 + ^3X3 0 = m^y^ + m^yg + m^y^ 35 or. -MpXp - m.Xg -muy. - muy. = — W, or. Xi = -YgXg - Y 3 X3 = -Y2V2 -V3 (2.27) Differentiating eqs.(2.27) we find the velocity components of mass m^ to be " .I - - ' 2 % - < 3 \ To determine the light travel-time effect associated with the eclip sing pair's motion, it is necessary to project x^ onto the line of sight using the sine of the inclination. The inclination will influence the companion masses and the sizes of the open orbits (figure 6) which are necessary to f i t the residual curve. An inclination of 90^ causes the plane of motion to coincide with the plane including the line of sight. This will result in the smallest companion masses and spatial excursions from the COM and therefore tend to minimize the interaction between the companions. As the inclination decreases, the spatial excursion must increase to give the same projected effect and the masses must increase to maintain the same periodicity. The result is that the companion interactions become stronger and maintaining stability becomes more difficult. A simplification of the curve-fitting is made by defining the pro jection of the initial position of the eclipsing binary pair as the origin of a coordinate system (figure 9) to which the light travel-time effect is referred. This results in an initial light travel-time residual of zero for the model. As the integration continues in the 36 Y' Y ORIGIN X' t=0 X trans COM path of binary Fig. 9. Coordinate translation 37 center-of-mass coordinate system, the projected value of the binary pair's position is translated (by subtracting its initial COM coordin ates) to determine the light travel-time effect at each step in time. If the integration is assumed to start at the ephemeris date, which is a time when the observed residual is also zero (see eq. 1.1), then the observed and model residual curves will coincide in itially. In the integration process, the time since the start of the calcula tions (i.e . the ephemeris date, by assumption) is found by adding the successive time steps. The clock may be caused to run into the future or into the past by selecting the time steps to be either positive or negative, respectively. Units The scale of physical systems being considered suggests that a con venient system of units to be used in the dynamical calculations is one in which distance is measured in astronomical units (1 A.U. is the mean distance between the earth and the sun), time is measured in years, and mass is measured in solar units (M^). This will cause velocity to be measured in astronomical units per year (A.U./yr) and the universal gravitational constant (G) to have units of (A.U.)3 (yr.)^Mg The 0-C residuals are most appropriately measured in units of days (although the conversion into minutes and seconds may offer a better perspective). Since distance is measured in astonomical units, the 38 light travel-time calculations are made most easily if the speed of light (c) is defined in astronomical units per day (A.U./day). CHAPTER III APPLICATION OF MUTUAL-INTERACTION MODEL TO RZ CASSIOPEIAE The eclipsing binary system RZ Cassiopeiae has a non-eelipsed apparent visual magnitude of +6?38 and a depth of primary eclipse of 1?5 (Wood, 1950). Therefore a mid-eclipse visual magnitude of +7?88 was used as input for the determination of the detectability thresholds for hypothetical companions. The distance in parsecs from the earth to the binary was found as follows. From the literature the spectral types of the visible compon ents of the system are known (Chambliss, 1976). The corresponding luminosities are found from the Hertzsprung-Russel1 diagram (Novotny, 1973). A2V log(L /L^) = +1.2 a O G5IV log(Lj^/L^) = -0.1 The total luminosity of the pair is used to determine their absolute visual magnitude (eqs. 1.4, 1.5), assuming as a value for the bolometric correction that which applies to the more luminous star (BC = -0.10). = +1.62 The difference between the apparent and absolute visual magnitudes then yields a distance of about 90 parsecs through a solution of eq. (1.6). 39 40 A data file of about 600 Julian Dates of minima was compiled from the literature for RZ Cassiopeiae. About 128 of these were selected as being a representative set, since it is impractical to repeatedly plot the larger number of points during the curve-fitting sequence and since also a maximum number of 150 is allowed by the subroutine HISTRY. An average eclipse period was determined for the unabridged file by an execution of the code AVEPER. The value obtained after 42 iterations was Pave = 1.19524788 days Both the original (RZCAS) and abridged (RZABR) data files are included in appendix 1. The 0-C residuals of the abridged file have been calcu lated through an execution of the code FILCHG, using the average value of the period. Those of the original file have been calculated using a value of the period (P = 1.19525189 days) common to much of the current literature. A comparison of the plots for the two files (appendix 1) shows the effect of changing the eclipse period. The trial procedure of fitting the residual history by a dynamical model required many hours of patient execution of the code NTERAC (appendix 2). The sensitivity of the model caused many unproductive choices to be made of the initial parameters of the multiple-body system These often resulted in close encounters among the bodies, sometimes causing one or both of the companions to escape* from the system. The *In an isolated multiple-body system, one body can never completely escape the attraction of the others. The term "escape" is used here to suggest that the component of the velocity of a body which is directed away from the system COM will go to zero and then be directed towards the COM at a time much greater than the duration of this study. 41 procedure in the trial method became one of trying to maintain stability in the system while continually improving the f i t of the model 0-C curve to the observations by refining the input. The orbital parameter input mode was chosen during the initial execution of the code, since approximate values of the binary orbital periods and semi-major axes could be estimated from the 0-C curve. A double periodicity is exhibited by the curve and therefore two companions were assumed. The starting values of orbital periods and semi-major axes due to assumed inner and outer companions were estimated to be 25 years, 1.3 A.U., and 100 years, 3.5 A.U., respectively. The analysis had adjusted the model 0-C value to be zero at the initial time through a spatial coordinate translation and therefore the placement of the 0-C curve which resulted from the model was found to be sensitive to the input values of the longitudes of periapsides chosen. The initial choice was simplified by referring to figure 10, which exhibits both the horizontal and vertical translations of the 0-C curve along the epoch and residual axes, respectively, which occurred when the longitudes were varied. First consideration in the curve-fitting procedure was given to the case where the inclination was assumed to be 90°, since this case would exhibit the least companion interaction. After 67 trials, a best fit was obtained and is shown in figure 11. The rms deviation between the observed and model residual curves is t 7*^39^ (i.e. t 0.00531 day). The center-of-mass system rectangular coordinates of position and velocity for the three bodies at the initial time (i.e. ephemeral J.D. = 2442340) are given in table 4. Also listed are the masses of the companions 42 0-C - t + t w 0° + t + t 0 to 180 +t Fig. 10. Effect of the longitude of periapse on the placement of the 0-C curve. 43 MODEL # 67: 0-G RESIDUALS 1 .OE-01 LlI LU OF-01 1875 ms YEAR Fig. n . 0-C curve f i t by interaction model 67 TABLE 4 COMPANION MASSES AND INITIAL RECTANGULAR PARAMETERS niy = +7?88 MODEL 67 MODEL 127 i = 90^ i = 82914 d = 90 pc BINARY INNER OUTER BINARY INNER OUTER PAIR COMPANION COMPANION PAIR COMPANION COMPANION M/Mg 2.4 0.263 0.288 2.4 0.287 0.330 X (AU) -2.83234 14.86341 -41.00514 -2.64463 15.30136 -38.64449 Y (AU) -2.46345 -9.12520 17.86768 -2.32152 11.26606 -28.63106 VX (AU/YR) 1.30292 -0.35300 -0.68683 0.52601 VY (AU/YR) 2.00634 -1.21160 2.19624 -1.02252 45 (M/Mg) in solar units. The equivalent orbital parameters are not pre sented because the motion of the companions relative to the binary exhibits continuous variation of the orbital parameters, and therefore the instantaneous values may not be representative of the mean orbits. In the spatial plots of the binary and companion motions (appendix 3) the positive x-axis is directed towards earth. Model 67 has been allowed to run for 6300 years into the past and 2000 years into the future and shows no sign of becoming unstable. Although an extended investigation gives insight into the stability of a system, it should be noted that round-off error becomes significant after such a long inte gration period, and that the model becomes less valid with increasing time. The second model considered was constrained to a plane of motion whose inclination was 82?14 with respect to the plane of the sky. This also is the inclination of the fundamental plane of the central binary pair's revolution about each other, and thus it has the aesthetic appeal of coplanarity which might be attributed to a common origin for all four bodies. After an additional 60 trials (i.e. model 127), a best f i t for this inclined orientation was found as is shown in figure 12. The resulting rms deviation between the curves is i 9*^30^ (i.e. t 0.0066 day). Again the companion masses and rectangular position and velocity components corresponding to the initial time are listed in table 4. A comparison of the two models shows that a change in inclination of only 8° requires the companion masses to increase by 10-15% to maintain a f i t of the residual curve and therefore increases the likelihood of strong inter actions between them. 46 MODEL *127: 0-C RESIDUALS UOE-01 III to > - < O 'w' o oI > - _J C tl 1 .OE- 1875- YEAR Fig, 12. 0-C curve f i t by interaction model 127 47 Model 127 has been run for about 3,000 years as seen in the spatial plots in appendix 3. It appears to remain stable for at least 800 years into the future and for more than 300 years into the past. However at about year -350 a close interaction occurred, causing the outer companion to be thrown far out into space. It exceeded the detectability threshold at about year -382 and remained visible until about year -534. The system then seemed to be well-behaved until about year -II80 when another close encounter between the companions caused the two to capture each other. The newly-formed pair revolved about a common barycenter while containuing to orbit the eclipsing binary. At the end of one orbit, the central pair exerted a large enough perturbation on the companion pair to again cause the outer companion to be thrown far from the COM, be coming visible again at about year -1334. This rather wild motion continued as is seen in the spatial plots. Although model 127 gave an adequate f i t to the observed 0-C residual curve, it is unlikely that such a system could maintain stability for a time span approaching the age of the main sequence A2 component of the eclipsing binary (2 billion years maximum). On the other hand, the model's behavior suggests that relatively short-lived gravitational en counters between stars which are migrating through space can occur and result in the dynamical effect which is observed in the 0-C residuals. If the investigation is restricted to systems which f i t the ob served behavior yet remain stable over a long period of time, it then appears that the possible companion masses would be smaller than those found in model 127 and that the inclination of the companion orbital plane would be greater than 82^. Since the masses would be at least as 48 great as those of model 67 to account for the amplitude of the residual curve, these two models may be regarded as bracketing possible companion masses for the eclipsing binary system RZ Cassiopeiae. Apparently the companion bodies are red dwarf stars of spectral type M3-M5. CHAPTER IV DISCUSSION Radial velocity residuals Additional credibility would be given to a hypothetical companion model if it explained the observed radial velocity residuals while f i t ting the photometric 0-C curve. The binary orbital elements are deter mined through a trial procedure of fitting the spectroscopic radial velocity curves which have been observed over several consecutive revo lutions. Historically these orbital elements have been the subject of continual revision. If instead of revising the elements, an investigator were to assume some average set, he might notice that the long term residuals between the observed and model radial velocity curves have a periodic behavior which could be explained by a spatial motion of the binary pair, caused through interaction with companions. Figure 13 shows a typical radial velocity residual curve associated with an interaction model (#67) which also fits the observed light travel-time residuals of an eclipsing binary. The amplitude of this curve is about 4 km/sec, which is twice as large as that used by A. H. Batten and E. L. van Dessel (1975) to support their hypothesis of a third body orbiting about the spectroscopic binary 70 Ophiuchi. A suggested further procedure, then, in the analysis of eclipsing binary stars with periodic 0-C curves and extensive spectroscopic 49 50 MODEL * 67: RADIAL VELOCITY RESIDUAL 10.0 V LÜ CO \ H Û < Ù1> - 10.0 1875 Ï 9 75- YEAR Fig- 13 51 observations, is to assemble from the literature a data file containing radial velocities and corresponding times. Assuming a set of binary orbital elements, the residuals of the observed radial velocities could be determined for each date. These values then could be read into the interaction model code NTERAC and displayed on the plot (figure 13) con taining the radial velocity residuals of the model. The most probable model would be one which simultaneously gives a best f i t to both the eclipse minima residuals and radial velocity residuals. Reduced 0-C residuals Figure 14 shows the difference between the observed 0-C residual values and the corresponding values which result from the hypothetical interaction of a binary with companions. The reduced residual curve offers a convenient way of estimating whether or not there may exist undetected periodicities which might be attributable to additional unseen companions. A good f i t of the 0-C curve should produce a reduced resid ual curve which shows observational scatter or noise which is equally distributed about thejabscissa. Osculating orbital elements How far in time a model can be used to represent the interactions between bodies is limited by the real time required to make the neces sary calculations. An interesting further project which could be undertaken would be to write a subroutine to determine the osculating orbital elements (ref. Danby, 1962) at specific intervals during the dynamic calculations of the code NTERAC. It would then be possible to 52 MODEL * 67: REDUCED 0-C RESIDUALS 1 .G E -02 ÜJ < <0 > - < Q . 0 (J I O > - q<: LU - 1 .0 E -0 2 - 1 0 0 . -50.0 YEARS Fig. 14 53 execute the model for a time period long enough to show patterns of variation in the orbital elements of the companions. A variation-of- parameters technique could then be used to make the large calculational steps necessary to reconstruct the motions of the system at a time several million or even billions of years ago. This method has been applied to the orbit of Pluto by Bensen and Williams (1971), who used time steps of 500 years. Error control Round-off error is cumulative as the number of calculation steps increases. I t could be reduced by using double precision for all vari ables used in many steps. Since this requires more core storage, however, it is preferable to reduce the step size in the integration scheme, since the error associated with a fourth-order Runga-Kutta method varies as the fifth power of the change in step size. Although the increased number of steps would increase round-off error, the result is s t ill a gain in accuracy. To see the effect that changing the step size has on the results, model 67 was run twice for 200 years using step sizes of 0.01 year and 0.10 year. I t was found that in this relatively stable model the two trials gave differences in position vectors for each body of less than 3 x 10 ^ A.U. in each year and differences in velocity vectors of less than 1 x 10 ^ A.U./YR in each year. Since the accuracy gained by reducing the step size by a factor of ten is very small in a stable case, the larger step size may be used to expedite the tria l fittin g procedure. When a near f i t is found, the step size may be reduced to obtain the final f i t . 54 An additional refinement to the code NTERAC would be to introduce a subroutine which would continually adjust the integration step size to a maximum value which would s till maintain an acceptable error tolerance. This could be done by making a parallel integration at each step in time using a lower-order scheme such as Simpson's method. A comparison of the results of the two methods at the end of each step would determine i f the next step should be integrated with the same or an even larger step size, or whether the previous step should be repeated using a re duced step size. The computation time lost in making the additional calculations is outweighed by the gain resulting from the use of the largest allowable step size (Strack, 1963). This method would be most important in cases where close encounters require very small step sizes to maintain accuracy. Minimizing companion interactions The analysis which has been presented has considered only those cases in which the companion motions are coplanar with the same direction of revolution as the central pair. It is possible that two companions could revolve in opposite directions about a binary. During a close encounter in such a case, each body would spend less time within the other's sphere of influence, and therefore the interaction would be less severe. I f the constraint of coplanarity is removed, the probability of a close encounter is decreased. These two additional degrees of freedom could be used to f i t 0-C residual curves in systems where otherwise the tria l procedure suggests that no stable configuration fits the 0-C re siduals. 55 Predictions A test of how well a hypothetical model describes an actual system is its a b ility to make predictions. Figure 11 and 12 show that the trend of both models 67 and 127 is that eclipses of RZ Çassiopeiae which occur shortly after the ephemeris Julian date w ill be observed to occur slightly earlier than predicted by the linear elements of eq. ( 1 . 1 ), Since the ephemeris Julian date (i.e . model year = 0) corresponds to late 1974, indication of whether either model correctly predicts the observed trend can be expected by 1980 or 1985. As more observations are made for an eclipsing binary, the 0-C residual curve w ill further reveal its behavior. Continual revision of the fittin g parameters w ill then better define the system. Although the controversy of explaining the apparent variation in the eclipse period of RZ Cassiopeiae continues, the results given in the preceding chapter give support to the hypothesis that the binary is experiencing a pertur bation caused by two red dwarf companion stars. CHAPTER V SUMMARY The observed time residuals for some eclipsing binary stars may be caused by a lig h t travel-time effect produced by unseen companion bodies. An object which has sufficient mass to cause a measurable perturbation of its central binary pair may be unseen because i t is "of low lumin osity, a fain t dwarf, close to and lost in the image of the primary star or too fa in t to be recorded photographically, even at a large angular separation from the primary" (Van de Kamp, 1975). While the companion hypothesis for explaining eclipse time residuals has often been postu lated, the determination of the masses and dynamics of such companions has not been rigorously pursued. A method of deducing the masses and dynamics of unseen companions associated with eclipsing binary stars is presented in Chatper I I . The general technique applied uses a physical model to generate light travel- time residuals which f i t the observations by adjusting the assumed values of companion masses and their in itia l positions and velocities. Models employing circular or e llip tic a l orbits of two companions about the central binary pair are considered and discarded since a substantial interaction between the two companions is not included by superimposing the simultaneous two-body analyses. Allowance for the mutual inter action among a ll bodies in the system results in a three-body problem 56 57 which can only be solved numerically. The Runga-Kutta method of inte gration is encoded, into the Fortran program NTERAC (appendix 2), which solves the eight simultaneous equations of motion (eqs. 2.24, 2.25) to describe the dynamics of the system at each step in time. Application of the mutual-interaction model to the eclipsing binary star RZ Cassiopeiae is described in Chapter I I I . These results indicate that the companions, whose presence is postulated in order to explain the observed eclipse time residuals of that system, have masses between 0.26 and 0.33 solar masses. I f the companions are considered to be main-sequence stars, they would be of spectral type M3-M5. A hypothesis reveals its valid ity through its a b ility to make cor rect predictions. The f i t of a model to the observed eclipse time residuals of RZ Cassiopeiae has been extrapolated into the future (figure 11). A discernible change in the eclipse time residuals and in the radial velocity of the binary pair is predicted by 1985. APPENDIX 1 0-C RESIDUAL FILES Observations of eclipsing variable star minima are generally re ported as heliocentric Julian dates. Quite often an observer will fa il to include in his publication the accuracy of his results. By noting the method of observation, a typical value for its accuracy may be assigned through reference to table 5. TABLE 5 ACCURACY OF OBSERVATIONS METHOD ACCURACY (days) Visual ±0.01 Photographic ±0.004 Photovisual ±0.002 Photoelectric ±0.001 Normalizing ±0.0005 In the following plots of the 0-C residuals of eclipsing binaries which exhibit variable periods, year zero corresponds to January 1, 1980 Residual values are indicated by an asterisk (*) with crosses (+) located above and below to indicate the observational accuracy. The eclipse periods are given in units of days. 58 59 In the tables of eclipsing binary minima, the observational accura cies and 0-C residuals are given in units of days. Julian dates are truncated to show only five digits to the le ft of the decimal (e.g. 2442000.1234 w ill be entered as 42000.1234). 60 KO AOL, PFZRIOD- 2 . 80290-^100 œ > - < Q _J < U O j co LJ [Z U I O t 50L__ - 30. 0 - 1 0 . 0 YEARS 61 CHP.OMOLOGY OF 9 OBSERVATIONS OF XOAOL TCALC = JD 4 1837.47 10 + E * 2.36395400 HELIOCEMTRIC 0-C JULIAN DATE + /- RESI DUAL OBSERVER REFERENCE 33333.4100 0.010 - 0 .037 5 DOMKE^JAHM AM 231(3), P. 1 13 357 13 . 4 170 0.006 -0.097 I S0AFRANIEC A.A. 7, P. 188 36073. 55 1 0 0.005 -0.09 3 4 SEAFRANIEC /\.A. 8 , P. 139 37107. zi 650 0.001 -0.0663 GERHART AM 233, P. 69 33937 .5230 0.010 — 0 «0704 MULLER,KRAUS S ER AM 28 9, f 4, P. 40435.4076 0.001 -0.0337 CALISKAN,IBAM0G IBVS #456 4 1 1 43. 56 0 0 0.001 -0.0109 HOLZL IBVS #64 7 4 13 3 7.4710 0.001 0.0000 I BAMOGLU IDVS #9 37 /12245. 4 793 0.001 0.0145 GUDUR,ERTUKEL IBVS #1053 62 RYAQR. PRRIOD- 1 . 0 n - 0 "i CO < Q to _J < Z) 0 Q M CO LJ DC U I O 1 , 0 0 - 0 1 - 70,0-60.0-50.0-40.0-30.0-20.0-10.0 . 0 YEARS CM^-OnOLOnY OF 9 OiiSFF^YiTI 0M3 OF 1YA0 63 TCALC = JD /I 04 7 6 . 3 2 /10 + E + 1.9 666 0 7 0 0 HFLIOCFMTFIC 0-C JTJLIAM D/iTi: + /- RES I DUAL OBSERVER REFERENCE 19 6 13.4505 0.001 -G . 0397 Z I rJMER A:J 4679, P. 460 23 3 04.4260 0.010 -0.0355 50 AFP.A.UI EC AJ 67, P. 7 3 4 5 4 3.9260 0.004 -0.044 5 KOCH^ KOCH AJ 67, P. 7 4 0 4 4 6.3 I 10 0.010 -0.0139 MOUSKE I CVS f79 5 40 4=^4 . 63 3 0 0.010 -0.0033 HAZEL I5VS ^79 5 /! 0 4 5 6 . 6 7 /; 0 0 . 003 0.0161 UONSKE IBVS #79 5 4 0 4 7 6.3240 0 . 00 1 0.0000 I3AM0GL6U IZHIP. I BPS #4 56 42303.3 0 12 0.00 1 -0.0007 OTtluEU^ ALKAU, 5E I3PC #1053 /i 2303.3015 0.00 1 -0.0004 OULHEiJ, ALKAU, SE IBVC #1053 64 BBB.. : I '/C’0 CO ■ \ ___ ■ CO < G -4 Q 'I* *1+ !|- 1—i ■+ CO 4 -T- L' pÂ- $ DC • ^ » r'i A" 4- 0 ; '■?0 ' '1? . ? i <0 . ? - 2 . ? . ? ilo. B “ c Y BA! CUP.OnOLOGY OF 33 3BSER’7AT I O^JS OF CFAT/R 65 TCALC = JD /-J 1752.^560 + E * 1. 5332 1700 HFLIOCEMTHIC 0-C JULIAN DATE + /- RESIDUAL OBSERVER REFERENCE 28497.7220 0.010 -0.0413 LAUSE AN 6404, P. 324 28513.5430 0.010 - 0 .0524 LAUSE AN 6404, P. 324 2852 1 .4727 0 .003 -0.0383 LAUSE AN 64 04 28 52 1 .4 850 0.010 -0.0265 LAUSE AN 64 04, P. 324 28534.1270 0.010 -0.0 503 LAUSE 6404, P. 324 28556.3090 0.010 - 0.0333 LAUSE AN 6404, P. 324 28 7 79 . 54 1 0 0.010 - 0.0349 LAUSE AN 64 0 4, P. 324 288 33.3 58 0 0.010 -0.0473 LAUSE AN 64 04, P. 324 28360. 28 50 0.010 -0.0350 LAUSE AN 64 04, P. 324 23868. 1940 0.010 - 0 . 0/120 LAUSE AN 6404, P. 324 28882.47 10 0.010 — 0.014 0 LAUSE AN 64 04, P. 324 289 17. 29 50 0.010 -0.0203 LAUSE AN 64 04, P. 324 28920.4400 0.010 -0 .0422 LAUSE fiN 6 4 0 4, P. 324 289 20.4 542 0.004 -0.0280 LAUSE 6404 28 9 3 6.28 9 0 0.010 - 0.0254 LAUSE AN 6404, P. 324 28950.5090 0.010 -0.0543 LAUSE AN 6 404, P. 324 289 55. 3250 0.010 0.0120 LAUSE AN 64 04, P. 324 28963.236C 0.010 0.0069 LAUSE AN 6404, P. 324 23966.3730 0.010 -0.0 175 LAUSE AN 64 04, P. 324 2897 4. 2970 0.010 -0.0146 LAUSE AN 64 0 4, P. 32 4 2397 7.429 0 0.010 - 0.049 0 LAUSE AM 64 04 29 004. 3 64 0 0.010 -G. 028 7 LAUSE AN 64 0 4 37 3 68.5060 0.001 - 0.0221 RUDOLPH AN 2 8 8 , P. 1 63 37 37 6.428 0 0.001 -0.0162 RUDOLPH AN 283, P. 1 63 4 0 56 7.4101 0.001 0.7336 BATTISTINI, BONI IBVS //3 1 7 40628.3 64 5 0.00 1 -0.0074 BATTIST I NI, BONI IBVS ^3 17 409 16. 5 1 07 0.001 — 0.0 0 6 7 EATTISTINI^ DONI IBVS #317 409 3 1 . 5513 0.001 0 . 7 3 49 BATTISTINI, BONI IBVS #317 409 39 . 4 67 1 0.00 1 0 . 7346 BATTIST IN I, BONI IBVS #8 17 416 63.5406 0.001 -0.0049 BATTIST I NI , BONI IBVS #3 17 41634.3730 0.001 -0.0047 EBERSBERGER IBVS #937 4 1 69 1 . 49 7 6 0.001 0.737 1 BATTIST IN Ij BONI ID\^S #317 4 1752.4560 0.001 0.0000 EBERSBERGER IBVS #937 66 BFAU2; PERIOD "8 3 2 1 7 0 0 CO y ~ < D CO _J < —) D I— ! CO LJ DC U O - 5 . 0 f l - 0 2 - . 0 - 4 0 . 0 30.0 - 20.0 -10.0 YEARS CHROîJOLOnY 0-' 11 OBSERVAT I orys 07 DFATJ2 67 TCALC = JD 2893 1. 4 14 0 + E * I . 5332 1 70 0 HELIOCEMTRIC 0-C JVLIAM DATE + /- R ESIDUAL OBSERVER REFER 28 49 5.3370 0.010 -0 .0294 LAT'SE Ar« 6404 28 5 14.3 47 0 0.010 - 0 . 0 180 LAUSE AU 64 04 28 5 3 3.349 4 0.007 - 0 . 0 142 LAUSE AM 6404 28612. 5 1 10 0.010 -0 .0 1 3 4 LAUSE AM 6404 2883 1 . 6570 0.010 -0 .0 1 4 3 LAUSE AM 64 0 4 28913.3350 0 .0 10 -0 .0 0 0 7 LAUSE /'.M 6404 23935.4790 0.010 -0 .0 2 1 7 LAUSE AM 64 0 4 28962.4055 0-005 - 0 . 0099 LAUSE AM 64 0 4 2897 3.47 1 0 0.010 - 0.0269 LATTSE /iM 640 4 28973.2790 0 .010 0.0314 LAUSE AM 6404 28 98 1.4140 0.010 0.0000 LAUSE AM 64 0 4 0-C RFISIDUALSi; DAYS) ip "D _ Q G , . 1 J c (> G? Q i -m- n4L tf (5) -T-| =4- 1 I Z 1 I—I -KS o r i i t 0 ) 0 -4K, 0 1 l\] — o -*- I CI'J — -H- -f4- ^vi 1. 1-4^■ 44 iij G' 'O' m 00 CM’^.n*:oLnnY or '^2 i o'jc or iboo 69 TCALC = JD /n 3 1 9 . /I ^ /| 0 + C * K. 2 67 3 10^0 HrL I OCE'JTP.I C 0-C JPLIAM DATE + /- DES I DUAL OBSERVED REPERENCE 2 1113 2533 0 .00 1 0.0606 HERTZSPRUM3 BAN 165 2 2 0 9 0 43 63 0‘.00 1 0 . 0 49 4 HERTZSPRUUG BAN 16= 24 641, 9723 0 .00 1 0.0211 SHILT AP . J. 64, P. 2 1 246^6 /13 2 2 0 .002 0.0219 UUMCH-KUIPER BAN 165 2 4 696 9723 0 .00 1 -0 . 0 59 4 SHI LT AP. J. 64, P. 2 1 2 6 393 4 39 3 0 .00 1 0.0133 OOSTERHOrr BAN 32 1, P. 12 2 = 67 1 60 6 1 0 . 00 1 0.0139 OOSTERH orr BAN 32 1, P. 12 25733 47 1 2 0 .001 0.01/19 00 STERH orr BArJ 32 1, P. 12 2 57 4 4 6 4 0 .00 1 0 . 012= OOSTERHOrr BAN 32 1, P. 12 26063 3 6 = 4 0 . 00 1 0.0 09 9 HurrER P. A. 33, P. 59 9 26069 3046 0 .00 1 0.014= DYBKA BAN 19 6 2 6364 4 194 0 .00 1 0.0014 KUIper BAN 321 2 '7 = 3 7 503 4 0 .00 1 -0.0016 PL HUT BAN 32 1 27143 7741 0 .0 01 -C .0 06 6 SCHILT AJ 60, P. 3=6 2 7 1 /j 3 7741 . 00 I -0.0066 SHAPLEY HD f907 23 3 1 4 6026 0 .00 1 -0.0 06 5 SCHILT A J 60, P. 3 56 233 14 6026 0 .00 1 -0.0065 SHAPLEY HB #907 23 63 5 4 3 5 1 0 . 00 1 -0.0104 PLAUT BAN 32 1 30 1 52 67 52 0 .00 1 -0.0140 POPPER /.J 62, P. 3 56 32339 7 3 33 0 . 00 1 — 0•0 0 9 6 EGGEU A J 6 0, P. 356 32 3 69 7773 0 .00 1 —0.0104 EGGED) AJ 60, P. 3 57 3 2 3 7 3 79 53 0 . 00 1 - 0.2 100 EG G EU AJ 60, P. 357 32330 '^=3 5 0 .00 1 -0.0099 EGGEiJ AJ 60, P. 357 3 4 13 2 6 173 0 .00 1 0.0037 iU'EE AJ 6 0, P. 357 34 1 32 5 134 0 . 0 0 1 0.0043 :R'EE AJ 60, P. 3 56 3 4 19 9 47 1 <=; 0 . 00 1 0 . 0 0 5 4 K'TEE BAN 43 5, P. 134 34459 73 20 0 . 00 1 0.004 6 PITCH AJ 69, P. 3 16 34473 = 309 0 . 00 1 0.0063 ■D^EE AJ 60, P. 3=6 3 4/(7 3 = 3 1 = 7,.00 1 O' . 007 4 }R'EE BAN 435, P. 134 34 = 0 1 = 6 1 7 . 00 1 0 . 00 59 K'-'EE BAN 43 5, P. 134 3 4 = 01 = 613 0 . 00 1 0.0061 }R'EE AJ 60, P. 357 34=03 7 0 4 7 0 .00 1 0 . 0O'6 5 EIUUEMDIJK AJ 60, P. 3 57 34 = =3 6 0 = 6 0 .00 1 0 . 006 2 ALEXANDER AJ 6 0, P . 3 = 7 34 = 63 5 1 =2 7 . 00 1 0.0077 aLEXh 'JDEE /.J 6 0, P . 357 3/1 = 33 = 14 1 7 .00 1 0.0035 ALEXANDER AJ 60, P. 3=7 3 4 636 72 56 0 .00 1 0.0063 ALEXANDER AJ 60, P. 35 7 3 4 533 6 009 0 .00 1 0.006 9 ALEXANDER AJ 60, P. 3 57 34=3 3 60 2 0 0 . 002 0.003 0 ALEXANDER AJ 60, P. 3 56 3 4 =2 5 5 64 6 0 .00 1 0.0075 ALEXANDER AJ 60, P. 3 57 3 4 = 97 ^056 0 .001 0.0061 ALEXANDER AJ 60, P. 3 57 34750 62^9 0 .00 1 0 .0033 X"EE BAN 43 5, P. 134 347 6r, 6 2 3 3 0 .001 0.0097 iC'EE /6J 60, P. 3 57 347 6 4 = 5 4 1 0.00 1 0.2039 trSEE BAN 43 5, P. 134 347 6 4 = 643 0 . 00 1 0 .209 1 IRTEE AJ 60, P. 3 57 3 4 76 3 = 707 0 . 0 n 1 0 . 0 0 3 4 K'"EE BAN 4 3 5, P. 134 34 76 3 57 1 2 0. O' 0 1 0.0039 XR'TEE AJ 60, P. 3 57 3477 c; = 324 0 .00 1 0 .0070 IR'^EE BAr: 4 3 5, P. 134 3/(346 7^17 0 .00 1 0.0101 DINNENDIJK AJ 6 0, P. 357 n_ r 70 A*J + /- ^22 1D9AL ;'.E"ECEr’CE 3 4353 7347 0.001 0 . 093 3 ’jnrjEi^Di jx AJ 60, p. 357 34393 6 339 9.00 1 9.0093 Î3I rjrjE"JDIJX /.J 60, P. 3 57 3 4393 639 = 9.991 0.9999 Cl ^jrj^rJDI JX /\J 69, P. 3 56 3 49 3 1 6 7 /13 9.99 1 0.0104 BIIJMEUDIJX AJ 60, P. 3=7 3 49 1 3 7 2 55 9.99 1 0.9112 CI'JME^JDIJX AJ 60, P. 3 57 3=^9 3^ 34 = ^ 9.901 0.0236 S7a FCAMIEC A./i. 10, P. I ll 3 -7/14 3 7 6 5 2 9.991 9.9495 ''EHLAC JCASC 5 6, r. 19 3 6^77 3^449 9.C91 9 .9 49 5 ’7 Erl LAM JCASC =6, P. 103 37/472 6 3 3 9 9.091 9.9 490 T'EHLAA JCASC 56 , P. 103 4356 1 4 27 3 0.901 -0.9263 E ‘ ID E 2 lE’fc A 530 4 1 133 4 3 6 9 9.09 1 -9.9172 9COEEL I CVS 6 64 7 4 1 33 4 = 323 0 .00 1 -0.09 3 3 EUL'IEM ILprS 6937 4 1 39 2 4320 9.091 0 . 12 5 0 EOCZ, II0L2L lE'fS 69 3 7 /I 143 = 4 156 9,901 -9.0979 on dec IC^C 6937 4 14 6 2 4 64 2 9.00 1 -0.999 3 AX IMCI IBVS 6937 /I 1 ^ 3 5 3920 0 . 9 0 1 -9.0061 HECX IE3'5 6937 4 1=99 3 140 9.001 -0.9102 c c x lEJrS 6 9 37 4 1 '7 =3 4 9 7 3 9.991 9.0037 T'OOEL lEJ'S 6 9 3 7 4 1 793 44 4 0 0.001 - 0. 13 9 3 SCMACOLD^ ^'OOEL ISprS 6937 4 13 19 4649 0.001 0.0000 '-'ECEC I BPS 69 3 7 4209 = 4 = 40 0.901 - 0 . 1 22 1 : 5ciielle :iam:j ILpfS 61053 A2 12.2 37 1 0 0.901 0.0139 :OCOBEL,SCXACOL IC^S 61053 4 2 13'^ 4 /10 e 0.001 0.095 1 :EEECSBEC0EC,GC I ECS 6 1053 4 2 2 19 4479 9 .901 - 0 . 12=1 GT’LMEM ISC'S 6 1053 42263 3230 0.091 0.0 09 4 GULMErJ I3CS 6 10=3 0-C RESIDUALSr DAYS) CD O O Î 0 V n 70 i— ! o o Q [\J 'J- -xj Ci Q Cv CHP.OMOLOGY OF 47 OBSERVAT I OPS OF I BO 02 72 TC7‘.LC = JD 41329 .7737 + Z * 0.2673 1000 HZLI GCEMTn C , 0-C JT.TLIAM DATE + /- EES I DUAL OBSERVER REFERENCE 27 563. 409 2 0 . 002 0.0536 UUIJCH-PLAUT DAM 32 1 33512.3470 0.001 - 0.0642 PGHL AN 289, #4, P. 19 1 38 513. 4 170 0.00 1 “0.0655 PGHL AM 239, P. 19 1 33663.3390 0.001 -0.0671 HELD,FLEISCHER AM 289 ^4, P. 19 1 38333.4550 0.001 — 0 . 0 60 4 OGRZ, ENDEES AN 289, #4, P. 19 1 33 8 3 2.4 6 60 0.001 -0.053 7 GORZ, EMDEES AM 239, (^4, P. 19 1 39922.9250 0.001 -0.0415 BROUN AJ 74, P. 542 399 45.4222 0.001 - 0 .0403 HINT I IBVS #322 39943.3630 0.001 -0.0455 BICKEL,NÜRNBERG IBVS #456 399 52.9210 0.001 - 0. 0402 BRO'^N AJ 74, P. 54 2 39956./1000 0.001 -0.0428 GORE, MEIER IBVS #456 39959.3490 0.001 .-0 . 0397 GORZ, EMDRES IBVS #456 399 59. 43 10 0.001 0.0923 GORZ,ENDRE5 IBVS #456 39968.4 "=.30 0.001 -0.0412 BICKEL, MEIER IBVS #456 39977 . 2920 0.001 -0.0399 HURUTAC, PGHL IBVS #456 403 1 6 .3460 0.001 -0.0334 PGHL,GUDUR IBVS #4 56 40319.2969 0.001 -C .0293 PGHL, XURUTAC I B\;S #456 403 2 5.4^56 0.001 -0.0293 DUMITRESCU IBVS #4 19 4033 1.3460 0.001 -0.0307 GUDUR IBVS #4 56 40339.38 16 0.001 -0 .029 5 DUMITRESCU IBVS #4 19 40339.6493 0.001 -0 .0296 RUDNI CK IBVS #789 4 0 3 4 6.6161 0.001 -0.0258 RUDNICK IBVS #789 403 63 . ^i8 4 0 0.001 — 0 . 0 3 0 0 BAUMDACH,MEIER IBVS #456 4 0382.7 6 76 0.002 -0.0237 SCARF AJ 76 , P. 5 0 /10 3 9 0 . 3 C 2 0 0.001 -0.028 6 SCARF AJ 76, P. 50 40392.6320 0 .001 -0.0232 RUDNICK IBVS #789 40420.79 71 0.001 - 0 . 028 2 S CAR F 7 6, P . 50 40700.3943 0.001 -0.0246 DUMITRESCU IBVS #503 4 0 7 1 4 . F 8 9 1 0.001 -0.0233 RUDNICH IBVS #739 40753.4 231 0.001 - 0.0222 GULMEN IBVS #530 40769.7628 0.001 -0.0 189 RUDNICK IBVS #73 9 4073 0.47 10 0.001 -0.0231 HOLZL IBVS #53 0 4 98 0 1.3966 0 .001 -0.0223 NI EHAU5 IBVS #8 44 403 1 2.8 78 7 0.001 -0.0204 MI EHAUS IBVS #8 44 4 1 102. 6556 0.00 1 -0.0140 RUDNICK IBVS 27, #789 4 1 1 10.9603 0.001 -0.0114 SCARF IBVS #8 44 4 1 1 3 1 .8469 0.001 -0.0139 NI EHAUS IBVS #3 44 4 1139.3450 0.001 - P? . 0 1 /( 5 GULMEN IBVS #647 4 114 1. 48 8 6 0.001 -0.0134 ME I ER IBS'S #64 7 /Il 1/(7.9143 0.001 -0.0151 SCARF IBVS #344 41392.4320 0.001 - 0.008 0 GORZ IBVS #9 3 7 41798.4440 0.001 0.004 1 VOGEL IBVS #937 41814.7746 0.001 -0.0017 BARLOU IBVS #844 /I 1 8 1 6 . 9 I 9 3 0.001 0 .0005 DARLOU IBVS #344 4 13 18 . 79 4f: 0.001 0.0011 SCARF IBVS #344 4 18 2 7.9021 0.001 0.0031 BARLOE" I BETS #844 4 1829.7737 0.001 0.0000 SCARF IBVS #3 44 73 DOCAS: PERIOD- 0 . 6BA66E9D CO < Q t o _J < ZD -f- 0 1 1 CO u [Z u I o r 30. 0 YEARS C-iTOMOLOEY OF 19 135 EPURAT! 0:J5 OF D0CA3 74 TCr^LC = JD /i 1 9 6 P . 3310 + E * 0.65 4 66595 M^LInCFMTHIC 0-C j v l ia :j date + / - ESI DUAL 03SEPVEP 3 39 2 6 . /-I 57 3 0.001 - 0 .0034 lU^EE BAM 45 5, P. 134 33931.9355 0.001 - 0 . 0026 SCPUELLEP AU 231(1), P. 25 33935.3575 0.001 - 0 .0039 :C”EE EAU 45 5, P. 134 34636.A560 0.001 - 0 . 0 03 3 :'U'EE 3AU 43 5, P. 134 33379.^242 0 . 00 1 - 0 . 0039 ^'lUKLEP /i J 7 1 #1 , P . 44 35333.63 13 0.001 - 0 . 0‘0 4 3 'UUKLEP AJ 7 1 // 1 , P . 44 35 399.3790 0.010 - 0 .0044 GPLOUITTS AU 23 9 f 4, P. 192 3 5 4 14.4460 0.010 - 0 . 0000 OPLO'UUS A:J 239 #4 , P. 192 39 03 1 . 33 60 0,010 0 .00 59 HAEER,B05KURT AU 239 ni\, P. 192 39070.3 500 0.010 - P.0060 KI5ILIRMAK AU 2 59 ^4, P. 192 39 122.3945 0.010 0 .0039 B03KUPT>AKYQL AU 2 3 9 ^'4 P . 192 39917.2540 0.001 - 0 . 003 5 ElCXEL^JEIER I B'7S 2 7, #456 4005 1 . 4750 0.001 - 0 .0073 IEA'JOOLU,KIZILI IBV3 2 7, #4 56 /.10 I 1 4 . 4 6 5 7 5.001 - G. 0 0 29 K I 5 I L I RM AK I B'^S 27, #456 /| 0 ^ 1 5 . 4 2 3 0 0.001 - P . P 0 1 5 OUDUR I BUS 27, #456 /I 1 2 G 0 . 3 /J9 9 0.001 - 0 . 00 19 SEMOOr^CA IBUS 27, #647 4 19 36.3666 0.001 - 0 .0011 S EZ ER I B';S #937 4 19 6 0.3310 0 .0 0 1 0 . G C 0 0 ^mOEL I3';s #937 42405.3625 0.001 - 0 .001 1 E BER s B ER 0 ER ^ " T EE IBUS #1053 75 RZCAS; PFIRIOD-- 19525 I 89 1 . 0 r - 0 i + 4--^ 4, k K-i CO 4--^ 4" + > - - 4 -k < 4-^- * A À + 4 :r , ■^H . 4 Q + 4 ] . 00-01 - G 0 . 0 -- 60. 0 -40. 0 - 2 0 . 0 . 0 YEARS 76 CHRONOLOGY OF 6 13 OBSERVAT I OrjS OF RE CAS T C AL C — JD 42 3 39. 7331 + E * 1.19 525139 HELIOCEMTRIC 0-C JULIAN DATE + /- RES I DUAL OBSERVER REFERENCE 16B86.88 10 0.010 0.0369 EPHEHERIS ODESSA IZVEST.4, P17 17355./1200 0.010 0 .0372 MULLER,KEMPF VAR.STAR 9. 2, P. 125 17355.42 3 3 0.001 0.040 5 GRAFF VJS 19 14 1 7 4 1 0 . /i 0 3 0 0.010 0.0336 MIJLAMD AM 4 2 11 17417.57 3 0 0.010 0.037 1 MU LAND AM 4 2 11 17429.5260 0.010 0.0375 MIJLAMD AM 4 2 11 17435.5020 0.010 0.0373 MI JLAMD AM 4 2 11 17/137.3960 0.004 0.0403 PARKHURST , J ORDA P.ALLEGHENY 3.16, P 1 4 17 44 1 . 43 2 0 0.010 0.0410 MIJLAMD AM 42 11 17/147./! 560 0.010 0.9388 MIJLAMD VAR.STAR 9. 2, P. 125 17454.630 0 0.004 0.04 1 2 PARKHURSTUORDA P.ALLEGHENY 3.1 6, P 1 /I 17 479.7350 0.004 0.0460 P ARKH UR ST, J0 R DA P.ALLEGHENY 3.16, P 1 4 17491.6320 0.010 0.0404 P ARKHURST,JORDA VAR.STAR 9. 2, P. 126 17 49 5.2730 C . 0 1 0 0.0457 MIJLAMD AM 42 11 17 502. 4330 0.010 9.0342 MIJLAMD AM 4 2 11 17564.5370 0 . 004 0.035 1 PARKHURST,JORDA P.ALLEGHENY 3.16, P 1 4 17532. 5 190 0.010 0.033 3 MIJLAMD AM 4 2 11 17537.3030 0.010 0.0413 MIJLAMD AM 421 1 1 7599 .26 10 0.010 0 .0463 MIJLAMD AM 4 2 11 17630.3300 0.019 0.0392 MIJLAMD P.ALLEGHENY 3.16, P 1 4 17630.3330 0.010 0.0422 MIJLAMD AM 42 11 17 649.4 49 0 0.010 0.0342 MIJLAMD ADJ 4 2 11 17667 .3370 0.010 0.0434 GRAFF ’/AR.STAR 9. 2, P. 125 1763 5. 303 0 0.019 9.0356 MIJLAMD AM 4 2 11 1777 1 . 3770 0 . 1 0 0.0465 MIJLAMD AM 4 2 11 17772.5620 0.010 0.0362 MIJLAMD 7iM 4 2 11 17777 .3 470 0 . 0 1 0 0.0402 MIJLAMD AM 42 11 17773.5400 0.010 0 .0330 MIJLAMD AM 42 11 17733.325 0 0.019 0.0420 MIJLAMD T^AR. STAR 9. 2, P. 125 17 7 9 1.6910 0.010 0.04 1 2 PARKHURST,JORDA VAR.STAR 9. 2, P. 126 1779 1.69 60 0 . 004 0 . 0/162 P ARK HURST,JORDA P.ALLEGHENY 3.16, P 1 4 17315.6030 0.010 0 . 0 43 2 MIJLAMD AM 4 2 11 17839.5020 0.010 0.0421 GRAFF VAR.STAR 9. 2, P. 125 17340.6970 0.004 0.0419 PARKHURST, JORDA P.ALLEGHENY 3 . 16, P 1 4 17363.3990 0.010 0.0341 MIJLAMD BAM 58 17 3 6 4.6010 0.010 0.0403 YEMDELL VAR.STAR 9. 2, P. 126 179 42.29 1 0 0.010 0 .039 5 MIJLAMD BAM 53 13 0 10.4230 0.010 0 .047 1 MIJLAMD BAM 53 13022.3300 0.010 0.0 46 6 MIJLAMD BAM 53 13035.5250 0.010 0.0438 YEMDELL VAR.STAR 9. 2, P. 126 13 047.47 4 0 0.010 0 .0403 MI JLAT'JD BAM 58 18047.4750 0.010 0.0413 MIJLAMD VAR.STAR 9. 2, P . 125 13043. 67 10 0.010 0.0421 MIJLAMD BAM 53 13 053.4470 0.010 0 .0370 MIJLAMD BAM 58 13090.5060 0.010 0 .0432 MIJLAMD BAM 58 13 1 4 5. 4330 0.010 0 .0437 MIJLAMD BAM 53 13 157.4570 0.010 0 .060 1 MIJLAMD BAM 53 18 132.5360 0.010 0 . 0339 MIJLAMD BAr^ 53 77 HEL I OCEMT!" I C 0 -C JULIAN DATE + / - RES I E'TJAL ORSERVER 1 3 2 2 4 . 3 7 4 G ^'.01 S 0 .0430 N U L AMD I:/ri 53 13 2 3 1.544e 0.010 0.0415 YEMDELL STAR 9.2, P. 126 1824 3.49 0G 3.010 0.0350 N U L AND 'JAM 53 1326 1.4250 0.010 0.04 1 2 MIJLAMD JAM 53 18334.3360 0.010 0.04 19 MIJLAMD JAM 53 13 34 6.29 30 0.010 3.0463 NIJLAMD JAM 53 13 3 59 . 439 0 0.010 0.0446 MIJLAMD JAM 53 1 3 42 1 . 59 1 0 0.010 0.0435 YEMDELL VAJ.GTAJ 9.2, P. 126 13542.3120 0.010 0.0440 JELYASHO MAH.STAR 9.2, P. 126 13603.2750 0.010 0.0492 KOSINSKA VAR.STAR 9.2, P. 126 18724.5930 3.010 -0.5435 YEMDELL UAR.STAR 9.2, P. 126 13 7 3 3.5510 0.010 0.04 2 7 G RAFF r.ALLEGHEirf 3 . 1 6, P 1 4 13 76 3 . 4340 0.010 0.0444 GRAFF VAR.STAR 9.2, P. 125 1 3 763. 4360 0.010 0 . 3 4 6 4 GRAFF P.ALLEGHEMY 3 . 1 6, P 1 4 139 22.4010 0.010 0.0429 EE'IP OR AD P. ALLEGHENY 3 . 1 6, P 1 4 13947.50 50 0.010 3.0466 EE’-IPORAD P.ALLEGHEMY 3 . 1 6 , P 14 189 3 3 . 3 63 0 0.010 0.047 1 CEMPORAD P.ALLEGHENY 3 . 1 6 , ? 1 4 19 03 7.343 0 0.010 0 . 0 4 3 2 DEMPGRAD % R . STAR 9.2, P. 126 19265.4360 0.310 0.0406 BEMPOEAD VAR.STAR 9.2, P. 126 19 326.3936 0.005 0.0454 LEHMEET AM /I 59 6 19326.3990 0.010 0.0 4 53 LEHMERT P.ALLEGHEMY 3 . 1 6, P 1 4 19323.7990 0. 003 3.0553 JORDAN P.ALLEGHENY 3 . 1 6 ,P 1 3 1933 1.3730 3.010 0.3432 LEHMERT P.ALLEGHENY 3 . 1 6 , P 14 19 33 1 . 373 5 0.305 0 . 0437 LEHMERT AM 4 59 6 19 4 2 4.4042 0.005 0.0403 LEHMERT AM 4 59 6 19 442.3 3 20 3 .005 0 .0394 LEHMERT fCl 4 59 6 1 9492. 53 10 0.0 10 0.0 3 73 YEMDELL VAR.STAR 9.2, P. 126 19534.3670 0.010 0.0400 PADOVA Vf\R, STAR 2 , P. 126 19 663.4530 0.010 0.0333 MAGGIMI VAR.STAR 2 , P. 126 19 67 5 . 4 04 0 0.010 0.0372 LEHMERT VAR.STAR 9.2, P. 126 19 67 5.4060 0.010 0.0392 LEHMERT P.ALLEGHEMY 3 . 16,P 1 4 19 63 1 .3770 0.010 0.0340 GRAFF VAR.STAR 9.2, P . 126 19 63 3. 76 50 0.010 0.03 15 JORD/iN \^AR. STAR 9.2, P. 126 19637.3570 0.010 0.0377 LEHMERT P.ALLEGHENY 3 . 1 6, P 1 4 19 63 7 . 36 1 0 3.010 0.0417 LA ZEA PI MO VAR.STAR 9.2, P. 126 19725.6010 0.010 0.0337 ''EMDELL VAR. STAR. 9.2, P. 126 19736.3601 0.010 0 .0355 GRAFF F.ALLEGHENY 3 . 1 6, P 1 4 19773.4 100 0.010 0.0326 GRAFF VAR.STAR 9.2, P. 126 19773.4120 0.010 0.0346 GRAFF P.ALLEGHENY 3 . 1 6, P 1 4 19773. 1330 0.010 0.0296 GRAFF P.ALLEGHENY 3 . 1 6 , P 1 4 19 797.3220 0.0 10 0.039 5 GRAFF P.ALLEGHENY 3 . 16,P 1 4 193 22.4133 0.010 0.0361 LEHMERT AM 4 73 6 1995 1 . 5020 0.010 0. 032 1 PADOVA VAR.STAR 9.2, P. 126 200 13.4 110 0.010 0.0070 HOFFMEISTER VAR.STAR 9.2, P. 126 200 13.4332 0.010 0.0342 LEHMERT AS I 4 78 6 2 00 13 . 4390 0.003 0.0349 HOFFMEISTER AM 4 72 3 20036.3631 0.010 0.0353 LEHMERT AM 4 78 6 20033.7520 0 .003 0 .023 7 JORDAN P . A LLEGHEM 3 . 1 6, P 1 3 20042.3460 3.010 0.03 69 HOFFMEISTER AN 4 72 3 20054.3000 0.010 0.0384 HOFFMEISTER AM 4 72 3 20066.2510 0.010 0.0369 HOFFMEISTER AN 47 2 3 20276.6100 0.010 0.03 15 DUGAN VAR.STAR 9 2, P. 126 H K Ll OCErjTRI C 0-C 78 JT^LIAn DATE + /- 2ESIDUAL observer REPEREMCE 20 5 57 . /i9 50 0.010 0.0323 DUG AN VAR. STAR 9 . 2 ^ P. 126 2 09/49 . 5 33 0 0.010 0.0327 DUG AM VAR. STAiR 9 . 2, P. 126 22/4 12. 5303 0.010 0.0372 DUG AM VAR . STAiR 9 . 2> P. 126 23 100.9950 0.010 0.0363 DUG AM VAR . STAR 9 . 2, P. 126 23435.6637 0.010 0.039 5 DUG AM VAR . STAR 9 . 2, P. 126 235 19.3390 0.010 0.0422 ODESSA IZ VEST .4 P .17 23803.5997 0.010 0.05 19 DUG AM VAR. STAR 9 . 2, P. 126 24805.4330 0.010 0. 045 1 ODESSA IZVEST .4 P .17 25 104. 2 43 0 0.010 0.0472 ODESSA IZ vest .4 P. 17 2633 6.3640 0.010 0.0426 :RUGEMER A. A. (E) 2, P. 96 2 63 9 3. 5340 0.010 0.04 1 1 RUGEMER A. A. CB) 2, P. 96 26399.5 110 0.010 0.0413 RUGEMER A. A. (E) 2, P. 96 26905.4384 0.010 0.0430 SKOBERLA A. A. (3) 2, P . 96 26907.8734 0.00 1 0.0425 RUGEMER Pi.. A . C B) 2, P . 96 269 1 1 .4640 0.010 0.0423 : RUGEMER A. A. ( B) 2, P . 96 26929 . 3940 0.010 C .0435 RUGEMER /1. A • CE) 2, P . 96 26930.5900 0.010 0.044 3 RUG EMER A . A . ( B) 2, P . 96 26933.9 553 0.001 0.0 428 RUGEMER A. . CE) 2, P. 96 2 69 47.3203 0.010 0.0410 SKOBERLA A. /-I. CB) 2, P. 96 2 69 43.5160 0.010 0.0415 RUGEMER A. A. CB) 2, P. 96 269 54. 4920 0.010 0.0412 MERGEMTALER, ' J AR A. A. CD) 2, P. 96 269 54. 49 50 0.010 0.0442 RUGEMER . A .CE) 2, P. 96 2 69 6 0 .4 69 0 0.010 0.0420 RUGEMER A . A . CB) 2, P . 96 2 69 66.447 0 0.010 0.0437 RUGEMER A. A. CE) 2, P. 96 26970.0311 0.001 0.0420 RUGEMER A. A. CE) 2, P. 96 269 7 2.419 0 0.010 0.0395 :RUGEMER A. A. C 3) 2, P. 96 2 69 7 2.4210 0.010 0.0/114 :RUGEMER A.. A. CE) 2, P . 96 26935.5660 0.010 0.0387 RUGEMER /i • A . C B) 2, P. 96 26935.5630 0.010 0.0/107 RUG EM ER A. A. CE) 2, P. 96 27040.5490 0.010 0. 040 1 HIMPEL Ai. A .C B) 2, P. 96 27 119.433 0 0.010 0.0/125 ELLSVORTH A. A. CE) 2, P. 96 27156.4905 0.010 0 . 0/122 SKOBERLA A . A . CB) 2> P. 96 27333. 33 50 0.010 0 . 0394 ELLSVORTH A • A . CE) 2, P. 96 27345.3360 0.004 0.0379 KORDYLE^-^SKI A . Ai. CE) 2, P. 96 27406.2961 0.010 0.0401 GADOMSKI A. A. C B) 2, P. 96 27603.5070 0.010 0. 0345 ELLS^'^ORTH Ai. A. CE) 2, P. 96 277 19.45 10 0.010 0.039 0 ELLSVORTH Pi. Ai . C B) 2, P . 96 278 11 . 43 12 0.010 0.03/13 HELLERICH A. A. C B) 2, P . 96 27372.4 370 0.010 0.0328 SEAPRAMI EC A. A. CB) 2, P . 96 27372.4392 0.010 0.0350 ELLSVORTH A. A. C B) 2, P. 96 27 3 7 2.44 00 0.010 0.0353 SZAPRAMIEC Ai. A. CE) 2> P. 96 27 37 8.4211 0.010 0 . 0406 SZAPRAMI EC Ai. Ai. CD) 2, P. 96 23 16 5.23 17 0.00 1 0.04 03 SZAPRAMI EC A . A . CE) 2, P. 96 23 37 4. 4 48 0 0.010 0.0380 MAK O^'IECKA Ai. A .CB) 2, P. 9 6 23 466.43 7 5 0 . 0 06 0 . 643 1 TECZA A. A. CE) 2, P. 94 23466.4377 0.001 0.043 3 TECZA Ai. Ai. CE) 2, P. 96 23 48 4. 4 1 10 0 . 0 0/1 0. 0378 TECZA A. A. CE) 2, P. 94 23 43 4.4 145 0.001 0.0413 TECZA A. A. CE) 2, P. 9 6 23514.2330 0.005 0. 0335 TECZA A . A. C B) 2, P. 9 4 23 55 1 . 3457 0.00 1 0.0334 TECZA A. A. CE) 2, P. 96 23551.3482 0.003 0.0409 TECZA A. A. CD) 2> P . 9 4 28 57 6 .43 62 0 . f^03 0.028 6 TECZA A. A. CE) 2, P. 94 79 H^LI OCE^JTP.I c 0-C JT^LIAM DATE + / - EES I DUAL 0D5EEVEP REFERENCE 23606.3250 0.003 8 . 036 1 TECZA {■\ • /i. C B) 2, P. 94 236 13 .2730 0.805 0.0366 TEMCHA UAR . STA^R' 9 .2, P. 23 64 3 . 3 7 4 0.002 0.0327 TECZA f \ • A . CD) 2, P. 94 23662.5000 0.005 0.0343 TECZA A. A. CD) 2, P. 94 23 663. 47 40 0.003 0.0320 TECZA A. A. CB) 2, P. 94 28 77 7 . 2429 0.005 0.0330 TEUCHA VAR, STAR 9 .2, P. 23734.4120 0.006 0.0306 TECZA A. A. CD) 2, P. 94 23333.199 0 8.001 0.03 13 TECZA Ai. A . CB) 2, P. 96 23339.3945 0.003 0.0315 TECZA /i. . A . C 3) 2, P. 94 23375.2546 0 . 003 0.0340 TECZA A. A . CB) 2, P. 9 4 29 878. 4475 0 .006 0. 034 1 TECZA /i. A . CD) 2, P. 94 29 1 45. 3345 0.003 0.0370 TECZA A. A. CB) 2 , P. 94 29 163. 3 137 0 . 006 0.0374 ;TECZA A . A . CB) 2, P. 94 29 17 8 . 43 63 0.005 0.039 0 TECZA A. A. CD) 2, P. 94 2926 1 .3286 0 . 002 0.0337 TECZA A. A. CD) 2, P. 94 29375.69 02 0.001 0 .0433 HUFFED,KOPAL APJ 1 14, P. 297 '3 8 0 23 . 63 1 2 0.081 8.0426 HUFFED,HOPAL /iPJ 1 14, P. 29 7 30265.3409 0.810 0 . 0424 '-'ALTER A. A. CB) 2, P. 9 6 3 0 322.7125 8.00 1 0.04 19 HUFFER,KOPAL APJ 1 1 4, P. 297 38633.2590 0.010 0.04 19 PAGACZEUSKI A. A. CB) 2, P. 97 30329.49 13 0.018 0.0344 MERGENTALEE A . A . CB) 2, P. 9 7 3 03 29.49 21 0.010 0.0347 BANACHI E'U CZ A . f \ ■CD) 2, P. 97 30368.5643 0.010 0.0303 BANACHI EUI CZ A . A . CD) 2, P. 97 30366.54 3 3 0.010 0 .033 1 BANACHIEUICZ A. A. CB) 2, P. 97 3 09 4 0 .6 49 3 0.010 0.0340 BANACHI I CZ A. A. CB) 2, P. 97 309 53. 5774 0.010 0.0323 BANACHIEUICZ A. A. CB) 2, P. 97 3203 5.7011 0.001 0.0340 HUFFER,KOPAL APJ 1 14, P. 29 7 32 1 1 5 . 53 2 7 0.001 0.0343 HUFFER,KOPAL APJ 1 14, P. 29 7 32 152.6358 0.001 0.0346 HUFFER,KOPAL APJ I 14, P. 297 32293 . 4608 0.018 0 . 038 0 PAG ACZE'-'SKI A . A . CD) 2, P. 97 32365.3970 0.018 0 . 0409 : PAGACZEUSKI A . A . C B) 2, P . 97 32445.4755 0.018 8.0376 NAZUR A . A . CD) 2 , P. 97 32 4 52.6 4 60 8.001 0.0365 HUFFER,KOPAL APJ 1 14, P. 297 32469.3370 0.007 0. 0440 SZAFRANIEC A .A. C B) 2, P. 9 1 32475.3630 0.010 0 . 0438 : PAGACZE'-'SKI A . A . CB) 2, P. 97 32562. 6 1 30 0.013 0,0404 : SZAFRANIEC A. A. CB) 2, P. 9 1 3 26 1 6 . 409 8 0.010 0.0500 : SZAFRANIEC A * A . C B) 2, P. 9 1 3264 1 . 50 10 0.085 0.0417 SZAFRANIEC . A . CB) 2 , P. 9 1 32673.5490 0 . 8 03 0.0 3 69 SZAFRANIEC A. A. CD) 2, P. 9 1 32684. 53 1C 0 . 005 0.842 7 SZAFRANIEC A . A i. CB) 2, P. 9 1 32763./ I 190 0.010 0 . 0 4 0 JASKO M . A. C B) 2, P . 97 3 277 0.53 24 0.006 0.0359 SZAFRANIEC A. A. CB) 2, P . 9 1 3273 1. 3330 0.010 0.0343 SZCZEPANOUSKA A. A. CB) 2, P. 97 3 279 4 . 43 9 0 0.003 0.0375 SZCZEPANOUSKA A. A. CB) 2, P. 92 3 279 4.43 9 3 0.001 0.0333 .PI OTRO^'^SKI A . A i. CD) 2, P. 97 3 2 794.4900 0.005 0.033 5 SZAFRANIEC A. Ai. CD) 2 , P. 9 1 32306.4330 0.010 0.8340 POCHER AN 2 79 3 2 3 0 6.441 1 0.001 0.037 1 PIOTROUSKI A. A. C 3) 2, P . 97 32820.7353 0.001 0.0383 HUFFER,KOPAL APJ 1 14, P. 297 32362. 6 139 0.001 0.0380 HUFFER,KOPAL APJ I 14, P. 297 32362.6252 0.004 0. 0443 SZAFRANIEC A . A . C E) 2, P. 9 1 32368.5955 0.004 0.0334 SZAFRANIEC A. Ai. CD) 2, P . 9 1 HELIOCEMTRIC 0-C 80 JULIAM DATE + /- RES I DUAL observer REFEREMCE 32368 5990 0.010 0.0419 SZ AFEAIJI EC A. A CB) 2, P. 97 32399 6768 0.003 0. 043 1 SZ AFRArJI EC (B) 2, P . 9 1 3294 1 5086 0.005 0.04 1 I SZCZEPANOVSKA CB) 2, P. 92 32946 23 7 0 0.010 0.0385 AHNERT CB) 2, P. 97 32996 49 2 6 0 . 007 0.043 5 SZCZEPAMOVSKA CB) 2, P. 92 330C2 4637 P. 003 0.033 4 SZAFRA>JI EC C B) 2, P. 9 1 33002 4642 ,0.005 0 . 0339 SZCZEPAMO'.^SKA C B) 2, P. 92 33026 37 1 6 0.006 G.04 1 2 SZCZEPPiMOVSKA C D) 2, P. 92 33027 5676 0.005 0.0420 SZAPRAMI EC CD) 2 , P. 9 1 33^39 5 173 0 . G 0 3 0.0397 SZAFRAMIEC CB) 2, P . 9 1 33 153 4565 0.001 0.42 9 4 PI OTRO'^SKI C B) 2, P. 97 33 155 450 1 0.005 0.0325 SZAFRAMIEC C B) 2, P . 9 1 33 155 4550 0.010 0.0374 SZCZEPAMO^'SKA CB) 2, P. 97 33 155 4600 ■0.0 07 0.0424 SZCZEPAMQVSKA CE) 2, P. 92 33 157 3472 0.00 1 0.039 1 HT7FFER> KOPAL APJ 1 14, P. 29 7 33 1 69 3005 0 . 0 0 1 0.0399 HUFFER,KOPAL APJ 1 14, P. 297 3 3 13 5 3393 0.001 0.0404 PIOTROUSKI C B) 2 , P. 97 3 3 13 5 3398 0 . 003 0.0409 SZPc RAMI EC CB) 2, P . 9 1 33 13 5 3400 0.010 0.041 1 SZ CZEPAMCSKA CB) 2, P. 97 33 135 3437 0 .005 0.0443 SZ CZEPAMOUSKA CB) 2, P . 92 33 19 1 3 130 0.0 10 0.0379 POHL AM 2 79 33 197 29-0 0 0.010 0.038 6 POHL AM 2 79 332 1 0 4373 0.001 0 .0336 PIOTROUSKI A .A . C B) 2 , A . 9 7 3 3 2 3 4 3367 0 . 007 G.0325 SZAFRAMIEC A .A . C E ) 2 , P . 9 1 33242 7 10 1 0 .001 C. 039 1 HUFFER,KOPAL APJ 114, P 29 7 33307 2540 0.010 0. 039 4 POHL AM 2 79 33332 3560 0.010 0.041 1 SZAFRAMIEC /l . A . C B ) 2 , P. 97 3 3 3 3 2 3 5 60 0 . 005 0.041 1 SZ/iFRAMI EC A .A , C D) 2 , P . 9 1 33399 2935 0.006 0 . 0 4 5 SZ AFR/Sji EC A • A • ( B ) 2 , P . 9 1 3 3 4 12 4330 0 . G 0 5 0.0413 SZAFRAMIEC /i. A. ( B) 2 , P. 9 1 3 3 4 18 4 12 1 0.001 0. 0 39 1 PI OTRO^'SKI A . A . C B ) P. 9 7 3 3 4 18 4 14 0 0.010 0.0410 SZAFRAMIEC A . A . ( B ) P . 97 3 3 4 3 0 3 68 0 0.010 0.0 42 5 POHL AM 279 33455 4 6 60 0.010 0.0402 SZAFRAMIEC P: . A . C B ) 97 3 3 4 5 5 4680 0 . 0 1 G 0 . 0 42 2 POHL AM 2 79 335 16 42 1 0 0.0 1 0 0.0373 EG RM /iM 28 1 C 3) P. 11 4 33 57 1 4 8 .'4 7 G . 007 G. 039 5 PI OTRO''SKI , STRZ \^AR. STAR 1 6. 1, P . 40 3 3 596 5038 0 . 0 0 7 0 .0383 PI OTRO'^SKI , STRZ ''AR. STAR 1 6# 1 .f P. 40 33596 0.010 0.0411 SZAFRAMIEC A. A. C B) 2, P.. 97 33675 3896 0.007 0.0375 PI OTRCSKI VAR. STAR 1 6. 1, P. 40 337 1 2 4 4 1 0 0.010 0.0360 POHL A)1 28 1C 3 ) J P. 11 4 337 12 4 4 /i 0 0.010 0 .0390 DOMKE AM 23 1 C3) J P. 114 3 3 7 18 42 3 0 0.010 0.04 18 POHL fiM 28 1C 3) J P. 11 4 3373 1 5670 0.010 0.0330 SOFROMI JE^'"I C AM 28 1C 3) J P. 114 3373 1 •^7 40 0.010 0.0450 BO RM AM 28 1C 3 ) J P. 11 4 33737 54 10 0.010 0.0357 POHL /iM 281C 3) J P. 11 4 33737 54 3 0 0.010 0.0373 EEHM AM 23 1C 3 ) J P. I 14 33737 5470 0.010 0.04 17 DOMKE AM 28 1C 3 ) J P. 11 4 33383 3640 0.010 G.0330 DOMKE AM 23 1C 3) J P . 11 4 33389 3420 0.010 0.0393 DOMKE AM 231C 3) J P . 11 4 3 4 0 0 5 28 10 0.010 0.039 3 POHL AM 28 1C 3) J P. 11 4 34079 3340 0.00 1 0.0367 POHL AM 28 2^ P « 235 81 H^LI OCEMT^-I C 0-C JMLIAM DATE + / - P.” S I DUAL OPSEPO/ER REFER EMCE 3/109 1. 339 0 0.001 0.0392 BOPOJ AM 23 2, P. 235 3/1 10/1. /13 10 0.00 1 0.0334 BORM AM 282, P . 235 34 135. 5530 0.001 0 .0339 POHL AM 28 2, P. 235 34269.4250 0.001 0.0327 BORH AM 23 2, P. 235 34349. 5 1 30 0 . 007 0. 0383 LENOUVEL^ DAGUIL VAR.STAR 16 . 1, P. 4 1 34 391.3460 0.001 0.0380 POHL /UM 28 2, P. 235 3/1/116.4463 0 . 007 0.0330 LENOUVEL^DAGUIL VAR.STAR 16 . 1 , P. 4 1 34440.3 53 0 0 .003 0.0396 UnOBLEUSKI UR AM I /i SUP . 1, P. 35 3 4440.3 58 0 0.001 0.0 44 6 DOMKE AM 28 2, P. 235 34446.3250 0.001 0.035/1 BORM AM 23 2, P. 235 34452.3070 0.00 1 0.04 11 POHL AM 28 2, P . 235 34453.2820 0 . 0 02 0.039 9 UR0BLEU5KI URAMIA SUP. 1 , P. 35 3 4 471.42 50 0.003 0.0351 OTLMMOUSKI URAMI A SUP . 1, P. 35 34575.4152 0 .002 0.0384 unODLE^'SKI URAMIA SUP . 1, P. 36 3 4 58 1 . 38 3 0 0.003 0.03 49 '•mOBLEUSKI URAMIASUP. 1, P. 35 34537.3600 0.004 0.0307 UROBLE^'^SKI URAMI A SUP. 1, P. 35 3 4 630.3940 0.001 0.0356 POHL AM 23 2, p. 235 3 4 636.3790 0.001 0.0443 POHL AM 28 2, p. 23 5 34703.3035 0 .007 0.0347 LENOUVEL^ DAGUIL VAR.STAR 16 . 1 , P . 42 347 15. 2590 0.003 0.0377 ^':ROBLE'''SKI URAMI A SUP . 1 , P. 35 343 56.2910 0.00 4 0.0300 UROBLE^-^SKI URAMIA SUP . 1 , P. 35 34913.45 00 0.002 0.0359 ^':ROBLEUSKI URAMIA SUP . 1, P. 35 3496 1 . 4770 0.004 0.0338 ^■'RO BLEU SKI URAMIA SUP. 1, P. 35 349 6 1 .4780 0.002 0.0348 UROBLEUSKI URAMI A SUP . 1 , P. 36 3 49 79. 4 09 0 0.006 0.0370 UR0BLEUSKI URAMIA SUP . 1, P. 35 3 499 1 . 359 0 0 . 003 0.0345 ::ROBLE''SKI URAMIA SUP. 1 , P. 35 3 4991.3600 0.004 0.0355 JODLOUSKI URAMIA SUP. 1, P. 35 3499 1 . 3620 0 . 003 0.0375 SZCZEPKOUSKI URAMIA SUP. 1, P. 35 3499 1 . 3630 0 . 003 0.0385 MARKS URAMIA SUP . 1 , P. 35 34997.3340 0.004 0.0333 SZCZEPKO’'^SKI URAMIA SUP. 1, P. 35 3499 7 . 33 50 0 . 003 0.0343 MARKS URAMIA SUP . 1 , P. 35 34997.3360 0.003 0.0353 VROBLE^-'SKI , OZ DZ URAMIA SUP . 1 , P. 35 35009 . 29 1 0 0 . 005 0.0377 ^'ROBLEUSKI URAMIA SUP . 1 , P. 35 3 50 10.43 10 0.004 0.0325 JODLOUSKI URAMIA SUP. 1, P. 35 3 5040.3 63 0 0. 003 0.0332 JODLO^'SKI URAMIA SUP . 1 , P. 35 3 5133.38 00 0.003 0.039 5 '-UROBLEUSKI URAMIA SUP. 1, P. 35 35155. 1033 ■0.002 0.0343 JODLOUSKI URAM I A SUP . 1 , P. 36 35 1 63. 2530 0 . 004 0.0312 '-'ROBLEUSKI URAM I A SUP. 1, P. 35 3 5 13 1.4010 0. 004 0.0315 ^■'ROBLEUSKI URAMIA SUP. 1, P. 35 35 199.33 16 0.001 0.0333 '.'ROBLEUSKI URAMIA SUP . 1 , P. 36 3 5 2 2 4 . /13 4 0 0.003 0.0354 '■mOBLEUSKI URAMI A SUP. 1, P. 35 35242.35A0 0.00/1 0.0 28 6 UROBLEUSKI URAMI A SUP . 1, P. 35 35242.36 19 0 . 002 0.0345 MARKS URAMIA SUP . 1, P. 36 35243.3350 0.003 0.0314 UROBLEUSKI URANIA SUP . 1, P. 35 35334.3960 0.003 0.0342 JODLOUSKI URAMIA SUP. 1, P . 35 35346.3 4 70 0 . 003 0.0327 UROBLEUSKIURAMIA SUP. 1, P. 35 35346. 35 10 0.004 0.0367 JODLOUSKIURAMIASUP. 1 , P. 35 35353.3030 0.005 0.0362 UROBLEUSKIURAMIA SUP . 1, P. 3 6 3 53 53.30 50 0 . 003 0.0382 MARKS,JODLOUSKIURANIA SUP. 1 , P. 36 3 5370.2460 0. 006 0.0267 UROBLEUSKI URAM I A SUP. 1, P. 36 35376.2310 0 . 004 0.0354 UROBLEUSKI URAM I A SUP. 1, P. 36 35383.3970 0. 003 0.0299 '•'ROBLEUSKI URAMIASUP. 1, P. 36 82 H E L I OCETTTEI C 0-C r’JLIAM DATE + /- EES I DUAL 0DSEP07E?. REFERENCE 35383.3989 0.002 0.03 18 ^TROBLEUSKI URANIA SUP. 1, P. 36 35^0 1 . 326C 0.004 0.030 1 MARKS URANIA SUP. 1, P. 36 3 5 0 1 . 3 3 1 0 0 .0 04 0.035 1 MASLA.KI E\U CZ URANIA SUP. 1, P. 36 35/40 1 . 3350 0 . 003 0 .039 1 UROBLE'-TSKI URANIA SUP. 1, P. 36 35/4 1 3. 2780 0.004 0.029 6 ^■U^.OBLEVSKI URAN I A SUP. 1, P. 36 35/4 1 3 . 28 1 0 0 . 004 0.0326 MARKS URANIA SUP. 1, P. 36 3 5 /432. 402/1 0.001 0.0300 LEMOUUEL,EROGLI AST. ITAL. 30, P. 20 35536.3860 0.001 0.0267 0UE5TER AN 23 5, p. 161 35554.3 190 0.001 0.0309 CUESTER AN 2 3 5, p. 1 6 1 35560.2970 0.00 1 0.0326 QUESTER AN 23 5, p . 16 1 35592.5630 0.002 0.03 13 SZAFRANIEC A. . 7 , p. 139 35622.4470 0.003 0. 029 5 SZ AFR/\NI EC A. A . 7 , p. 139 35726./1320 0.006 0.0276 ; SZAFRANIEC A . A. 7 , p. 139 35775.4393 0.00-1 0.030 1 LEMOUREL,BROGLI AS T . I T AL . 30, P. 20 35848.3520 0 . 0 0 2 0.0319 SZAFRANIEC A.A. 3, p. 139 353 60. 3090 0 . 0 0 2 0.03 64 SZAFRANIEC A.A. 8, p. 139 35379.4270 0 .001 0. 030/1 RUDOLPH AN 23 5, p. 1 61 35904.5260 0.002 0.029 1 SZAFRANIEC /i./i. 3, p. 1 39 359 09.3140 0.002 0. 036 1 SZAFRANIEC . A. S , p . 19 0 35934.4097 0 . 0 0 .1 0.0315 SZAFRANIEC f\ • C\ • 3 , p . 190 35934.4097 0.001 0.0315 RUDOLPH AN 28 5, p. 1 6 1 35953.5290 0.001 0.0267 RUDOLPH,QUESTER AN .23 5, p. 161 359 59. 50 70 0.001 0.028 5 DORR AN 28 5, p. 161 35983.4 160 0.001 0.3324 DORR AN 23 5, p. 161 36023./I 545 0.003 -0. 567 6 :SZAFRAMIEC A.A. 8, p. 190 3 6026.4400 0.001 0 .0274 RUDOLPH AN 23 5, p. 1 6 1 36026.4440 0.002 0.331/1 SZAFRANIEC h . A. 8 , p. 199 3607 5.4490 0.001 3.0311 RUDOLPH AN 235, p. 161 36106.5240 0.001 0.029 5 DORR AN 23 5, p. 161 36166 . 23 3 0 0.001 0.02 59 BRAUNE AN 2 3 5, p . 161 36 173.459 0 0.001 0.9304 ERAUNE AN 23 5, p . 1 6 1 36288.4430 0.001 0.2702 RUDOLPH AN 23 6, p. 2 10 3 63 03. 52 1 0 0.001 0.9239 ERAUNE AN 28 6, p. 2 1C 36369.4800 0.031 0 .030 1 RUDOLPH AN 23 6, p. 2 1 0 3 64 54.3 3 60 0.005 0.0232 SZELI G IEUICZ,MA A. A. 17. 1 , P. 60 36454.3 42 0 0.004 0.3292 MARSZ ALEIC, FL I N A. . 17. 1 , P. 60 364 60.3090 0.006 0.3200 SZELIGIEUICZ A.A. 17 . 1,. p. 60 36/160.3130 0 . 004 0.02 4 0 PANKO"'^ A. A. 17. 1, P. 60 36712.5200 0.001 0.0323 RUDOLPH AN 23 6, p. 2 1 0 368 1 6.4975 0.001 0.0234 SURKOVA IBVS 2 7, ^50 1 36323.6663 0 . 307 0.0237 ENGELKEMEIR VAR.STAR 16• 1 , P . 43 36884.6236 3 . 007 0 . 020 1 ENGELKEMEIR VAR.STAR 16. 1, P. 48 3699 3. 39 50 0.001 0.0236 MEN DE AN 28 3, P . 1 63 37000.5650 0.001 0.022 1 MENDE AN 283, P. 1 63 37006.5390 0.001 0 . 0 193 MEN DE AN 283, p. 163 37017.2920 0.00 1 0.0156 M EN DE AN 238, P . 1 63 37018.4900 0.001 0.0183 BRAUNE AN 28 3, P . 1 68 37024.46 60 0.001 0.0181 BRAUNE AN 23 3, P . 1 63 37048.3750 0.001 0 . 0220 MENDE AN 233, P. 168 37 079 . 4500 0.00 1 0.0205 MENDE AN 23 3, P . 168 371/13.9886 0.005 0.0155 UI SCHNE'-^SKI 3AV RUND 22(3/4), P24 3714 6.3820 0.002 0.0 184 SZAFRANIEC• A . A. 13. 1 83 OCENTP.I C 0-C JVTLIAM date + /- PESIDUAL ODSERVER REFEREMCE 37 139. 408 0 0.001 0.0153 POHL AM 23 3, P. 69 37202.5530 0.001 0.0 125 RUDOLPH AM 233, P. 1 63 37227. 655 1 0 . 007 0.0 143 EU8 ELKEHEIR VAR.STAR 16. 1 , P. 49 37246.7736 0 . 037 0.0 138 RUI E VAR.STAR 16. 1, P. 4 9 37263. 5 1 26 0.007 0.0143 RUI E VAR.STAR 16. 1 , P. 4 9 373 11.3250 0.001 0.0166 MEUDE AM 283, P. 1 63 373 12.5 13 0 0.001 0.0143 M EW DE AM 288, P. 163 373 17.3020 0.301 0.0 173 MEM DE AM 28 3, P. 1 63 373 17.3030 0.001 0.3183 POHL AM 233, P. 69 37403.3620 0.001 0.0 192 MEMDE AAJ 283, P. 163 37 52 6 .4 645 0 . 009 0.0108 S2P0R,ClEMMOLOM /"i.Ai. 17. 1, P . 60 37526.4705 0 . 806 0 . 0168 SZELIGIFO'^ CZj Cl i-i.A. 17.1, P. 60 37 5 33. 4260 0.001 0.0 197 FERMAMDES AM 23 3, P. 168 37 544.4060 0.001 0 .023 5 FERMAMDES AM 23 3, P. 1 68 37 5 4 5.59 9 0 0.001 3.0212 FERMAMDES AM 233, P. 1 63 37 550.3720 0.001 0.0 132 JUMGELUTH AM 288, P. 1 63 37556. 35 10 0.005 0.3160 SLO^'IH A. A. 17.1, P. 60 37556.3545 0.005 0.0195 LUDO' ^I ECHA, CZER A.A. 17.1, P. 6 0 37 562.3 37 0 0.001 0.0257 FERMAMDES AM 2 3 3, P. 1 68 37563.5230 0.301 0.02 14 FERMAMDES /iM 23 3, P. 1 68 3 7 569. 50 1 0 0.001 3.0182 FERMAMDES /iM 28 8 , P . 1 69 37570. 69 09 0.007 0.0128 RUIZ VAR.STAR 16 . 1, P. 5 0 37574 . 2-300 0.001 0.0 162 FERMAMDES AM 288, P. 1 69 3 7 5 7 5.4710 0.001 0.01 19 FERMAMDES AM 233, P. 169 3 7 532.6436 G. 007 0.0133 RUIZ VAR.STAR 16. 1, P. 5 0 37532.65 10 0.001 0.0204 FERMAMDES AM 288, P. 1 69 37537 .43 1 0 0.001 0.0 194 MEMDES AM 233, P. 1 69 37533.6204 0 . 007 0.0 136 EMGELKEMEIR VAR.STAR 16. 1 , P . 5 1 37623.2330 0.031 0.0189 MEMDES AM 288, P. 1 69 37624.4 3 30 0.001 0.0186 MEMDES AM 28 8 , P. 1 69 376 4 2.4020 0.001 3.0333 HO FF MAM AM 2 3 3, P . 169 37643.38 3 0 0.001 0.0136 HQFFMAM AM 23 3, P. 1 69 37660.3 4 20 0.001 3.3203 H o f f : I AM AM 2 33, P. 1 69 37661.5308 0.007 0.0 136 VAM GEMDEREM VAR.STAR 16. 1 , P. 5 1 37 667 .5 1 00 0.001 0.3 165 HQFFMAM AM 28 3, P. 1 69 3 7 69 7 . 33 50 0.001 0.3 102 : FERMAMDES AM 28 3, P. 1 69 3774 6 . 39 60 . 0 G 1 0.3159 FERMAMDES /iM 283, P. 1 69 37777.4630 0.001 0.01 Ul FERMAMDES AM 23 3, P. 1 69 37733.4530 0.001 0.0201 SCHUBERT AM 23 8 , P. 1 69 37381.4580 0.001 0.0 145 HOFFMAM AM 23 3, P. 1 69 3 7 8 8 7.4300 0 . 007 0.0102 SZELIGIEUICZ A.A. 17.1, P. 60 3 7 3 3 7.4440 0.008 0.0242 FLIM A.A. 17.1, P . 60 37899.3330 0 . 008 3.0 137 SZELIGIERU CZ A.A. 17. 1, P . 60 37899.3850 3.003 0.0127 SLOUIK A. A. 17. 1, P . 6 0 37899.3940 0 . 0 0 4 0.0217 FLIM,CZERLUMCZA A. A. 17.1, P . 60 37905.3580 0 . 002 8 .3394 SLOUIK A.A. 17. 1, P. 60 37905.3630 0.005 0 .3 144 SZPOR, SZELIGIE'J A . A . 17.1, ? . 60 379 1 1 .3360 0 . 005 0.3112 SZPOR /'i-.A. 17.1, P . 60 379 1 1 .34 60 0.001 3.0211 SCHUBERT AM 288, P. 169 37912.5334 0.031 3.3 133 SURKOVA IBVS jy 50 1 379 17.31 10 0 . 0 03 0 .0099 SZPOR A. A. 17.1, P. 60 37917.3160 6 . 0 0 1 0.31/19 MEMDES AM 23 3, P. 1 69 84 0-C + / - ;0 I DUAL OBSEPU^Un REFER EMC rr 27903. 2 3 3 0 c .0 0 2 O'. G 1 0 6 SZPOR A. A. 17 . 1, P. 60 37 9 2/1. 43 7 0 0 .001 G.0 1 44 R I EM AM! J /iM 233, P . 1 69 379 42. 4 190 0 .0 0 1 0 .0 176 MEMDE AM 238, P. 169 379 54. 3630 0 .0 0 3 0 .0 0 9 1 SZPOR A. A. 17 . 1 , P . 6 0 37954. 3720 0 .0 0 1 0 .0 18 1 RI E:'l PiMM AM 23 3, P . 169 3 7 9 6 0. 3370 0 .003 0.00 63 SZPOR A. A. 17 . 1, P. 60 3 79 60. 3 4 60 0 .0 0 1 G . 0158 MEMDE AM 288, P . 1 69 c 37973. 43 3 0 .001 0 .0 1 0 1 SCHUBERT AM 283, P. 1 69 3 3 0 0 3. 3730 0 .0 0 1 0 .0 1 3 3 ORLOVIUS r.M 233, P. 69 33003. 3 79 0 G.0 0 1 0 .0 1 9 3 FERMAMDES AM 288, P. 1 69 3302 1 . 29 60 0 . 0 0 1 0 .0 03 0 ORLOVIUS /iM 233, P . 69 3302 1 . 3030 0 .00 1 0 .0 1 5 0 SCHUBERT AM 233, P . 1 69 33022. 49 4 5 0 .0 0 1 0 .0 112 JAMSEM IB VS #9 30 33 022. 49 3 0 0 .0 0 1 0 .0 147 SCHUBERT AM 283, P . 1 69 33052. 37 3 0 0 .001 G.0034 SCHUBERT, GROBA: /iM 292, P. 13 5 33039. 4 2 3 0 0 .0 0 1 0 .0 106 JAMSEM IDV5 /y930 33242. 4 190 0 . GO 1 0 .0 0 9 4 JAMSEM IBV^S //9 3 0 33 243. 3990 r, . 007 0 .0 13 1 LUEO''U ECKA A .A . 17.1 , P. 6 0 33 243. 4 0 3 0 (7.0 0 4 0 .0 1 7 1 SLO'.M K A .A . 17.1 , P. 60 3 3 236. 6435 0 .0 07 0 .0 0 9 6 STOKES VP.R. STAR 1 6 .1 , P. 52 33287. 84 16 0 .0 97 0 .0 1 2 4 STOKES T'AP. STAR 1 6 .1 , P. 52 33293. 5987 0 . 007 0 .0 1 2 2 STOKES RA.P. STAR 1 6 .1 , P . 52 33299. 79 3 2 0 .007 0 .0 1 15 RUIZ . STAR 1 6 .1 , P. 52 33304. 5727 0 .0 0 7 0 .0 1 0 0 RUI Z VAR.STAR 1 6 .1 , P. 52 333 10. 5 5 49 0 . 007 0 .0 1 5 9 STOKES VAR.STAR 1 6 .1 , P. 52 3 3 3 11. 7423 0 .0 0 7 G .0031 RUI Z '/AP . STAR 1 6 .1 , P. 52 33 315. 3260 0 .001 9 .0 0 6 0 ORLOVIUS AAJ 233, P. 69 33402. 5779 0 .0 07 0 . G 9 4 5 STOKES 1 6 .1 , P. 53 38 4 15. 7266 3 .00 7 0 .0 0 5 4 STOKES 1 6 .1 , P . 53 33499. 403 0 0 .0 1 0 0 . 0 1.42 V^OLLSTEIM AP 23 9// 4, P . 19 1 335 11. 3500 0 .0 10 0 .0 0 3 7 '^OLLSTEI M AP 239 #4, P. 19 1 335 11. 3560 0 .0 1 0 0 .0 1 4 7 SCIU'.^EMKE AP 28 9 4, P. 19 1 33 59 1 . 4 /13 0 0 . 095 0.0198 ELI M . A . 17.1 , P. 60 33 64 0. 4 3 39 0 .0 0 1 0 .0 0 5 4 MAK IBVS 12 33652. 3860 0 . O'G 1 0 .0 0 5 0 KRAUS SEP, JOB G El AM 23 9/^4, P. 19 1 33652. 3390 c.0 10 0.00 3 0 ORLOVIUS /'Li 2 3 9 // 4 , P. 19 1 33670. 3 150 0 .0 0 1 0 .0 0 5 2 : POHL PAJ 289#4, P. 19 1 33670. 3200 0 . 007 0 .0 1 0 2 SAMOJLO A.A. 17.1 , P . 60 33676. 29 1 5 0.00 1 0.9054 SURKOVA IBVS 27, #501 33 69 1 . 3279 0 .00 1 0 .0 0 3 6 BURKE,ROLLAMD AJ 7 1, P. 33 33696. 6093 0 .00 1 0.00/10 BURKE,ROLLAMD A J 7 1, P . 38 337 14. 5385 0 .0 0 1 0 .0 0 4 4 BURKE,ROLLAMD AJ 7 1, P . 38 38 74 5. 6 1 53 0 . 00 1 0 .0 0 4 6 BURKE,ROLLAMD AJ 71, P. 33 33329. 28 13 0 .0 0 1 0 .0 0 3 5 KRI5TEMS0M ASTROM.AP. 3 0, P .26 1 333 42. 4290 0 .0 02 0 .9029 SZAFRAMIEC A .A . 1 6, P . 153 339 34. 4 67 0 0 . 002 0.0065 SZAFRAMIEC A.A. 16, P. 153 33977 . 48 9 0 0 . 0 03 - 0 . 0 0 0 5 TRUSKOETSKI A. Pi. 1 7 .1 , P. 60 33977. 49 1 5 0 .0 3 3 0 .0 0 2 0 MIKULSKX, KREHO A.A. 17.1, P. 69 33977 . 4930 0 .0 0 3 0 .0 0 3 5 S/\MOJLO, BAR SKI A.A. 17.1, P. 60 39 003. 5638 0 .0 0 1 0 .0 9 2 7 BURKE,ROLLAMD AJ 7 1, P. 33 39025. 3008 0 .0 0 1 0 .0 0 1 2 M IM T I, JOM IBVS #148 39032. 47 3 0 0 .0 0 1 0 .0 0 19 M IM T I, JOM IBVS #143 :{%LI OCKIJTRI C 0-C 85 J U L I AM DATTI + /- RESIDUAL 0D5ERRER REFEREMCE 39046. 3 1 66 0 . 2 0 1 0 .0 0 2 5 UECK/iTHORM P. GOODSELL OBS. #15 39050. 4 180 0.010 0.0 13 1 KIZILIRHAK AM 289/'4, P. 19 1 39052. 7928 0 .0 0 1 0 .0 9 2 4 STOKES VAR.STAR 16, P. 39 39057. 5737 0 .0 0 1 0 .0 0 2 3 HECKATHGRN P. GOODSELL 0BS./«15 39062. 3562 0 .0 0 1 0 .0 0 3 3 M IM T I, DRAGUSIM IBVS (t 148 39063. 33 16 0 . 0 0 1 0 .0 0 2 9 M IM T I, DRAGUSIM IBVS 148 39 14 1 . 2450 0 .0 1 0 0 .0 0 6 0 LEITMEIRE AM 23 9//4, P. 19 1 39246. 42 00 0 .0 0 1 - 0 . 0 0 1 2 SCHUBERT,GRODAM AiM 29 2, P. 13 5 39 327 . 6970 0 . C 0 1 - 0 . 0 0 1 3 STOKES IBVS #180 39362. 3 68 0 0 .0 0 1 0 .0 0 7 4 SCHUBERT,GRODAM AM 29 2, P. 13 5 39436. 47 2 0 0 .0 0 1 0 .0 0 5 7 SCHUBERT,GROBAM AM 29 2, P. 13 5 395 1 I . 7690 0 .0 0 1 0 .0 0 1 9 STOKES IBVS #22 1 39 694. 64 60 0 .0 1 0 0.0053 BALDUIM IBVS #79 5 3970 1 . 8 100 0 .0 1 0 - 0 . 0 0 2 2 BALD'UM IBVS #79 5 39737. 6737 0 .0 0 1 0 .0 0 4 0 STOKES IBVS #24 7 39737 . 67 50 0 .0 1 0 0 .0 0 5 3 BALDUIM IBVS #795 39 7 49. 6255 O' . 0 0 1 0 .0 0 3 3 STOKES IBVS #247 39763. 7520 0 .003 0 .0 0 5 7 S/lMMER I DUS #79 5 39 7 7 4. 7230 0 .0 0 8 0 .0 6 0 5 SAMMER I BUS #795 39734. 28 7 6 0 .0 0 2 0 . 0030 MIMTI IBVS 2 7, #32 2 39785. 4834 0 .0 0 1 0.0036 EMDRES,GORTZ AM 291, P. Ill 39793. 3490 0. 0 03 0 .0 0 2 4 SAMMER IBVS #79 5 39803. 4 170 0 .0 0 1 0.0084 SCHUBERT,GROBAM AM 29 2, P. 13 5 39310. 5370 0 . 003 0 .0 0 6 9 BORTLE IBVS #79 5 398 17 . 7500 0 .0 1 0 - 0 . 0 0 1 6 COOK IBVS #795 39322. 54 5 0 0. 0 03 0 .0 1 2 4 SAMMER IBVS #79 5 39330. 3920 0 .0 1 0 - 0 . 0 0 7 4 CRAG G IBVS #79 5 39835 . 6730 0 .0 1 0 - 0 . 007/1 CRAG G IB,VS #79 5 39835. 6860 0 .0 1 0 0 .0 0 5 5 COOK IBVS #79 5 39845. 2470 0 .0 0 1 0 .0 0 4 6 SCHUBERT,GROBAM xGM 2 92 , P . 13 5 39347. 64 0 0 0. 007 0 .0 0 7 1 S''AM BERG I BUS #79 5 39356. 0050 0.010 0.0053 SAMMER IBVS #79 5 398 59 . 59 1 0 0 .0 10 0 . 0056 BALD'''IM IBVS #79 5 39860. 77 60 0.010 -0.0047 SAMMER IBVS #79 5 39860. 7 3 40 0 .0 1 0 0 .0 0 3 3 COOK ir:vs #.795 3 9 3 7 2. 7 l\ 0 0 0 .0 1 0 0 .0 0 6 3 COOK IBVS #79 5 39 8 7 7. 5 1/10 0. 00 1 - 0 .00 0 2 ? ? ? ? ? IBVS #23 5 39378. 7 120 0 .0 1 0 0 .0 0 2 5 COOK IB'..'S #79 5 39382. 29 9 0 0 .0 0 1 0 .0 0 3 3 SCHUBERT,GROBAM AM 29 2, P. 13 5 3938 4. 63 50 0 .0 1 0 - 0 . 3007 COOK IBVS #79 5 39 38 4. 63 9 0 0 . 0 1 rr. 0 .0 0 3 3 CRAG G IBVS #795 39 3 8 4 . 69 2 0 0 . 008 0 .0 0 6 3 BALDV'IM IBVS #79 5 39890. 6 6 5 0 0 .0 08 0 .0 0 3 0 LUCAS I BUS #79 5 39 39 0. 6690 0 .0 0 7 0 .6 0 7 0 BALD'.UM IBVS #79 5 39896. 647 9 0 . 008 0 .0 0 3 3 BALD''UM IBVS #79 5 39^02. 6050 0 .0 1 3 - 0 . 0095 DOBKOUSKI IBVS #795 39903. 58 50 0 . 008 - 0 .0053 THOMPSON IBVS #79 5 39908. 5980 0 . 0 08 0 . 0072 BORTLE IBVS #795 399 1 5 . 7 6 60 0 . 003 0 .0 0 3 7 BALDUIM IBVS #79 5 39^ 19 . 3 59 0 0 .0 0 1 0 .0 1 10 SCHUBERT,GROBAM AM 29 2, P. 13 5 39 9 4 5. 6420 0. 0 03 -0.0016 SAMMER IBVS #79 5 39945. 6400 0 . 0 07 0 .0 0 2 4 THOIIPSON IBVS #79 5 86 HELI OCrrJTP.I c 0-C JTTLIArj DATE + /- EES I DUAL oeseevee REFEREMC 39957 . 5320 0.010 -0.0141 DOBKO’-^SHI IBVS i*' 79 5 399 63.577 0 0 . 003 0.0047 EALOrJEH IBVS /?795 40 0 37.63 20 0 . 003 0.0040 EALOMEK IBVS //79 5 40054.4 163 0.001 0.0052 K1ZILIEMAK,KURU IBVS 27, iff 400 5 6.3070 0.003 0.0050 EALD^UN IBVS if 19 5 4003 0.7070 0 . 003 - 0.0000 EALOMEK IBVS #795 40034.3022 0.002 0. 009 4 SURKOVA IBVS #394 4 0 03 5.45 6 5 0 . 002 ?. 003 5 SKATOVA IBVS #39 4 4003 5.4973 0 . 0 02 0.0093 SUEKOV^A I BVS #394 4 0 097.4453 0.002 0.0052 SURKOVA IBVS #394 40093.639 0 0 . 003 0.0032 BORTLE IBVS #79 5 40 09 3.64 10 0 . 0 03 0.0052 EALOMEK IBVS #79 5 40093.6490 0.010 0.0 132 HAZEL IBVS #795 40116.5750 0.010 0.0104 heasley IBVS #79 5 4 0 1 17 .7640 0.010 0.0042 MOLTHEMIUS IBVS #79 5 40 12 1.3 5 64 0.002 0.3 103 SURKOVA I BVS #394 40 127 .3272 0.001 0.0053 I DAMOGLU IBVS 27, # 40 1 29 .7 1 50 0 . 003 0.0026 S'-fAMEERG I ERS #795 40 1 29 .7200 0 . 0 03 0.0076 EALD'UU IBVS #79 5 40 139 .23 73 0 . 002 0.0134 SURKOVA IBVS #39 4 40 147.6470 0.010 0.0059 HAZEL IBVS #79 5 40147.649 0 0.010 0.0079 EALDUIM IBVS #79 5 ^10 15 1.2413 0.002 0.0149 SURKOVA I BVS #39 4 40 1 73. 7 20 0 0 . 003 0 . 002 3 MOLTHEMIUS I BVS #795 40 173.7220 0 . 003 0.0043 BALDUIM IBVS # 79 5 40 13 2. 3089 0.001 0.0055 ROSSATI ASTROM.AP. 30, P.261 40 13 4.69 9 0 0 . 003 0.005 1 S'-'AMBER G IBVS #79 5 40 189 . 430 1 0.001 0. 005 1 ROSSATI ASTROM.AP. 30, P.261 40196.6523 0.001 0.00 53 LANDIS I BVS #79 5 40 19 6 . 6540 0. 0 03 0 . 0075 BORTLE IBVS #795 40202.6291 0 . 0 0 ! 0 . 0064 LAMDI S IBVS #79 5 40203.6055 0.001 0.0065 LAMDIS I BVS #79 5 40 2 03. 609 0 0 . 003 0.0100 BORTLE I BVS #795 4 0220.5500 0.310 -0.0015 SI MMQMS I BVS #79 5 40220.5570 0 . 0 03 0.0055 BORTLE IBVS #795 ^10 22 7 .7320 0 . 0 03 0.009 0 CRAG G I BVS #79 5 ^102 33. 7120 0. 303 0.0127 SHEETS IR I BVS #79 5 40245.6530 ^ . 303 0.0062 EALD'-'IM IBVS #79 5 4 0 27 0.7600 0 . 007 0.0079 BALD'-'IM IBVS #79 5 40 27 4.3 37 5 0.001 -0.0003 SURKOVA IBVS 27, # 4023 2.7 100 0.010 0.00 54 CRAG G IBVS #79 5 4029 4. 6640 3 . 003 0.0069 BALDUIM IBVS #79 5 403 13 . 563 0 0.010 0 .0059 BORTLE I BVS #795 4 0429.7070 0.007 -0.0136 SUAMDERG IBVS #79 5 4 0 429.7 22 0 0 .008 0.0014 DALOMEK IBVS #79 5 /10 4 3 6 . 3 9 7 0 0 . 003 0•0049 BALDWIN IBVS #79 5 404 4 2.3740 0.010 0.0057 BALD'v'IM IBVS #795 40 4 4 7^6500 0 . 003 0.0006 EALOMEK IBVS #79 5 40453.6240 0.007 -0.0016 EALOMEK I BVS #79 5 404 53. 629 0 0.010 0.0034 HAZEL I BVS #79 5 4 0/153 . 6330 0 . 007 0.0074 AMDERSON IBVS #795 /10 /| 5 4 . 3 2 0 0 0 .003 -0.0009 EALOMEK IBVS # 79 5 87 H^LI OCEMT’^I C 0-C JULI AM DATE + /- REG I DUAL 013 s EH VER —’ TT-FZREMCTT 40454 3220 C7.010 0.0011 S^’EETSI E IDVS ffl9 5 40 4 66 7760 0 . 0 03 0 0 02 6 BALDRIM IBVS 4 0 5 0 2 63 50 0 . 0 03 0 0040 GRTi'EIM IBVS 405 19 3669 0 .00 1 0 0024 DERIRCAM IBVS 27, if 52 Q 40533 7 130 0 .003 0 0055 S'^EETSIR I DVS Ü795 40533 7 1 3G 0 . 0 03 0 0055 GREEM I EUS i>19 5 40539 63 7 0 0 .0 10 0 00 3 3 BALD''IN IBVS ni9 5 40 5 57 6 1 39 n.00 1 0 0 0 1/1 LAMDIS IBVS // 79 5 4^5 57 6 14 0 0 • 010 0 OC 1 5 G'^'AMDERG IBVS H195 40 557 6 1 50 0 .010 0 0025 BALD''I M IDVS /'79 5 4 0746 4 6 07 0 .00 1 -0 0 0 16 ICI ZI LI RM AK IBVS 2 7, // 5 3 0 40753 4 125 0 .00 1 -0 0 02 3 DE*'I I RCAM I EVS 2 7, // 5 3 0 40739 49 00 r, .^0 1 -0 0 0 1 /i gtjrkova IBVS 2 7, f 5 01 403 19 3702 0 .00 1 — 0 0025 DElI I RCAM I BVS 27, f 530 4 10 3 3 5 193 0 .00 1 -0 004 1 HRRCZEG, FRIEBOE AGTRor'. AP. 3 0 26 1 4 1 14 4 47 63 0 . 0 0.1 -0 0052 HERCZ OG,FRIEBOE ASTRon.AP. 20 P. 26 1 4 1162 4 0 60 Ÿj. 00 1 -0 0 0 4 0 IBAMOGLR I BVS 27, 647 4 113 1 5297 n.00 1 _ n 0 0 4 2 BOZKURT,IBAMOGL AGTROM . AP . 3 0 P.26 1 4 119 9 4 533' 0 .00 1 -0 0 04 5 GEMG CMCA IBVS 2 7, Z' 64 7 4 13 3 3 3257 0 .00 1 -0 0053 GORZ f T'T T c /•' 9 3 7 /I 1 3 5 3 A4 5G .010 - 0 0 C 5 3 KLIMEK I BVS if 621 /î 1 5 1 1 4 2 0 6 Z .00 1 -0 0 0 29 AKir’CI IBVS /^9 37 4 15 42 49 3 0 0 . O'04 -0 002 1 CAD AM IBVS ^740 4 1 560 4 2 /I 0 0 .00 1 - 0 0 0 49 ELERSBERGER IB^'S 9 3 7 4 15 6 0 43 3 0 0 . 00'3 0 G 0 n 1 Z ALTTSKI IBVS fX 74 0 4 1566 40 22 0 .00 1 -0 0029 ECERSEERGER IBVS /'9 3 7 4 15 6 6 4 0 4.1 0 .001 - 0 00 10 U M R 1 3 E C K ASTROM. /:P. 2 0 P. 26 1 4 1 57 3 3530 0 .00 4 0' 0 00 3 5EDZIELQMSKI I BVS :/ 7 /I C 4 1 53 4 3 3 2 6 0 .00 1 _ 0 OC 1 3 iE CI M CI I B S / 9 9 3 7 4 159 7 43 0 1 0 . 00 1 - fT; 00 1 6 DMRBECK /lSTROM.AP. 3 0 P. 26 1 4 1 6 09 4 3 29 0 . 00 1 - 0 0 0 1 3 DENREE CK OM.AP. 30 P. 26 1 4 17 03 6392 0 . (:) 0 1 -0 0009 CHAMBLI5S I B"S 43.33 4 17 2 6 5 63 0 0.00 1 _ f7. 0 0 09 CHAAIBLI SS IBVS 433 3 4 17 3 2 5 /] 4 2 r?.00 1 — 0' 0009 CHAMBLISG IB^'5 43 3 3 4 1 3 60 4 37 5 S.00 1 0 0 0 0 /I HMCK I EVS 4937 4 19 2 1 3940 0 . 0 0 1 - 0 0 0 0 9 HOLZL IBS'S 4937 4 19 3 3 3 4 5 0 0 . 00 1 — 0 0025 BAYGUM IBVS a 9 21 4 1934 54 13 c . c J — 0 00 09 EDERSBERGER IB'/S 49 27 4 19 5 /; 3 5 6 1 0. 00 1 -0 0 0 59 MARGRAVE;, LUKES IB'..'S 4 10 19 /I 1 9 9 0 7 133 0 . 00 1 -G 0007 CHAMBLI5S IBVS 4.33 3 42094 7056 0 .00 1 — 0 0 0 0 9 CHAMBLIS S IBVS 433 3 42235 7330 0 . 0 04 -0 0 03 2 KROBUSEK IBVS 49 5 4 42235 74 3 0 0 . 0 04 -0 0 03 2 MALLA'ÏA IBVS 49 5 4 42265 6260 n. 0 04 - 0 00 1 5 KROBUSEK IBVS 4 9 54 42239 5303 0 . 00 1 -0 00 1 7 SC/"E I BVS 4 1053 4 2 3 0 0 23 3 4 0 .001 -0 00 14 I5/HM/ER IBVS 4 1053 42303 3 7 54 0 .00 1 - 0 000 1 KARLE,UAUCHER PASP 8 7, P. 9 09 423 1 4 6350 0 .004 0 0022 KROBUSEK IBVS 4954 42325 33 8 9 n . 00 1 -0 00 12 ER/BY IBVS 4 1053 42339 7265 0 .00 1 -0 0066 DOOLITTLE,EVAMS IBVS 4 10 19 Sà'VjA ■ - 0 ’0b- 0 • 09 - 0 "08- 0 02 c - 20 - ( 0 1 n mXI O') M O > r ço o > —<[ (/) - : i 0 ’ 8 -aoiaiJd ‘cjavzcd 88 89 u' J —0O0L02 Y OF 123 OL'OCF^'i-.T'l 995 OF ' Z J ■. 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STAP 16 . 1 , P. 4 0 33737 •^430 0 G 1 0 0.0155 ppiirj AH 231(3), P. 114 3 3 3 3 3 3 6 4 0 0 0 1 0 0.0162 DOMKZ AH 231(3), P. 114 3 4 0 7 0 3340 0 00 1 2.0156 POHL /ri 2 3 2, P. 235 3 4 1 C zi 43 1 0 0 GO 1 0.0124 PO^.-: /iH 23 2, P. 23 5 342 69 42 5C 0 0 1 0.0122 E OPH AH 23 2, P. 23 6 3 4 /14 6 3250 e 00 1 0.0155 POP H 6/1 23 2, P. 235 3 4'=^7 5 4 1^2 0 0 02 0 .0 139 ”POBLZ'-^SKI '^pAH 1/2 sur. 1 , F . 3 6 3 /J -7 I c; O': 9 0 0 0 0. 3 0.0137 ^’P0Î3LE’-55KI "''AHI/-. 2UP. 1 , P . 3 5 3496 1 47 3 0 0 C.0166 ''POLLCGKI UPAHI/i 2 UP. 1 , P. 36 34997 3 1 60 0 0 0 7 0.0172 ''POPLZ'^SKI ^ 02 D.2 T'P/.HI 2 UP. 1, P. 3 5 3^199 33 1 5' 0/7 1 0.0159 ''^OLLP'^GKI '2.//IIA sur. 1, P. 36 3 5 2 4 2 36 19 ro 0 02 0.0173 HAPK5 UPAHI A SUP. 1 , P . 3 6 3 /I 3 2 /i 0 2 4 7r 1 0.0134 LPHC'^ZL, LPOOLI AST. ITa l . 3G , P. 2 0 2 c: c; A, f?, 20-7 0 r/ 0 G 1 0.0165 C ' fp 2 T PP AH 236, F. 1 6 1 35775 4393 0 00 1 0.0147 LPHOr:''PL, PP03LI /.ST. ITAL. 3 0, P. 3^379 4 27 0 0 0 G 1 0.0153 PH’DOLPil AH 23 5, P. 161 3^933 4 I 6 O' 0 00 1 0.0177 DOP^ /iH 23 5, P. 1 6 1 3627 4 4 9 0 0 0 0 1 0 .0 1 6 6 PH^DOLPH //I 23 5, P. 1 6 1 36 166 23 3 0 0- 00 1 0.0113 DPAUHP a:j 2K5, P . 1 6 1 3 6 3 0 3 ^2 10 0 00 1 0 .01^3 LPAPHE AH 2 3 6, P . 2 1 2 3 6 4 5 4 3 420 e 0 04 0.0160 H6GI2Z/1LEK, ELI H /i. i t.. 17 . 1 , P. 60 367 12 5200 c G (D 1 0.0205 PT'DOLPH A’/ 2 3 6, P. 2 1 C 36323 6663 0 007 ,0 . 0 03 3 E'JGELKEHEIP "AP.STAP 16. 1 , P. 3 7 0 0 0 ‘=6 50 0 0 0 1 0.0103 H EH DE ,GJ 23 3, P. 1 63 37379 4^=00 0 0 0 1 G . 0 0 9 /I HEHDE i/1 233, P. 1 63 3 7 2 r?/ 2 5 530 0 0 0 1 G . 0 0 1 9 PT'DOLPH AH 233, P. 1 63 37317 2 0 3 0 n 0 0 1 0.0031 POHL /ri 233, P. 69 3 7 4 c 3 3 62 0 0 0 0 1 0.009 2 H EH DE AH 233, P. 1 63 37^74 23 0 0 0 'j'O 1 0.0063 FE'^.HAHDEG AH 233, F. 1 69 37623 23 3 0 0 00 1 G.0 0 96 i l EH DE S /A! 2 3 8, P. 1 69 3 7 4 6 216 0 0 0 1 0.0071 //] 238, P. 1 69 3 7 703 4 5 3 0 2 00 1 ^.01 14 3CHHPEPT /M 2 3 3, P . 1 69 379 1 1 3 4 6 0 0 00 1 0.0129 2CHPBEPT AH 28 8, P. 1 69 3 3 0 0 3 37 90 0 0 0 1 0.0113 FEPHAHDES //î 233, P. 1 69 330^2 3 7 3 0 0 0 0 1 0 .0 0 06 2 CHHEEPT,EPOEAH AH 29 2, P. 1 3 5 33039 4 23 0 0 00 1 0.0029 J/G 12 EH lEVS A9 30 33242 4 190 0 00 1 0 .0 0 2 2 JAH2EH lEUS 69 32 33 3 1 5 3260 0 00 1 - 0 .0009 OPLO'UUS AH 23 3, P. 69 33 4 1 5 7 2 66 0 007 - 0 . 0 0 11 STOKES \UiP . 5 T AP 16 . 1 , P . 53 33^40 4 3 39 G 0 3 1 -0.0004 ‘IAK I EVS // 1 1 2 33676 29 1 ^ 0 00 1 - 0.0003 SUPKOVA I EVS 2 7, /y 50 1 337 I 4 5335 0 00 1 -0.0012 BTJPKE, POLLAHD AJ 7 1, P. 3 3 33329 23 13 G 0 0 1 -0.0017 KPISTEHS OH ASTPOH.AP. 30, P. 26 1 33934 467 0 G 0 02 0.0017 SEAFPAMI EC A. A. 16, P. 153 39 046 3 166 0 O'O 1 -0.0020 HECKATHOPH P. GOODSELL 0E3 . # 1 5 91 HF.LI QCE^JT^-I C 0-C J:;LI A:7 DATF + / - SI D^V.L oun '^’T’TT*4 — ^ f’TT'TP” ^ ^ . V W - J 392/46. 4 2 0 0 0 00 1 -0.0050 sciiuBEP.T^ nnoDA:i AU 29 2, P. 155 39227. 69-70 0 0 0 1 -0.0049 STQXES I B"S ^130 39/43 6 . /I 7 2 0 0 0 0 1 0.302 6 SCHUBZPT, 0 2 0 2 A'} AU 29 2, P. 13 5 39 5 I 1 . 7690 0 0 0 1 - 0.0010 STOKES I B'/S (^•22 1 3977/4. 7230 0 0 03 -0.0016 s a :j:ie 38 IBUS A 79 5 393/45. 247 0 0 0 0 1 0 .0 0 23 SCHIJDEPT^ OPOB/.M AU 29 2, P. 13 5 /t02 '^/î . 4 1 63 0 00 1 0.0042 ; TWCAS.; PERIOD- .42332800 > - < Q CO _J < Z3 Q I— I CO LJ cr u o - 70.0-60.0-00.0-40.0-30.0- 20. 0-10.0 .0 YEARS CHROUOLOIY OF 33 335F F AT I QMS OF T 'T fu 93 TCALC = JD 4 10 7 1.3000 + F * 1.42332300 HFLIOCFMTFIC 0-C JFLI AN DATF + /- P-FS I DUAL OESFPVEP REFERENCE 19319.3792 0.010 0.069 3 ZINNER AN 4 679, P . 45 3413 3.4^7 0 0 .00 1 0.0255 PQHL AN 23 2 P. 235 3 42 53.29 00 0.001 0.0133 roiiL AN 23 2 P. 23 5 3 4 4 5 5.4170 0.001 0.0301 POHL AN 23 2 P. 235 34005.3930 0.001 0.0366 PQHL AN 23 2 P. 235 3 5332.4000 0.001 0.0 197 RUDOLPH, JAHN a: J 2 3 5 P . 1 63 3 544 2. 3 3 00 0.00 1 0.0134 POHL AN 23 5 F. 1 63 3 59 59 . 4 44 0 0.001 0.0277 RUDOLPH AN 23 5 P. 1 63 36105.57 0 0 0.001 0.0359 RUDOLPH AN 23 5 P. 163 36 166.5390 0.00 1 0.0151 RUDOLPH,BRAUNE, AN 23 5 F. 1 63 36296.5120 0.00 1 0.0103 RUDOLPH AN 236 P. 2 1 0 36306. 5 1 10 0.001 0.9110 :ERAUNE AN 23 6, P. 2 1 0 3 63 49. 23 60 0.00 1 0.0213 ERAUNE AN 23 6, P. 2 1 0 363 59 . 29 50 0.00 1 0.0320 ERAUNE AN 23 6 P. 2 1 0 3 7 53 3.4 66 0 0.001 0.0407 FERNANDEZ AN 28 3 P. 1 69 3 7 69 6 . 29 5 9 0.00 1 0.0313 FERNANDES AN 23 3 P. 1 69 379 03.39 00 0.901 0.0193 KIZILIRMAK AN 23 3 P. 69 37903.3930 0.001 0.0273 FERNANDES AN 238 P. I 69 37923.3330 0.001 0.0207 ERAUNE AN 233 P. 1 69 379 33.3340 0.001 0.0134 MASUCH AN 23 8 P. 1 69 3 3 59 0.4 340 0.003 0.0375 FLIN A.A. 17, P. 61 33740.33 50 0.001 9.0141 KRAUSSER AN 239#4, P. 1 33753.2 3 70 0.001 0.0111 POHL AN 239 6/1 P. 1 9 33 3 3 0.3630 0.09 1 0 . 007/1 KRAUSSER AN 239^4 P .19 1 3397 7 .43 1 7 0.010 0 .0033 KIZILI RMAK AN 239 #4 P.19 1 4010/1.4320 0.001 0.9073 IEAN00LU,OUDUR IBUS #456 40204.4 133 0.001 0.0059 E lCKEL IBUS #456 4 0 5 3 4 . 3 5 6 0 0.001 0.0051 DEM IRI CAN lEVS #530 4 0 7 5 1.4610 9.001 0.0042 ENDRES lE^S #530 4 09 04.29 3 4 0.001 0.0055 KARACAN ISO'S #64 7 4 99 64.23 2 0 9.00 1 0.00 /14 M EI E'R IDVS #647 41201.33 42 0.001 0.004 1 HOLZL lEUS #647 4 16 7 1.3000 0.001 0.0000 DEM IRCAN IBUS #937 41933.3395 0.001 0.0007 PATKOS lEUS #1065 /I 199 1.24 5 5 0.00 1 0.0000 PATKOS lEVS #1065 42003. 33 50 0.001 -0.0004 PATKOS lEUS #1065 42265.4322 0.00 1 - 0.0022 IEANOGLU,GULMEN IBUS #1053 42265.4336 0.00 1 -0.0003 IBANOGLU,GULMEN IBUS #10 5 3 0-C RESIDUALS^. DAYS) X X n n T1 1] f'l "in I I /J H- 4 o o X LJ X L/V.J L-j s .' ( LO -P:* Ciro'TOLo9Y OF -3 JDEFFJ'ATI or’3 OF KXCEP 9 TCALC = JD 4 0 520.42 50 + E ^ 2. 3 3 7 3 3 5 2 0 H^LI OC'2' J'^^ I C 0-C Jf'LI Arj DAT0 -r / - 22 s I DVTAL 0T^ q TTT? T rrr'^ EEFEEEUCE 1/49 3 1 4000 0.010 0.1193 LAULOV FAE.STAR 12, P2 1 I S2-] 1 3500 2.010 0. 120 1 LA^TEo'T ttaE. STAR 12, P2 1 17 196 1 9 00 0.010 0.0320 LAT:ro^7 Ttar . STAR 12, P2 1 192^< 4 100 0.010 0.0=97 LATTE 0^^ FAR. STAR 12, P2 1 25 124 47 00 0.010 0.0710 L/^tj.eqv F/iP . STAR 12, P2 I 2^13 1 = 0 0 0 0.010 C.039O L/J'EO'T far .STAR 12, P2 1 2 5 4 4 2 36 = 0 0.01 0 0.03 3 4 LALEOV t taP . STiAR 12, P2 1 2 = 3 5 1 4 0= 0 0.010 0.0947 FEES A /V J 6 7 P. 7 2 = 3 =3 4 170 0.010 0.0947 AJ 6 7, P. 7 2 3 =7 4 39 3 0; 0.010 0.0922 LAUROV TTAE .STh R 12, P2 1 23 =9 = 43 3 0 0.010 0.09 12 LaUP.O^' TTAE. STAR 12, P2 1 23 6 27 143 0 0.0 1 0.1195 LAUF-OV TTAE .STAR 12, P2 1 23 3 1 2 4690 C . 0 1 0 0.0923 LAFPOF ’Ti\E . STiiE 12, P2 1 23922 3320 0.010 7.1006 LAPPOF T TAT'.. S T AE 12, P2 1 n T -7 >7 c 3 3 90 0 .010 0. 19 2 9 LAUFOF TTAE. STAR 12, P2 1 3 2 3 1 3 10 0 0 0 .010 0.142 1 LATTpQTT TTAE .STAR 12, P2 1 3 2=39 2230 0.010 0.1393 lattrot; TTAE . STAR 12, P2 1 3'^603 2 2 9 0 0 . r-i 2 0 0.1162 : L/iUROF FAR.STAR 12, P. 2 1 3 2 6 10 2 500 0.020 0.12=3 : L/iFRQTT TTAE. STAR 12, P . 306 17 2 3 40 ^.010 0. 14 7 2 LAt.tr Qtt \Ui71 . S T ^\R 12, P2 1 3 2 2 5 9 3 70 0 0 .010 0.0974 PPE3 A AJ 67,P. 7 3 2 2 0 4 23 =0 0.010 0.297 6 FEE 5 A AJ 67,P. 7 32232 3300 0.010 0.0946 FEE SA AJ 67, P. 7 326 1 2 09 00 0.010 -1.13 10 F EE SA AJ 6 7, P. 7 329 54 56 1 0 0.010 0 . 0390 FEES A AJ 6 7, ? . 7 33099 4 6 4 0 0.010 0.0773 FEES A AJ 6 7, P. 7 33 134 = 100 0 .010 0.0632 FEES A AJ 67, P. 7 3 3 15 5 = 5 = 0 0.010 0.0722 FEE SA /i J 6 7, P. 7 3 3 445 426 0 0.010 0.1136 LAUEO^' t.’AE . STAR 12, P2 1 33 = 37 970 0 0.010 0.08 32 LAFROF TTAE . STAR 12, P2 1 33339 49 4 0 0.010 0.0330 LATJEOV TTAE. STAR 12, P2 1 34039 Of 3 0 0.010 0.332 5 LAUEOF FAE. STAR 12, P2 1 3404 1 4 150 0.010 0.0322 L AT TR OF FAR. STAR 12, P2 1 3 4 0 6 0 1140 0.01 0 3.0325 LAFEO'^ FAE. STAR 12, P2 1 3406 1 3020 0.001 - 1 . 0663 LAUEOF AJ 67, P. 7 3 4 0 6 2 45 10 0.010 0.33 2 2 LATtEQ\t FAE.STAR 12, P2 1 34033 1 520 0.010 0.332 5 LAUEOV FAR.STAR 12, P2 1 3/1337 3370 0.010 0 .073 6 LAUEOF t;aR. STAR 12, P2 1 34394 3 49 0 0.010 0.073 6 LAUEOF FAE.STAR 12, P2 1 3 4/157 4 5=0 0.210 0.37 65 LAUEOF TTAE. STAR 12, P2 1 3 4 5 4 3 92 10 0.^03 0.061 1 :(OCH, KOCH AJ 6 7, P. 7 34623 30 =0 0.001 0.06=7 FEE SA AJ 6 7, P. 7 3 4 6 3 0 4 1 50 0.001 0 .0737 FEE SA AJ 67, P. 7 3 4763 3 190 0.010 0.0749 LAUEOF far .STAR 12, P2 1 34903 33 30 0.003 0.0735 KOCH, KOCH AJ 67, P. 7 349 49 4 63 0 0.001 - 1 .0332 FEES A AJ 67, P. 7 34933 3 = 00 0.010 0.07 1 1 LAUEOF FAR.STAR 12, P2 1 3 5 2 4 0 4 = 2 0 0 . 006 0.0662 KOEDYLET'TSKI SAC 23, P. 133 96 H^Li ocEirni c 0-C J’^LIA'I date + /- DE S I DUAL OBSEPU'EP. REEEREMCE 3S247. 4 63 0 00 1 0702 FRESA J 67, P. 7 35275 . 5 100 00 1 0642 FPESA AJ 6 7, P . 7 3623 1 . 4 59 e 0 0 1 043 1 RUDOLPH AM 23 6, P 2 1 0 363C9. 53 10 00 1 0330 Rî'DOLPH AM 2 8 6, P 2 1 0 3^460. 5 4 4 0 0 0 1 0 69 2 DORR AM 23 6, P 2 1 0 37 5/17 . 3340 006 0434 KUBICA A. A. 17, . 6 1 3*756 1 . 42 10 0 0 1 0 6 14 : POHL AM 233, P 70 3772 1. 3 49 0 00 1 0506 3PAUME AM 23 3, F 1 7 0 3 7 7 9 0. 45 10 0 0 1 0 3 2 5 DUEBALL AM 23 3, P 1 70 37935. 4 0 0 0 00 1 0667 POHL AM 233, . 70 37936 . 73 0 0 0.010 0 2 5 4 :AMGIOME PA3P 75, . 407 3 9 0E7 . 2 7 4 0 0.010 0 193 : Kl 0ILIRMAK AM 289^4, P. 192 39057 . 2300 0.010 0253 : Kl ZILIRMAK AM 239 44, P. 192 3932 1 . 5820 0 1 0 0 192 BALD'-'I M I BPS 4 79 5 /10 09 7 . 3730 00 1 0047 I RAM03LU I BUS 2 7, 445 6 /10 I 3 9 . /14 2 0 00 1 00 1 6 I DAM0GLU I BO'S 27, 4456 /10 2 3 7 . 6 170 0 07 0036 DORTLE IBVS 4795 40473. 6 6 00 0 1 0 0 193 HAZEL I BPS 4 79 5 4 0513. 4 190 0 0 1 0 0 5 0 BA5E1BACH, G 0R3 I BUS 27, 4 4 5 6 4 0 5 2 0. 4 2 60 0 0 1 0000 GUDUR IBUS 2 7, 4 530 97 SWCY G ; P'F_RIOD-~- 4 . R7284000 CO > - < o œ _j < 3 Q t-4 co LJ Œ U I O - 2 2 .5 YEARS CII'^OMOLOOY OF 5 6 OECELV'AT I O'JS OF S’^CYO 98 TCALC = J :: 4 3 454. 63 50 + E ^ 4.572 3/10 0 0 HELI OCErjT^.I C 0-C JTJLI AMDATE + /- EESI deal OBSERVER r T pT7^ ÎTMp T- 13 03 1 3220 0.010 -0.3423 SCHMELLER, H. AM 23 7 13456 3240 0.010 -0.3 136 SLO^^OCXOTOVA VAR.STAR 10. 1,P. 22 14 5 5 3 3 0 50 0.010 -0.3 142 SLOVQCKOTO^Yi VAR.STAR 10.1,P.22 14653 9 3 6 0 ^.001 -0.303 6 clovqckotova VAR.STAR 10 ^1(35)25 14736 7 3 2 0 0 .010 -0 . 3003 SLQV'OCKOTOVA VAR.STAR 10. 1,P. 22 1473 2 /-14 3 0 0.010 -0.3132 5L0"0C-C0T0VA FV^.R. STAR 10. 1,P.22 14 7 9 6 19 20 0 .010 -0 . 2373 SLOVOCKOTO^'A ”AR.STAR 10. 1,P. 22 1 43 0 5 3 13 0 0.010 -0.3074 SLGT/QCKOTGF'A vaR.STAR 10. 1,P. 22 14329 39 1 0 0.003 -0.3073 SLQVGCKGTGVA VAR.STAR 10. 1,P.22 143 14 46 1 0 0 . 0 08 -0.3101 SLOVGCYGTOVA VAR. STAR 10. 1,P. 22 14323 1320 0.010 -0.3 07 6 SLG‘'0CK0TG3Yn VAR.STAR 10. 1,P. 22 14332 7520 0 . 0 07 -0.3105 SLGVOCKGTG^'A VAR.STAR 10 . 1, P .22 14337 3 27 0 0 . 0 1 0 -0.3 03 3 5L0^-0CK0T05V. VAR.STAR 10. 1,P.22 1 43 4 6 4 7 0 0 0.010 -0.3 110 slg^^ockgtgfta FV.R. STAR 10. 1,P.2 2 14346 47 40 0 . 707 -0.3070 5Lovoc;:oToVii 'ViR. STAR 10. 1,P.22 1 43 5 5 6 2 40 O'. 0 1 0 -0.3027 SLOVOCYOTQVA VAR.STAR 10. 1,P.22 14 3 6 0 19 60 0.007 -0.3035 SLGVGCROTG^'^A VAR.STAR 10. 1 , P.22 14364 7 64 0 0.010 - 0 . 303/1 SLO^^OCKOTGF'A VAR . ST/iR 10. 1,P. 22 143 69 3460 0.010 -0.2992 SLOVCCEOTG^^A VAR. STAR 10. 1,P. 22 14373 4 3 50 . 0 0 3 -0.3059 SLGV-OCKGTOVA ’;ar . star 10. 1,P.22 14 9 0 1 3540 0.010 -0.301 1 slovqckotova VAR.STAR 10.1,P.22 14 9 19 6270 0 . 0 03 -0.3194 slovocicotgva VAR.STAR 10. 1,P.22 14923 73 70 0.001 -0.3051 SLOF^OCYGTOFa VAR.STAR 10 ^1(85)25 149 33 3 560 0.007 -0.3 09 0 SLOVOCKOTOVA VAR.STAR 10. 1,P.22 14933 3600 0.7 1 0 -0.3050 SLG90CKGT0VA vaR.STAR 10. 1,P. 22 14 9 4 2 5046 0 .010 -0.3066 SLO^^OCKOTOVA VAR.STAR 10. 1,P.22 1/19 4 7 03 5 0 0 . O' 1 0 -0.293 5 SLG'^OCKOTGVA VAR.STAR 1 0 . 1 , P.22 1^49 1 2 5 40 0 . 0 0 1 -0.297/1 SLGLOCYOTOVA ''AR. STAR 10 #1(85)25 16433 2 7 60 0.001 -EL. 23 0 5 SLOVOCKOTOVA ':AR. STAR 10 #1(85)25 17366 14 4 0 0.00 1 -0.2718 SLOVOCKOTOlYi "AR. STAR 10 #1(35)25 13 440 623 0 0.010 -0.4102 SLG'-'OCK OTO'L\ AM 23 7 13 6 19 09 3 0 0.00 1 -0.2760 SLOVOCKOTOVA vaR.STAR 10 #1(85)25 19 3 4 1- 6 0-3 0 0.001 -0.2 79 7 SLOVQCKOTCA VAR.STAR 10 #1(85)25 2 14 7 2 43 7 0 0.00 1 -0.3392 SLOVOCKOTOVA mar . STAR 10 #1(35)25 2399 6 62 3 0 0.00 1 — 0.4 103 SLOVOCKOTOVA VAR.STAR 10 #1 (85)25 249 6 1 43 2 0 0.001 - 0 . /i 2 1 1 SLO VOCiKOTOS'A mar .STAR 10 #1(85)25 23322 5 1 50 0.301 - 0 . /12 5 5 slof^ockotova VAR. STAR 10 #1(85)25 33^37 50 1 0 0.001 -0.3383 SLOVOCKOTOVA V/iR. STAR 10 #1(85)25 3 3 16 0 6 69 0 0 . 0 0 1 -0.3362 7 7 7 7 7 AJ 64C 1272) P. 2 59 3 4 15 7 6720 0.001 -0.3 123 SLOVOCKOTO’'A VAR.STAR 10 #1(85)25 3 4 633 47 60 0.010 -0 .23 49 3CHMELLER AM 28 7 35250 52 1 0 0.006 -0.272 1 SZCEEPAMO'-'SKA SAC 28, P . 103 35250 62 1 0 0.010 -0.272 1 SCHMELLER, H. AM 28 7 3529 6 2540 0.010 -0.267 5 SCHNELLER, H. AM 28 7 3 5 3 4 6 5600 0 . 009 -0.2627 SZCZEPAMO'^SKA SAC 28, P . 103 3 5 3 4 6 5 6 00 0.710 -0.26 27 SCHMELLER, H. AM 23 7 35963 9 1 60 0.010 -0 . 240 1 SCHMELLER AM 23 7 36402 9030 0.0 10 -0 . 2453 SCHMELLER AM 28 7 99 H^LI OCE^JT^I C 0-C JT'LI AN DATE + /- EE5 1DUAL OBSERVER REFEREUCE 3 6 A 3 0 . 3 /4 3 D 0.010 -0.2428 SCllUELLER AH 23 7 3 6^139 . /j9 6 0 0.010 -0.2355 SCHMELLER AM 28 7 36457.7950 0.010 -0.2278 5CHMELLER AM 28 7 36787 .0520 0.010 -0.2 153 SCMUELLER AM 23 7 39640.6690 0.008 -0.0505 HAZEL IBVS f795 39 7 0 4.7 08 0 0.007 -0.0312 HAZEL IBVS #79 5 4 0079 .7 I 50 0 . 008 0.0029 HAZEL IBVS #795 40 4 54.68 50 0.010 0.0000 HAZEL I CVS #79 5 100 UUiCYG; PERIOD- 3.31771000 1 .0FI-01 CO < Q CO < ZD D I—' CO I u o 0 E - 0 1 - 80. 0 60. 0 -4 0 . 0 YEARS CHP.OMOLO9Y OF 96 3DSEE6V.T I ONS OF G 101 TCALC = JD 36164.3150 + E * 3.3177 1000 :li oce ,MTPI C 0-C Jl LI AN DATE + /- D ESI DUAL OBSERVER .REFER 6722 53 10 0 . 00/1 - 0 .0034 DLAZKO AM 5270 6729 16 10 0.004 - 0 .0083 BLAZKO AM 5270 6752 3350 0.004 - 0 . 0033 BLTiZKO Arj 5270 6 9 3 1 2990 0 . 004 - 0 . 0 163 DU G AM > P. I G HT CO l-^T . P R 693 1 3 1/10 0.004 - 0 .0 0 13 GRAFF /■-M 5270 699 1 2720 0.004 0 . 003 1 GRAFF /iM 5270 699/4 59 00 0 .004 0 . 0034 GRAFF /AJ 5270 '7 0 6 /j 2/150 0.00 /I - 0 .0135 GRAFF /iM 5 2 70 7 107 33 5 0 C . 004 - 0 .0033 GRAFF AM 5270 7 117 3370 0.004 - 0 .00/(9 GRAFF AM 5270 7 130 6 030 0.004 - e. 0097 GRAFF AM 5270 7 1 3"7 2/450 0 . 00/1 “0 . 0032 GRAFF AM 5270 7 160 /16 /-1.0 0 . 0 0 4 - 0 .003 1 GRAFF /\M 5270 7/4 5 2 /|22 0 0.00 /I - 0 .003 6 GRAFF AM 5 2 7 0 7/1 62 33 0 0 0.004 - 0 . 0037 dlazko Ari 5 2 7 0 7/4 7 2 3320 0.004 - 0 . 0049 GRAFF AM 5273 7/495 •^5 10 0.00 /I - 0 . 0093 ELAZKO AM 5270 7502 1930 0.004 - 0 . 0033 GRAFF AM 5270 7327 3 23 0 0.004 - 0 . 0033 GRAFF /,M 5270 3 7 3 9 /13 0 0 0.010 0 .0123 MIJLAMD BAM 53 3 799 /i23C 0.010 0 . 0071 MIJLAMD BAM 58 3332 5930 0.010 - 0 . 0050 MIJLAiJD BAM 53 3 3 /4 2 5 6 7, 0 . 00/1 0 . 0089 GRAFF AM 5 2 7 0 3372 /I 1 7 0 0.004 0 . 0065 GRAFF /iM 5 2 7 0 3 3 3 2 33 10 0 .010 0 .017/1 MIJLAMD BAM 53 339 5 6 3-5 0 0.010 Q. 0005 MIJLAMD BAM 53 3935 /I /17 0 0.004 0 . 0000 GRAFF AM 5 2 7 0 3935 /i5 1 0 0.010 0 . 0040 MIJLAMD HAM 53 39/15 /1000 0.010 - 0 .000 1 MIJLAMD BAM 53 3 9/45 /10 60 0.004 0 .00 59 AM ‘^2 70 3953 67/10 0.010 0 . 003 1 MIJLAML B AM 53 3995 17 00 0.004 0 . 0042 GRAFF /R'J 5270 9 1/1/1 /163 0 0.010 0 .0053 MIJLAMD BAM 53 9 1 6/1 3760 0 . 0 1 0 0 .0070 MIJLAMD BAM 53 9237 3670 0.010 0 .0034 MIJ LAM D BAM 53 9260 59 10 0.010 0 .0034. MIJLAMD 3 AM 5 3 9 320 29 3 0 0.010 - 0 . 0033 MIJLAMD BAM 58 9363 /4 3 30 0.010 0 .001 4 MIJLAMD BAM 53 9 5 19 3660 0.010 0. 002 1 MIJLAMD BAM 53 9522 63 00 0.010 - 0 .0016 MIJLAMD BAM 5 3 9572 /1/150 0.010 - 3.0023 MIJLAMD DAN 5 3 9635 48 60 0.010 0 . 0022 MIJLAMD BAM 53 9 6 5 3 7 03 0 0 . C 1 0 0 . 0003 MIJLAMD DAM 58 9665 35/10 0.010 0 .0103 MIJLAMD BAN 53 9663 6630 0.010 0 .007 1 MIJLAMD BAN 58 9673 6 150 0.010 0 .0010 MIJLAMD BAM 58 9635 25 10 0.010 0 .0016 MIJLAMD BAM 58 9927 4390 0.010 - 0 . 0033 MIJLAMD BAM 53 HELI OCI^MT^I C 0-C 102 JTJLIAM DATE + / - RESIDUAL OBSERVER T) tTTT TTOEREUCE 1 9 9 r'. 0 . 6 1 9 0 0.010 - 0 . 000/1 NUL AND RAN 53 20010.3910 0.004 - 0.0040 GRAFF AN 5270 20023.65^0 0.010 - 0.00 19 NUL AND LAN 58 200S3.5 1 20 0.010 - 0.0032 NULAND BAN 53 20166.3010 0.004 - 0.0164 GRAFF AN 5270 202/42. 6 130 0.010 - 0.0067 NULAND BAM 53 20252.5740 0.010 - 0 .3038 NULAND DAN 53 20215.6200 0.010 0.0057 NULAND BAN 58 20325.5630 0.010 - 0.00/15 NULAND DAN 58 20335. 5 1 50 0.010 - 3.005 6 NULAND BAN 53 20355.4 160 0.010 - 0.0108 NULAND BAN 58 22100.5150 0.004 - 0.02 73 GRAFF AN 5270 22611.4350 0 . 00/1 - 0.0346 GRAFF AN 5270 2262 1 . 3330 0.004 - 0 . 03/18 GRAFF /iN 5270 2264 1 . 2920 0.004 - 0.0370 GRAFF AN 52 7 0 23 079 .2320 0 . 00/1 - 0.0343 GRAFF AM 5270 30 5 50.63 0 0 0.004 - 3 . 069 7 ^•mi TNEY i\J 55C 1 139) , 230 3 0 5 7 3.9110 0.004 - 3.0626 TNEY AJ 5 5(1139) , 230 30530.5640 0.004 - 0.045 1 VHITNEY AJ 55( 1 139) , 230 3 1930. 60 10 0.004 - 0.0817 ”HITNEY AJ 55(1189) , 230 32053. 6 100 0 . 0 04 - 0.0623 "Oil TNEY AJ 55(1139) , 230 32353.3400 0.00 4 - 0.0616 VHITNEY AJ 55(1139) ,230 32 4 31.3350 0 . 00/1 - 0.0562 "'THITNEY AJ 55( 1 189) , P.230 32736.3370 0. 0 04 - 0.049 2 I TNEY AJ 55(1139) ,230 3 23 0 6 .7 49 0 0.004 - 0.043 5 VU TNEY AJ 5 5 (1139) , 230 33058.3920 0 . 00/1 - 0.04 64 5Vi I TNEY AJ 55(1139) , 230 33151.7910 0.003 - 0.0/133 ''HI TE AN 62( 1254) , 372 33463.6560 0.303 - 0.643 1 ^'VU TE AN 62 (1254) , 372 33 506.79 00 0.003 - 0.0393 "HITE 62( 1254) , 372 33539 .7390 0.003 - 0.0330 NHITE AN 62(1254) ,372 33964.64 0 0 0 . 003 - 0.0333 '■'HI TNEY AN 62( 1 254) , 372 3 4 329.59 2 0 0 . 003 - 0.0294 "HITNEY AN 62 ( 1 254) , 372 3459 1 - 69 20 0 . 603 - 0.023 5 "HITNEY AN 62 (1254) ,373 34634.5390 0.003 - 0.0273 "HITNEY . AN 62(1254) , 373 350 19 .633 0 0 .003 - 0.0170 'TH I TNEY AN 62( 1254) , 373 35029.6390 0.303 - 0.0192 "HITNEY AM 6 2 (1254) , 373 35253.5650 0.003 - 0.0152 SZAFRANI EC SAC 28, P. 1 08 35263.5 190 0 .003 - 0.0143 SZAFRAiJI EC SAC 23, P . 1 03 3 5331.54 6 0 6 .003 - 0.0233 "HITNEY AN 62( 1 254) ,373 35341.5150 0 .007 - 0 .0079 SZAFRAMIEC SAC 28, P . 103 3 5 3 6 4.7340 0 . 003 - 0.0129 "HITNEY AM 62( 1254) , 373 35467.5320 0 .003 - 0.0139 ’■'H I TNEY AN 62 (1254) , 373 3 5636. 5600 0 . 003 - 3.0048 "HITNEY i^iN 62( 1254) ,373 3 5709 .73 30 0.303 - 0 .0057 VHITNEY AJ 6 2 (1254) , 374 3 5 726.3660 0 . 007 - 0.0113 SZAFRANIEC SAC 28, P . 1 03 3 53 02. 63 2 0 0 .603 - 0 .0026 "HITNEY AJ 62( 1 254) ,3 74 36011.6970 0 .303 - 0.0033 "HITNEY AJ 62(1254) , 374 36164. 3 1 50 0.007 0.0000 SZAFRANIEC SAC 30, P . 106 103 TWDRA i PERIOD- 2.80687000 i CO >- < Q _J < 3 O f-H CO LiJ 0 : u I o 1 . 37L__ - 80 . 0 6 4 - 3 2 .0 - 1 6 . 0 YEARS 104 CHRONOLOGY OF 127 OBSERVAT!ONS OF TVDRA TCALC = JD 4 1 503.4 655 + E * 2.80 68 7000 HELIOCEMTRIC 0-C JULIAN DATE + /- RESI DUAL OBSERVER REFERENCE 19ZJ9 • 7650 0.001 0.71 15 SLOVOCKOTOVA ’•'AR.STAR 10. 1C85)P32 M935 .2250 0.001 - 1.2 159 POHL IBVS #443 1 659 1 . 0/150 0.001 1.3576 SLOVOCKOTOVA VAR.STAR 10. 1 (S5)P32 18754.3350 0.001 1.1009 POHL IBVS #443 19 077 .6600 0.010 1.0858 NULAND BAN 58 19 09 4.43 50 0.0 10 1 . 069 6 NULAND BAN 58 19097.2390 0.016 1.0667 NULAND BAN 58 19 125.3610 0.010 1.0700 NULAND BAN 53 19 15 3.4230 0.010 1.0633 NULAND BAN 58 19 164. 6390 0.010 1.05 13 NULAND BAN 58 19 195. 5350 0.010 1.0723 NULAND BAN 58 19223.5700 0.010 1.0336 NULAND BAN 58 19237 .6 190 0.010 1.0532 NULAND BAN 53 19 240.4 53 0 0.010 1.0853 NULAND BAN 58 19 254.4540 0.010 1.0470 NULAND BAN 58 19 324.6260 0.001 1.0472 SLOVOCKOTOVA VAR.STAR 10. 19327 . 4270 0.010 1.0414 NULAND BAN 53 19327 .4347 0.006 1.049 1 LEHNERT AN 4 59 6 19338.6530 0.010 1.0449 NULAND BAN 53 19336. 3820 0.010 1 .052 1 NULAND BAN 53 19428.4640 0.010 1.0310 NULAND BAN 53 19 4/12. 53 10 0.010 1.0337 NULAND BAN 58 19 5 13.279 0 0.010 1.0262 NULAND BAN 53 19543.5330 0 .007 1.0234 POHL IBVS #443 19 543.5430 0.010 1 .0284 NULAND BAN 53 19 546 .3480 0.010 1 .0265 NULAND BAN 53 19 560.39 00 0.010 1 . 0342 NULAND BAN 58 19 6 16.499 0 0.010 1 . 0058 N U LAN D BAN 58 19653 . 5990 0.010 1 .0027 NULAND BAN 58 19661.4120 0.010 1 .0033 NULAND B/iN 53 19672.6330 0.010 1.0074 NULAND BAN 58 19804.5580 0.010 1 . 0045 NULAND BAN 5 8 19307 . 3570 9.010 0.9966 NULAND BAN 53 19813.5830 0.010 0.995 1 MIJLAMD BAN 58 1932 1 . 39 1 0 0.010 0.9963 NULAND BAN 53 19852.2470 0.010 0.9767 NULAND DAN 58 19978.5535 0 .003 0.9749 : LEHNERT AN 4 73 6 19 995.4040 0.010 0.9833 NULAND BAN 58 20006.6240 0.010 0 .9758 NULAND BAN 58 20020.67 20 0.010 0.939 5 NULAisID BAN 53 20023.4580 0.010 0 .9686 NULAND BAN 58 20023.4604 0 . 003 0.97 10 :LEHNERT AN 4 73 6 2 0 023.464 0 0 .003 0.9746 HOFFMEISTER AN 472 3 20026.2320 0.010 0.9857 NULAND BAN 53 20037 . 49 1 0 0.010 0.9673 HOFFMEISTER AN 4 72 3 20037 .49 50 0.001 0.9713 SLOVOCKOTOVA VAR.STAR 10. 20037 . 4979 0.010 0.9742 :LEHNERT AN 4 78 6 2 0 040.29 10 0.010 0.9 604 NULAND BAN 53 105 HELIOCEÜTPIC 0-C JT’LIAM DATE + /- DECIDUAL 0E3EDVED REFEREMCE 200^0.3G 1 G 0.010 0.9704 HOFFMEISTER AM 47 23 20 0 5/-J. 3 3 50 0.010 0.9700 MIJLAMD DAM 58 20054.3420 0.010 0.9 770 HOFFMEI STER AM 4 7 23 20065.38 1 0 0.010 0.98 17 HOFFMEI STER AM 4723 20121.6890 0.010 0.9592 'J I JLAMD DAM 53 20 138.5260 (^.010 0 .9 549 MIJLAMD DAM 53 20169. 40 1 0 0.010 G.9 544 MIJLAMD DAM 53 20169.4070 0.007 0.9604 POHL IBVS /}f44 3 20239.57 60 0 .008 0 .9 576 MIJLAMD DAM 58 20242.3 79 0 0.010 0.9537 MIJLAMD DAM 58 20259 .4 130 0.010 1.1465 MIJLAMD DAM 58 2027 0 . 447 0 0.010 0.953 1 MIJLAMD DAM 58 20357./13 30 0.010 0.926 1 MIJLAMD DAM 5 3 20385.502 0 0.010 0.9264 MIJLAMD DAM 5 3 20 4 58.48 5 0 0.010 0.9303 MIJLAMD BAM 58 228 10. 3930 0.01 0 0.686 7 POHL IDVS jt'443 230 15.2720 0.001 0.659 2 SLOUOCXOTO'Ul \'AR . S T AR 1 0 . 1 C85)P32 237 T1. 3240 0 .010 0.6074 POHL IDWS A443 24 5 67.3 420 0.001 0.530 1 SLOVOCKOTOVA \7AR. STAR 10 . 1 C35)P32 24746.9580 0.010 0.5064 POHL IBVS #443 25364.4380 0 . 003 O'. 47 50 MEROEMTALER A./i. 1, P. 36 26627 .4220 0.010 0.3675 POHL I3VS #44 3 27629.4140 0 . 00/1 0.3069 POHL IBVS #443 27724.8250 0.001 0 . 23 4 3 SLOVOCKOTO^^A iViR.STAR 10 . 1C 3 5)P32 3 28 24.6510 0.001 0.0275 SLOVOCKOTOVA VAR.STAR 10, # 1 C 3 5 ) 3 2 3 3060.4 270 0.010 0.0265 POHL AM 2 79, P. 173 33265.3080 0.010 0.0060 POHL AM 2 79, P. 1 73 333 10.2380 0.010 0.0260 POHL IDVS #443 3 3 3 10.2420 0.010 0.0300 POHL AM 2 79, P. 178 33 3 24.2 640 0.010 0.0177 POHL AM 2 79, P. 173 33436.5510 0.0 10 0 .0299 POHL /AJ 2 79, P. 1 73 33 43 6 - 559 0 0.010 0 . 0379 DOMKE AM 2 79, P. 173 33509.5250 0.010 0.0253 DOMKE,POHL AM 23 1C 3), P. 114 3 3 700.386 0 0.001 0.0191 DOMKE,POHL,JAHM AM 23 1C 3), P. 114 3 3 7 4 5.3130 0 .001 0.0362 DOHKE,POHL,JAHM AM 23 1 C 3) , P. 114 33756.5330 0.010 0.023 7 DOMKE AM 28 1C 3), P. 114 33 7 59 . 3 40 0 0.010 0.0288 POHL IBVS #443 33798.6370 0.001 0 .0 29 6 SLOVOCKOTOVA VAR.STAR 10,# 1 C8 5)32 33888.4570 0.00 1 0.0298 DOMKE,JAHM AM 231C 3), 114 3 39 47.389 0 0.010 0.0 175 DOMKE AM 23 1 C 3) , P. 114 3 4 079.3220 0.001 0.0277 POHL AM 282, P. 23 6 3/1135.4610 0.001 0.0292 POHL AM 23 2, P. 236 34163.5330 0 . 00 1 0.032 6 DOMKE AM 282, P. 236 34203.4380 0.010 0.0276 POHL IBVS #443 342 53.33 50 0.001 0.0147 POHL AM 232, P. 236 34455.4350 0.00 1 0.020 1 POHL AM 232, P. 236 34 542.4600 0.00 1 0.032 1 DOMKE AM 282, P. 23 6 34876.4683 0.001 0.0229 POHL AM 23 6, P. 2 10 35283.4770 0.001 0.0354 POHL A.M 23 5, P. 163 35370.4850 0.001 0.0304 RUDOLPH AM 285,P. 163 35951 . 5 100 0.010 0.0334 POHL IBVS #443 3595 1 . 5120 . 0 . 00 1 0.0354 QUESTER AM 285,P. 163 106 HELi ocErirni c 0-C JULIAM DATE + /- RESIDUAL OBSERVER REFEREMCE 36111.5010 0.001 0.0328 RUDOLPH /'uM 23 5, P. 1 63 36 1 2.3 . 3350 0 . 004 0.0255 AFRAMIEC SAC 30, P. 1 0 7 36355.3350 0.001 0.0462 :BRAUME AM 2 8 6, P. 2 1 0 370 15.3030 0.014 0.0276 32AFRAUIEC A. A. 13.1 3 7 17 2.43 7 0 0 .003 0.02 19 f l i:j A. A. 17, P. 61 33 539 ^ 445 1 0.001 0.0343 :J0BGEHS>KRAU5S Aî'J 289 #4, P. 19 33539.4451 0.00 1 0.0343 UURHBERG IBVS #443 3367 1 . 3693 0.001 0.036 1 MURUDERG IBVS #443 33991.3455 0.010 0.023 6 KI2 ILIRMAK AM 23 9 #4, P . 1 39 033.4520 0 . 003 0.032 1 S2AFRAMIEC A . A . 16, P. 158 39266.4245 0.00 1 0.03/14 HTTB5CHER, BRAUME AM 29 2, P . 135 39305.3390 0.001 0.0299 SCHUBERT AM 29 2, P. 185 39962.5210 0.001 0.027 1 SCHUBERT AM 29 2, P. 185 39979.35 15 0.001 0.0 164 POHL IBVS #456 4003 0. 399 5 0.001 0.0171 GUDUR,IBAMOGLU I 3VS #4 56 /( 0324.6040 0.010 0.0239 BORTLE I BVS #795 40333.6300 0. 003 0.0156 BORTLE IBVS #79 5 40439.6720 0 .0 03 0.0 102 MOMSKE IBVS #795 4 04 7 3.3520 0 . 0 0 1 0.0078 POHL,MEIER I BVS #456 40377.5390 0.001 0.0 0 5 5 EMDRES I BVS 27, #530 4 1 063.4066 0.00 0 0 . 0060 BATTISTIMI, BOMI IBVS #3 1 7 4 1 357 .5200 0.010 0.0 117 KLIMEK IBVS # 637 4 1 39 5 . 4670 0. 002 - 1 . 3374 BATTIST IMI, BOMI IBVS #8 1 7 41503.46 55 0.00 1 0.0000 GROBEL IBVS #937 0.0000 0 .000 - 1 .0857 4 17 6 4.5000 0.001 — 0.0 04 4 GROBEL IBVS #937 42253.5032 0.001 -0.0 103 :EBERSBERGER IBVS #1053 0 “ 0 “ 0 I "0 ' Oci "'0 ' 0C ~0 ' 01/ "0 " 0f] "0 * 0 9 "0 ‘ 0Z. 0 1 n X) n O') - f - p L_ > r” 60 o > -< 60 IS65J0 --aoiaijd 'dii’Hxi zoi 108 CHPOr^OL00Y or 32 ODSLHP/.T I 02’S OF T X H p. TCALC = JD 4 113 2.45 11 + L * 2 . 0 9 3 10 0 0 'lELI OCZMTP.I C 0-C JVLI/rj DAT F + /- PLSI DUAL ODSORVrP EEFEDEMC 13967./1064 0.001 0 .0 06 1 LAZZAPI MO AM 4 7 11 193 4 0.2330 0.001 0.907 1 DAL AM O''SKY AM 5159 19 636.2760 0.001 9 .002 1 DALAMO’-'SLY AM 5 159 19 96 4. 3 4 4C 0.001 -0.0043 LAZZAPIMO AM 47 11 19 999.3630 0 .010 0.0029 'J ALAMO’-'SKY AM 4 7 69, P . 232 2 0 0 3 6 . 4 4 0 0.031 0 . O' 0 5 4 DAL/iMO’^SKY AM 5 159 20063.2240 0.001 0.0043 2ALAMO"SKY AM 5 159 229 69.3 1 40 0.001 0 .002 0 AM 5159 3 3 7 7 9.4962 0.010 0.0020 DOMKL AM 231(3), P. 114 33349 . 63 1 0 0.01 0 0.0035 DOMKE AM 231(3), P. 114 3333 0 .4 4 00 3.010 0.0 154 JAHM AM 231(3), P . 114 3 3332.4930 3.031 0.0135 J AH M,DOMKE AM 2 3 1(3), P . 114 339 11.3 3 00 0 . 0 1 0 0.0332 DOMKE AM 231(3), P. 114 3 4I 19.3760 0.001 0.0134 DOMKE AM 2 3 2, P. 23 6 3 4 12 1. 420 0 3.001 0.0036 DOMKE AM 23 2, P. 23 6 3 4 7 7 . 7 '7 e 0 0 . 0 02 0.0004 FITCH AJ 69, F. 3 1 6 3 4 3 . 4 4 6 0 0.001 9.3913 DO'IKE /iM 23 2, P. 236 3 5 227.6600 0 . 0 0 1 0. 0 39 6 LICHTEMKMECKTED AM 23 5, P. 1 63 3629 6 . 5930 0.001 9.9112 DM.'DOLPH A'J 2 3 6, P. 2 I 0 3632":;.416 0 0.301 - 0 . 3 3 3 1 PTTDOLPH AM 23 6, P. 2 1 0 3737 4.3970 9.001 0.0003 FE2MAMDES AM 233, P. 1 7 0 33 22 0 .4 43 0 0 . 0 0 l 0 .0037 POHL AM 23 3, P. 7 1 399 79 . 130 0.001 -0.0041 OU CUP. IEM5 A456 4 0003.3573 0.031 - 0.0021 OUD\TR I DUS #456 4033 9.4232 0.001 -0.90 11 OUDPP IDES #456 4 0 4 2 6 . 0 1 5 0.001 0.0007 HOLZL I LUS #4 56 /I 0 7 3 5 . 4 7 1 4 3 . 30 1 -0.0009 DALTISTIMI IBUS #9 5 1 403 34.343 1 9.001 - 0.0001 YILDIZ I EUS #53 0 A! 13 2.451 1 0.001 0 . 0 300 HALT ISTIMI IBUS #951 4149 I . 42 2 3 9.001 -0.0003 0 AM E A I BUS #93 1 42 2 79.3030 0 . 0 3 1 - 1. 0 2 63 : I LAM00LU,LEEDS IBUS #1053 42230.3332 0.001 0.0034 oudt ;p. IB'/S #1053 109 TXhr:2 ; PfIRI OD- 2 . 02931 000 5 . 0 C - 0 2 CO > - < Q to _J < ZD 0 Q I—I CO LJ QC U I o - 5 . 0 2 - 0 2 - 70.0-60.0-50.0-40.0-30.0-20.0-10.0 .0 YEARS c h r o :jolo CY or 5 OBSCrVATIOMS or T/vHE2 110 TCALC = JD 4 1768. 4 6 7 4 + E * 2. 05981000 HELI OCETÏTRI C 0-C JRLIAM DATE + / - RDS I DUAL OBSERVER REFERENCE 1 9 6 3 9 .9 2 6 2 0.001 “0 .0024 LAZZARIMO /iM 4 7 11 3/4/499 . 4 M 0 0.001 0 .0 1 6 1 JAHM AM 282, P. 23 6 4 M 5 5 . 3767 0.00 1 0 .0 0 0 4 PEXUMLU I BVS /i'937 4149 2.4 530 0.001 0 . 000 1 PEKUMLU IBVS #937 41763.4 674 0.001 0 . 0000 IBAMOGLU IBVS #9 3 7 0-C RESIDUALS»: DAYS) Q m n N O /U 'D r i o I—I o h) Q UJ ro o s Q Q 112 CHRONOLOGY OF 15 03SERVATI0NS OF ZOP.l TCALC = JD 37267. 5240 + E 4= 5.223 29 000 HFLIOCEMTRIC 0-C JULIAN DATE + /- RESIDUAL OBSERVER REFERENCr 27 45 0.143 0 0.010 0.007 5 LAUSE AN 260, P . 292 2 7 455.3373 0.010 - 0.00 15 LAUSE AÎJ 260, P. 29 2 2748 5.3420 0.010 0 .0032 LAUSE AN 260, P . 292 275 16. 5350 0.010 -0.0235 LAUSE AM 260, P. 292 2772 4.7030 0.010 0.0129 LAUSE AN 260, P. 292 27870.4040 0.010 0.0217 LAUSE AN 260, P. 292 28 02 6.4 600 0.010 - 0.0210 LAUSE AN 260, P . 292 28073.3083 0.010 - 0. 0023 LAUSE AN 260, P . 292 23073.3090 0.010 —0.0016 LAUSE AN 260, P . 292 28 1 5 1 . 3 1 50 0.010 -0.0449 LAUSE AN 260, P . 292 28250.2260 0.010 0.0036 LAUSE AN 260, P . 292 29 0 04.7 57 0 0.010 0 . 057 5 EOCHKORE^rA rAR.. STAR 1 5 # 4, P. 437 33583.6230 0.010 0.0283 BOCHKOREVA VAR. STAR 15,^4, P. 437 34 140. 3 59 0 0.010 0.0123 EOCHHOREVA WAR. STAR, 15#4, P.437 37267.5240 0.010 0 .0000 BOCHKOREVA VAR.STAR 1 5f^ 4, P.437 113 ATPF..G,; PERIOD- 1 - 0 r - 0 ' i CO > - < Q CO _J < Z) 0 Q I—I CO LJ CL U 6 1 . 0 L - 0 1 L - 30. O - 20 . 0 - 1 0 . 0 YEARS CHP.O'JOLO^Y OF 26 ODSEPVAT I 0r:3 OF ATFZG 114 TCALC = JD 42645.7662 + E * 1.146G96CC HELIOCEMTaiC 0-C JTTLIArj DATE + /- EES I DUAL obseevee REFERENCE 33504.5250 0 .0 0 1 0 . 0205 DOMKE,POCHEE AN 23 1 (3), P. 115 33556.3370 0 .0 1 0 0.3159 DOMKE AN 231(3), P. 115 33333.4 630 0 .0 1 0 0.0163 DOMKE AN 231(3), P. 115 34272.4060 0 .0 0 1 0.0171 POHL AN 232, P. 236 34303.3500 0 .0 0 1 0.0 165 DOMKE AN 232, P. 236 350 19.6660 0.004 0.0225 ’^HITMEY AJ 62( 1254), P • 373 35034.5720 0.004 0.0293 'VII TNEY AJ 62(1254), P. 373 35332.5450 0 .0 0 1 O.C173 JAHN,RUDOLPH AN 23 5, P. 164 35333. 7 100 0.004 8.023 6 ’■VHITNEY AJ 62(1254), P. 3 73 35726.3 100 0.003 0.0253 ’■Vi I TNEY AJ 62( 1254), P. 373 36065.5270 0 .0 0 1 0.0143 RUDOLPH AN 285, P. 164 36 100.4340 0.001 8.0220 LICHTENKNECKE AN 23 5, P. 164 36 1 06. 4 54 0 0 .0 0 1 8.0 193 RUDOLPH AN 28 5, P. 164 37 17 5.473 0 0 .0 03 8.023 0 FL I A.A. 17, P. 62 37 544.5070 0.006 8.0141 KUBICA A.A. 17, P. 62 37544.5150 0 . 006 0 .0 2 2 1 KU8MINSKI A. A. 17, P. 62 37872.3 190 0 .0 0 1 0.042 6 POHL AN 283, P. 7 1 37904.4020 0 .0 0 1 0.8349 KIZILIRMAK AN 28 8, P. 7 2 379 1 1 . 2870 0 .0 0 1 8.0433 ASLAII AN 28 6, P. 7 2 38 23 6. 347 0 0.081 0,0378 BECKER AN 23 3, P. 7 2 39 337 . 4060 0 .0 0 1 -0.0093 : BEAUNE AN 29 2, P. 137 4 0407.4 380 0 .0 0 1 -8.0026 IBAMOGLU IBVS A 456 40436.3630 0 .0 0 1 -0.8023 I BAN00LU IBNS ^456 4 0.6 77 . 3370 0 .0 0 1 -0.003 1 ENDEES,SENGONÇA IBVS 530 41661.2729 0 .0 0 1 0 . 003 1 AL KAN IBVS #937 42645.7662 0.001 8.0000 DOOLITTLE BLUE NT. OBSERVATOR’ APPENDIX 2 FORTRAN CODE LISTINGS The Fortran codes listed in this section are stored on magnetic tape at the UM Department of Physics and Astronomy. Also available are detailed descriptions of the codes, which may be consulted during exe cution or*modification attempts. 115 116 Program FILCHG This Fortan code determines 0-C residuals for the observed times of minima of eclipsing binary stars, using the linear elements of eq. (1.1) A disk file containing the information exhibited in appendix 1 is cre ated by the in itia l execution. Later executions allow for the addition or deletion of observations and for the residuals to be recalculated using new values of the ephemeris date and period. ^ F TLr:H3 . F , 117 G THIS PROGRAM CRhATtS, TES, AND M 0 DIF T F S FCLIp STNG BINARY C OlsFRV AT I ON FILf S. PRFS^'NT MAXIMUM NUMOFR OF FmTp i FS j S 700 . DODDLE PRECISION T T, PERIOD,! NFW , TCn. CK,TSA\/E,poUM,T1,T3B,FN 1 , TCALC,DFlTiSAVT nlMENS ION TT (/0 0) ,DOgS(7QO), SAVT(700) , HoLo( 70 0 * ,NFPOCH(700) 1 , OP t 7 , 700 > , 00 NEW ( 7) , S AvO ( 700 ) , S A \/0 Ô ( 7 , 7 0 0 ) , I 0 ( ? 0 ) , 20DINPT( 7 ) , OBLAST(7) BL ANK=' ' ICOUNT=0 ITAe=o DO in 1 = 1 ,70 0 TT ( I ) =0 . DO BS (I)=0 . SAV T { I) =0 . HOLD( I )=0 . NE POCH(I) = n SA vn( I )=0 . 00 10 M=1,7 03 ( M, I ) =BLANK 10 SAVOB(M,I)=BLANK 00 20 1=1,7 OBKEW (I » = BLA NK 0 J INPT MAY BE USED WhEN INPUT IS SAmF AS FqR pRECEdINS ENtRY.*) DO 210 1=1,IMAX type 120,1 120 FORMAT(/I5,'ENTER JD:*,S) accent 130,TT(I) 130 FORMAT(D) TYPF 1 40 140 FORMAT(' ENTER ACCURACY(DAYS) : ' , T) accept 150,DINPT 150 FORMAT(F) DO BS (I) =niNPT IF(DINPT.LT.0.0 00 01)DOBS(I)=DOBS(I-1) TYPE 160 Ibu hORMAFC» fcMTER 03Stf?VFR NÛ H E • * , / I ^ X t ' Program DETECT This Fortran code is used to determine the detectability of a low luminosity companion which is in the proximity of a brighter star or close binary. The input parameters which must be specified by the user are the distance in parsecs from the earth to the stellar system and the apparent visual magnitude of the visible central star(s). The out put is given in a data f ile which may easily be plotted on the Calcomp plotter as shown in figure 3. Oc-TiCr .F\ 125 t' PROGRAM TC OETLPMINF VIS'JAL OE T FC: F A P T L I T Y OF COMP «NI0N<; . G STEPS tHROijS h MASSfS FRO^ 0 • Cl 1 Tl 1 . f, 0 (M/MSUN) aNO C FI NOS SEPARATIONS ( A ij ) A? WHICH Dt TpCT A 0 IL IT Y I NO&X 0 = 1.0. niMFNSION OOLM(10*,3OLC(3]),FMASS(150),SFPAu(190» I t FLM (30 > » ''LPH (.70 ) DATA B0LM/?2.0,13,1,12.0, 11,5,11.0,10.5,9.7,^.1,8.7,0.♦,7.0,7,5 1 , 7 . 2 , 6 . 8 , G. 6, 6 .3,6.1 ,6.0 ,5 .8 ,5,5,5,1 ,4 . 9 , 4 . 6 , 6 . 6 ,3 . 5 , 3 .3,3 .0 2,2.4,?.2,2.1/ DATA DOLC/- 5 .fl,- 5 , 8 ,-4.6,-4.0,-3.4,- 2 . 9 , - 2 , 6 ,- 2 . 3 , - 2 , 0, - 1 , 7 1 1, -1.45,-l.l7,-0.89,-0. 62 ,-3.50,-0. 40 , - 0. 30,-0. 24 , - 0 . 19,-0.13 2,-0.09,-0.07,-0 , 06,- 0 .05,-0.Of,,-0.03,-0.01 , 0.01,-0.02,-0.03/ DATA FLM/-3. 0,-1. 0,-0. 8 ,-0.3,-0.4,- 0 . 2 ,- 0 . 0 , 2 34^ 0 .0 / DATA ALPH/2.9,2.9,3.13,3. 33, 3.75,4.G,4.0,23»4.0/ TYPF 10 10 FORMAT ( ' ENTER OIS TANCE(PC) : * 3 ) ACCEPT 20,niST 20 FORMA T( c) TYPE 30 30 FORMAT(' ENTER APPARENT VISUAL MAGNITUDE AT 1 MID-POINT OF PRIMARY ECLIPSF:') ACCEPT 20 , AP TMAG 09 40 1=1,150 FI = I FMASS( I )=F1*0.01 FL OGM=ALOGIO (FMASS(I) ) DETERMINE DIFFLRENCc IN MAG^II TUOi J= 7 CALL INTRP(FLM,ALPH,FLOGM,ALPHA,J) xlumi = fmass( I)♦ ♦ alpha B0LMAG=4. 7 7-2 .5 ♦ALOGIO CVLDm!) J = 3 0 CALL INTRP(OOLM,BOLC, BOLMAG, Qc , J » ABMAGI=90 LMAGfBC A=»MAGI = ABMAG-H-5.^ALOG10(OtST/in.) DELMAG=ABS(APMaGI-APTMAG) SEPLOG=n.2?^OELMAG-1.0 S-PSEC=10.♦♦SEPLOG SE PAU( I ) = SEP SEC*0 1ST 40 C 0 N TI NU F 50 FORMA T(15 0(? FI 0.2 /)) C WRITF FILE FOR CALCOMC» OLITT ER...... CALL oFILF (1 , 'GRAPH' ) WRITE ( 1,60 ) 60 format( 'GRAp MOI' , / 1'TITLE13DETECTABILITY',/ ? ' XAXIS155FPARATTON (A U )',/ 3 ' YAxIS23COMPANION MASS (M/MSUN)',/ 4 ' SPEC SO. 0 150 . 0 0 .0 1. 50 1 1 1 5 15 . 0 2 3 3 ' , / 5 ' DATA 150 ' ) W(ITF(1 ,5 0 ),(FMASS(I),SEPAU(I),1=1,150) WRITE(1,70) 70 FORMAT( 'PLOT 020107',/ 1 ' STOP ' ) end f i l e 1 ST OP SUBROUTINE INTRP( X, Y, X1 , F I , J ) C LINFAR INTER POLAT I ON SUBROUTINE. C J= NUMBER OF ENTRIES IN ARRAY. n 3IVTN APPAYS X(N) AMH Yfl), SÜ'^f^nUTTNP'M L L F IN I 126 C FOR F ACM VAL UF OF XI THf 3 OR RFS POND IN GVAL'JF OF Y S'JCH C H A T F1 = Y(X1). OIMuNSION X( .30) , Y ( 30 ) TOROER^O IF (y(D,&r.X (JI)IOROFR = l 1=1 IQ I F Program NTERAC This code makes the dynamical calculations of the three-body mutual interaction model and displays the resulting light travel-time effect on a plot of the 0-C residuals observed for an eclipsing binary star. As shown in figure 15, the main routine CONTRL directs the logical flow of information through several subroutines. The in itia l position, velocity, and mass must be known for each body before the dynamical calculations begin. This may be accomplished through either subroutines PARAMor RECTIN. Subroutine PARAM accepts the elements which describe the orbit of a binary about the two-body center- of-mass due to a companion, since these may be inferred from the observed 0-C residual curve's cyclic pattern. The companion mass and orbital semi-major axis are found by subroutine MASS where the solution of the quartic equation (eq. 2.16) is found by the subroutine ZEROS, which is provided through the courtesy of its author, R. J. Hayden. Subroutine PARAM then proceeds to calculate the companion's in itia l position through a converging iteration of Kepler's Equation as described pre viously (eqs. 2.6, 2.11). The rectangular components of the position are found in the usual manner. The expressions which yield the velocity components are obtained by differentiating the position equations as outlined in a NASA Technical Note (Strack, 1963). The analysis is re peated to account for the other companion. Finally the fractional masses are determined for each companion and are used to determine the in itia l rectangular position coordinates of the binary based on the three-body center-of-mass (eq. 2.27). Since the dynamical motion of the 128 j'JX HT HR \G . F4 , T *40104 . RHI RECTIN PAR>«\M MASS ZEROS G(X) DETECT INTRP Cei CALCOMP PLOT o UNIT 1 DYNAMO TYPE DISPLAY FUNCTIONS HISTRY UNIT 8 UNIT 5 DISK PRINT FILE NTRP UNIT 9 UNIT 1 Fig. 15. Interaction model flow chart 129 three-body system follows open paths rather than the constraint of orbits, the superpositioning of simultaneous two-body systems is used in subroutine PARAM only to define the in itia l configuration. A more direct way of defining the in itia l conditions of the system is to simply enter the position, velocity, and mass of each body through subroutine RECTIN. In practice, i t is d iffic u lt to choose a set of rectangular input parameters at random which will describe the in itia l conditions of a system which will remain stable. The subroutine RECTIN is, however, quite useful for continuing the dynamical calculations of systems whose masses, positions, and velocities are known. The subroutine DETECT determines detectability thresholds which are the maximum separations between each companion and the binary, as mea sured perpendicular to the line of sight, at which the companions could be located without being detected visually. During the dynamical cal culations the separation of each companion from the central binary pair is repeatedly checked against its particular threshold so that detect able cases may be recognized. The dynamical calculations are made by subroutine DYNAMC which employs a fourth-order Runga-Kutta integration scheme. The eight func tions which are called are the equations of motion (eqs. 2.24, 2.25). A plot of the motion in time of all of the bodies is made on a graphical CRT display. The displacement as a function of time of the eclipsing binary pair along the line of sight is used to generate light travel - time residual data. This is plotted on a CRT display along with the observationally-derived 0-C residual file which is recalled from the disk by subroutine HISTRY. An rms deviation is calculated in order to 130 determine the accuracy of the f i t by numerically comparing the model residual curve with the observations through the linear interpolation subroutine NTRP. An evaluation of how closely a simulated curve fits the system's past behavior guides in the selection of the input param eters for the next tria l so as to achieve a better f i t . The parameters which give a best f i t are then considered to describe, based on the in itia l assumptions, a possible multipi e-body system which is capable of satisfying the existing eclipsing binary star residual observations. The code creates a permanent record of the input data for each tria l as is shown in table 6. Also listed in this log are the final rectangular parameters, which are useful i f further calculations are to be made. The comments are a subjective appraisal of the model. To run the code, the source program NTERAC.F4 must be accompanied in execution by the graphical display subroutine package P40104.REL. TABLE 6 TYPICAL JIODEL LOG 131 TPIAL no , 127 ______niPAoy 2 . L] 30" DIST ANCT(orj = 05,30 Apparent *'(0-itt'J0 5= 7,«ja INCL I JA TI cr-C0'.r.» = fZ, ]4 OIKARV 0R37TT 1 ______ORGITALPl RIOO- i7 ,jr3 0 " 5EM -NA J09 ( Atj) = 1. 130 j" ECCENTRIC 17Y=______0. ngou'' PtHia^S«^ PASSAGE (YR»= " ' C.OOOCO LOKGITUCE Cr oro ; APSE (PEG) = 1 25. COCiuD COMPANION OR'^TTI 1 COh'C* AN TON AlS= 0.29721 CRPITAL r^'^IonCYR 1 7 . 0 0 C I r' SEM-'-iA JOR AYIS(aiJ»= ' q .19170' ECCEMTPTSI'^Y t C.OJuLO ^ERIA = SE PASSAGE (Y? »=______C. T 0 3 3 r LONGITUnE rf 7 I AO S Ê ÎD 3G ) = "3 3 5. COO uC" BINARY 0 99 IT 1 ? ______OREITAL »ERIOn= ' ' 89.0 0000 SEMI-1AJCR AXTSfAUÏr 3.00000 ECCENTRICITY: _ 0,"G000_ PEPIAPSE oASSAGE( YPI= 0.0 0000 LONGITUOE OF PER I APSE (O-GI= 239 . f 0CÛ0 COhPANTON r^SITt 2 COHPAMION >*ASS= 0 . 32903 ORPITAL PEOI0P(Yo>= 80.O3CÜ? S E FI -MA J OR": VIS (A or = 27.65034' ECCENTRICITY: C.POPOr PEFIA^SE PASSAGE(YP)= C.GOOCC LONGITUCE OF PÉ^ I AP IS (ÔFG» = 5 OOOC NO. OF YCADS- 3 0 0 STEP ST^E (YP)r , 1 5^^ NTH POINT FLOTTE 0= 20 starting rectangular FACAMETERSt 1 gama = G,11967 y- 5.27219 Y = -7.52947 vx- 2.70305 VY = 1.94 071 2 GAMfl: 0 .1 3743 y- 14.652 45 Y = 23.44 0 0? vx= -1.67434 VY = 1.0 4624 binary to CONPANICN a HAyIM'M S7FERATIC7(AU»= 17.12 4 BINARY TO rnMPA'jION 9 HAYJFiJ'^ S-PE F A T I C ^ f AU ) : 43.941 1ÎA XI NU" "RACIAL VELOCITY (KK/SEC»= 4.776 XyFAflStAU»- -2. 644F-* YTRANS(AU *=- 2 , 3 2 1 5 2 ______ FINAL rectangular OARAVrTEPSi y- -3.30020 Y- 11.77710 VX= -1.3064U "V“Ÿ= -0. 0 7 506 X= -34. 72 2 ‘*4 Y= 9,6"900 VX= -3.76 6 03 VY- -1. 34 0 30 CONSENTS I FROM I 1 0 ♦ 350 Y R PLOT CN CÂL CÔMF...... ^ AC . 4 1 09 MASTrR CONTROL FOR N - 300 < P^OBLFM SUP^POUTINFS, C0MM0N/C0NTRL/lTRlAL»C,Pr,yt3),Y(n,Vy(3 ),VV( 3),FMASS(3) 1, XTRANS,YTp ANS " COMMON/STAP/OTST, APTMAG,riN3 dimension word ( 3 5 ) PI=3.14159265 G=6.6 732E-QO*3.1559E07»3.15 53F07/1.4959789 3E13/ 11 .495 97 8 93 F l3 *1 .9 8 9E 3 3 /1 . 49'597893F13 IS TRT = 0 WRITE(5,10) FORMaT(* in p u t ; oPRITAL ELEMENTS(0)7 OR RECTANGULAR COORDINATE IS ( 1 )? ' , S) RFAD(5t20 ), I SwTCH format( I » WRITE(5,30) FORMAT (» ENTER QINA==*Y MaSSI'S) Rr AD(5 ,4o ),FMASS(1) F orm at( fi WRITE (5,50) FORMAT( ' ENTER 01STANCE(PC)? ' ^ ) read (5 ,4 0 ) fOTsT WR ITE (5,60) FORMAT( ' FNTFP aPPArFNT Vi SUAl mAGn TTUDF A T 1 MID-POINT OF PRIMARY FCLIPSEî') RE AD(5 ,4 0 ) , A PTMAG WRITE(5,70) FORMA T (' enter INCLINATION OF BINARY OR31 T (0EG) t ' , T) READ(5,40 ) ,FINC WRITE (5,80) flO FORMAT(' LAST TRIAL NO AD{ 5,20 * , I TRIAL 90 PAUSFOr nA u I I CC- r ITRTA L=TT RIA L f 1 WRITF(8,100) , ITRIAL,FMASS(1» ,0 1ST, APTMA G, FTNO WRITE (9,1 00) ,I t RIAL,FMASS(1) ,OIST,APTMAG,FTNC 100 FORMA T C I TRIAL NO. ' , 14, / ' BINARY M A SS = ' » F 1 Q . 5 / , 1' DISTANCE( PC I = ' , F8.2 /, ' APPARFNT MAGNITUDE:' , F8. 2 /, 2' INCLINAT ION(OEG) = ' , F8.2) i F ( ISWTCH .EO . 0 ) GO TO 110 CALL RFCTTNRFCTIN GO TO 120 110 CALL PARAM 120 CALL DFTFCT(FMASS(2),VTSl) CALL DETECT(FMASS( 3 ) ,7152) CALL DYNAMC(7 IS l,VIS2,ISTRT,TIMF) 1 30 WRITE(9 ,1 4 0 ),XTRA nS,YTRANS 1 40 FORMA T( ' XTRANS(AU) = ' , FlO.5 ,/ ' YTRANg(Ay) = ' , FIO .5) WRITF(9,150),TIME 1 50 FORMA T( / ' FINAL RECTANGULAR PARAMETERS: YcAR=' ,F9.2) J 2 = l J3 = 2 WRITF(9,160) ,(J2,X(2),Y(2) ,7X(2),VY(2), 1J3,X(3),Y(3),VX(3),VY(3)) 1 60 FORMAT( 2 ( /1 2 f5X, ' X=' , F 10 .5, 7 7X, ' Y - ' , FIO .5, 1 /6 X ,' 7X =F10.5,/6X , • V Y= ',F 10.5/) ) WRITF( 5 , 170) WRITE(8,170) WRITF(9,170) 1 70 FORMA T( / ' COMMENTS!') 1^0) , (WüPn (J) , 1 = 1 , 180 FORMA T(3 6A 41 133 WRirr (8,1 Fo 1 , (WnpD( J), j= 1, 3r^) WRlTB(9,l9Q),(W0Rn(J),j::t,3fS) 190 F0RMAT(?(1X,18A(4)/) ISTrT=1 G] TO 90 FMO SUMc-DUriN'^ PA? A M ,3- C ACCFPTS INITIAL OSCUl ATJ iG 1R 01T A L PAPA ANT C, CTNVcRTS THEM TO ?ECTANg'JLA? CO OR 01 NATE PARAMETERS . COMNoN/rONTPL/lTRIAL,G*PT, X(3)1 Y ( 3 ) ,V X (?) ,VY ( 3» ,F MASS(3) 1, xtrans,ytrAns COMMON/STAR/OIS T, APTMf\G,FIN: dimension PERI0n(?>»A(2),-CS(;>),T'I(Z) tW(?>,FN(?)^GAMA(?) N= 3 N= N-1. FM12=FMASS(1) no 81 J = ltN INPUT PARAMETERS ARE OF OINARy 0 A RYpFNTFR OrSi T. WRITE(5,10) 10 FORMAT( / / ' PERIon(YR)? SEMI-MAJOR AxIS(AU)? ECOENTPIClTY? ', 1 /' PeRIAPSE PASSAGE(YR)7 LONGITUDE OF PER I APSE (□FG)? ' » RE ad(5,20) » TFMPI» TEMP?, TE MP3,TEM^^,TEMPS 20 FORMA T (SF ) WRITE(8»30), t e m p i, TE M'^ 2 , T Em^ 3 , T EmP^ » TEMP5 3 0 FORMAT (SF8 ,2 ) C _ »NUM 1 r I i • bT. 1 ) Monr=1 CALL TPLOKT (?,T) ,QMINC(e, I) ,MOnE) 4 70 CONTINU.. CALL HQMp CALL Wa IT(NWORD) IF (NWORn.EQ, 'G')GO TO 60 IF (NWORn.HiO. 'G ' ) RFTURN IF (NWORO.e O. ' R ' ) GO TO 3bO C + f f + + R A DIAL V&LOCITY RFSIOUAL CURVE VT 0P=6. V'30T= -VTOP 0INCV=1. call erasf CALL SETUP(TMIN,VBOT,TMAX,VFOP,MOOEl,MOoE2) CALL AX IS (GRIGIN,ORIGIN,DTNCT,niNCV) CALL home WRITE(5,4.5G) ,IT r i Al MOnE=-l J = 2 03 4ftO 1 = 1 , NUM CALL TPLOTd (J, I> , VSAVEd ) ,MGOF) 4 80 continue call home CALL WAIT(NWORO) IF ( nWoRD.EÛ, 'G ' ) GO TO 60 IF (NWORD.EQ. 'RMGO TO 360 C f f f f+ + fWR ITE RFSIDAL DATA FILE FOR CALCOMP PL 0 T> ♦ + f f + 1-f f 4-+++ + + ++♦+ +4- X1=-GAMA (1)^ X2-GaM a(2) * < 3 yi=-GAMA(l)^ Y2-GAMA( 2> »' 3 R2 3=SQRT((X3-X?)**2f(Y3-Y?)»^2) R12=SQ9T((X2-Xl)**2+(Y2-Yll»*?) F1=FACT0K*( ( X1-X2)/R12*»3+GAMA(2)»(X3-X2)/R2 3*»3) RE TURN ENO FUNCTION F2(X2,Y2,X3,Y3) COMMON/FUNCT/factor, GAMA (2 » X1=-GAMA (1 ) ’^X2-GAMA(2I »X3 Y1=-GAMA(1)^Y2-GAMA(2)»Y3 R2 3 = SQRT ( (X3 -X2) »^2+ (Y3-Y2 ) ''♦e ) R12 = sORT((X2-Xl)4^#2f(Y2-Yl)^*?) F2=FACT0R^((Y1-Y2)/R12»^3+GAMA(2)^(Y3-Y2)/R2 3*»3) RE turn ENO FUNCTION F3{X2,Y2,X3,Y3> C OMMON/FUNCT/FACTOR,GAMA(2) X1 = -GAMA(1)»^X2-GAMA (2)^X3 Yl = -GAmA( 1) ^ Y2-GAMA(2 )♦Yi R23 = sORT((x3.X2)-^*2+(Y3-Y2)^»2) R13=S0RT((X3-Xl)4ff2f(Y3-YlM*2) F3=FACToR^((Xi-X3)/R13^*3+GAMA(l)»(X2-X3>/R2 3**3) RE turn END Function f a { x2 , y 2 , x3 , y 3 ) COMMON/FUNCT/FACTOR, GAMA(2) Xi=-GAMA(1 )^X2-GAMA(2»♦XT Yl=-GAMA(l)yY2-GAMA(2>*Y3 R 2 3 = s O RT((X5-X2»^’^2+(Y3-Y2)’^*2J R13=SQRT((X3-Xl)»*2f(Y3-Yl»»*2) FA=FACT0R*HYl-Y3)/Rl3**3fCAMA(l)»(Y2-Y3»/R2 3»*3) RETURN END FU notion FF ( vx2 ) F5=VX2 Return FNO FUNCTION F 6 ( VY2) FG=VY2 RETURN ENO function F7(VX3) FT=VX3 RE turn END FUNCTION F8(VY3) Ffl=VY3 RE TURN ENO ‘iUti^nUTlNF HTST^MNJM) C P^OGVAM TO CORELATF O lS . )ATA TO MOOFL OAT A. 147 : NGTf.I MAXIMUM NUMBFR OF NTRIFS IN O-C Fllf. IS 150. DOUBLE PRECISIOM QT,QY,nri d im e n s io n QT (150) ,QY ( 150» ,n'JM0B(7) COMMON/HlST/T(2 $S01) ,oMINC(2, 301) $ 0 0 j S (15 J ) , IS A ° , iMAy^ISIAPT 1 , D IF (301) IF(ISTART.GT .0)GO TO 100 10 no 20 1=1,300 T (lÿ l)= 0 # OMINC(1,I)=0. 20 CONTINUE ISTART=1 WR IT F (5,30) 30 FORMAT ( ' SPECIFY INPUT FILE NAMFî SS) R-AD( 5 , 4 0 ) , F ILL 4 0 FORMAT(A5) CA LL IFILE(I ,FILF) RE AD( 1 , 50 ) , IMAX, FCLf^ER, OTl , l(NOUM,QT(I),DonS(I),QY(I),(OUM0 5(J),J=l,7),I=i,IMAX) 50 FORMAT(I10,2n2Q.10/,150(I7,017.10,F8.5,F9.5,2X,3A5,2x,4A5/>) WRITE (9,60) , FILF, FCL^^EP 5.0 FORMAT ( ' INPUT FILF ' , A5, ' WRITTEN WITH PF RI 0 0= ' , 1PD1 5. 9 ) WRITe (5 ,7 o ) 70 FORMAT( ' ERROR 3ARS(1) OR N0T Program BINOBS When planning an observational program for eclipsing binary stars, it is advantageous to know well in advance the time when an eclipse is expected to occur. The Fortran code BINOBS produces a day-by-day chron ological listing of times of occurrence for as many as 20 systems. It is useful to execute the code prior to the observational season each year. A sample of the output from this code is given in table 7. The format is such that the schedules of minima for any one night are con fined to a single page. This allows the observer to carry with him to the observatory only information which is relevant to that night's viewing. TABLE 7 ECLIPSING VARIABLE SCHEDULE OF MINIMA FOR NIGHT BEGINNING ON 7/17 JULIAN DATE: 42977.0000 STAR JD OF MINIMA UNIVERSAL TIME STANDARD TIME DAYLIGHT TIME ATP EG 0.0183 12:26 5:26 6:26 DOCAS 0.0565 13:21 6:21 7:21 XXCEP 0.0599 13:26 6:26 7:26 TWDRA 0,0971 14:19 7:19 8:19 I BOO 0.1858 16:27 9:27 10:27 I BOO 0.4537 22:53 15:53 16:53 I BOO 0.7215 5:18 22:18 23:18 DOCAS 0.7412 5:47 22:47 23:47 BFAUR 0.8443 8:15 1:15 2:15 RYAQR 0.9609 11:03 4:03 5:03 I BOO 0.9893 11:44 4:44 5:44 RZCAS 0.9910 11:47 4:47 5:47 tn O r, fltNOBS.F'i 151 c PiOûRAM TO c a lc u la te FCltPSING VARIABLE OBSERVATION SCHFOUAL, IMPLICIT nOÜBLE PRECISION (A-HtO-Y) 01 ME NSI ON ZS TAR (20 ) , TR NOilN (20 ), PERIOn (? Q) , MAXOA Y ( 12) DIMENSION THOL n (50)$ ZSHOLD(50 )tTSAVF(5n),ZSSAVF(5o) NO Te * ITZONL IS STD* Ttm^ DIF, BeTWieN OB^E'^VATORY AND SMT. IT Z0NE = 7 DATA ( ma X D AY (J ),J = t,lî? > /3 1 ,2 8, 31, 30 ,5 1 ,7 0 ,3 1 ,3 1 ,3 0,^1,3 0,3 1 / 10 TYPE 20 20 FORMAK'IHOW MANY BINARIES BEING CONST PFPE 0? », > ACCEPT 3 0 ,NSTAR 30 FORMAT(I) IF (NSTAR.GT,2 0 .OR. NSTAR.l t • 1 )GO TO 10 00 flO N=l,NSTAR TYPE f+0 4 0 FORMAT( / ' ENTER STAR n AMEI',S) C NOTE: MAXIMUM FIELD WIDTH IS 5. accept 5 0 , zSTAR(N)zSTAR(N)ACCEPT 50 FORMAT(A5 ) TYPE 60 50 FORMAT(' e n te r EPHEMERAL JO, AND PERIOD:», S) ACCEPT 7 0 ,TKNOWN(N), PERIO 0(N) TO FORMAT(2D) 80 L,continue U I 1 U C 00 10 0 N=l,NSTAR TYPE 90,ZSTAR(N),TKNOWN(N),^FRIOO(N) print 90, ZSTAR(N) ,TKN0WN(N),PERI00(N) 90 FORMAT( A in , 2015.8) 100 CONTINUF TYpF 110 110 FORMAT( / ' AT WHAT JO DOES THIS FORCAST BEGIN?»,F) ACCEPT 3 0 ,IBEG T3EG=IBFG TYPE 120 120 FORMAT ( » FOR HQW MANY DAYS? », S) accept 3 0 , L T OP TYPE 130 1 30 FORMA T( » BEGINNING JO IS WHAT MONTH, OAY, YEAR?(12,31,75) % »,S) ACCEPT 140, MON, I oAt E, lYR 140 FORMA T (31) I0ATF=I0ATE-1 IYR=TYR-72 LEAP=M00(IYR,4) IF(LFAP.EO,0)MAXOAY(2)=29 FOLLOWING UPDATES EPHEMERAL JO TO BFGGINING OF FORCAST + + + + ♦«- + 00 170 N=l,NSTAR 00 150 1=1,100000 E= I START=TKN0WM(N)+E»P£RI00(N) I^(START. Gc.TBEG)GO TO 160 150 CONTINUE 160 T Program OCPLOT To obtain a Calcomp plot of an O-C residual file, execute the Fortran code OCPLOT. The only input required is the name of the file which is to be accessed. Plotting specifications and titles are deter mined automatically and a disk file named GRAPH.DAT is written. To complete the plotting, simply run the library code SPLOT which reads this file. .RUN SPLOT (2302,11) Examples of these plots are given in appendix 2. The residual values are represented by asterisks (*). Located above and below each residual is a cross (+) which indicates the observational accuracy of that value. The maximum number of O-C entries which may be plotted by this code is 800. Year zero corresponds to January 1, 1980 and there fore all eclipses observed prior to this date will be plotted as nega tive dates. OCPLOT.F 4 154 CREATE DATA FILE FqR O-C PLOT OM CALCOMP PLOTTER..*. IS JANUARY 1, 1 0 8 ] ...... VISION PERIOD,Tl,TT ^FPOCH(flO(]> ,TT (flOJ ) ,nOBS(flOO) , HOLD ( 8] Q * ,00(7, 800) TYPE lO 10 FORMAT ( ' enter FILENAME: ' , ?:) ACCEPT ?0,FlLE 20 FORMAT(As) call IFILECl*FILF) REAG(1»30)iIMAX,PERIOOtTl, l(NEPOCH(T),TT(I)tOOBS(I) , H]LD(I) , (Oo(J, I ) , J=l, 7» ,I = 1,TMAX| 3 0 FORMA T(T10,2n2Q.10/,800(l7,T17.10,F8.5,F9.5,2X,3A5,2X,VA5/)) YMX=G. □ OBMA x = 0. XMN=0. 03 40 1 = 1 ,IMAX IF (DOOS(I).OT.OOBMAX)nOBMAX= OOBS ( I ) IF (Û3S (HOLD ( I) ) .G T .YmX)YMX=!\8S(H0LD(I)) TT (I) = (TT(I) -442 9 8. ) /3 69. 25 IF(TT(I).LT.XMN)XMN=TT(T) 40 continue YMX=YMX+00DMAX YMAX=0.05 IF(YMX.GT.0.05)YMAX=0.i 0 IF (VMX.GT.0.10)YMAX=0,15 IF(YmX.GT . 0 . 1 5 ) YMAX=Q.2 0 I-(YMX.gT.0.20)YMAX=0.25 IF(YMX.GT.G.25)YMAX=VMX Y MIN=-YMAX XMIN=-1Q. << = 1 IF (yMN.GT.-lO.)GO TO 50 XMlN=-2fl. K< = 2 IF (xMN.GT._20.)G0 TO 50 XM lN = -3 0 . K< = 3 I F ( XMN.GT. - 3 0 . ) Go TO 50 XMIN=-40. K< = 4 IF (XMN.GT . - 4 0 , ) GO TO 50 XM TN = -5 n • KK = 5 I-(XMN.GT.-5 0 .)G0 TO 50 XMIN=-60. K< = 6 I F (xMN.GT.-bO.)GO TO 50 XMIN=-70. K< = 7 IF(XMN.GT.-7 0 .)G0 TO 9 O XM TN = -8 n. K<=4 IF(XMN.GT.-8 0 .)G0 TO 50 XMIN=-9 0, K<=4 I F ( XMN.GT.-9 0 . ) Go TO 50 XMTN=-ino. K< = 5 5 q call OFILE ( 1 , 'GRAPH') MftXr=tMAX/?+l WRITE(1,60) iFILziPLRIOn^^MM^YMINfYMAXtKKfKKiMA XI 6 0 FORMAT ( ' VFRSNO3 ', / ' GR AP ^ ) 1 ', / ' Tl TL F?6 ' , A^>, ' I pf^RI On= ', l'^12.ftt/'XAxIS0GYFARS',/'YAXlSiqo-C RFSlOUALS(lAYs)',/ 2'SPFCS'*F6.Qt ' 0 . ' , 2F9. ' 1 ? S ll,' 2 .08 *,H »' 2 ' , / 3'DATA ST3> ITF(1,70)(TT(T) »HOLG(I»,03QS(T>,T=1,IMAX) 70 FORMAT(AOO( 6F10.6 /) ) IMAX=ImAX/2 WRTTE(ltflO), IMAXtlMAX,IMAXiIMAx»IMAX,lMAX a 0 FORMA T( 'PLOT 010207',15,7'PLOT 040507',15,/'ALTFR02034107',/ 2 'PLOT 010706',I5 ,/'ALTFR05064107*,/'P lot 040705*,15, 3/'ALTFR0203 4?07',/'PLOT 01070 5',15, 4 / 'ALTER0 50 6420 7 ',/'P L O T 0 40 70 5 ' , 1 5 , /'STOP') i^NO FILF i EsjD APPENDIX 3 SPATIAL CONFIGURATION PLOTS In the following plots, the direction to the earth is that of the positive abscissa. 156 157 MODhlL # 67 100 TO 1'600 Y-1 70 . 0 #'T'T%L = ) 0 < ,m -7 0 . 0 b 0 . 0 0 50 . 0 PROJECTED ON PLANE INCLUDING LOS 158 MODEL 67: -100 TO 1 0 0 rp< ZD 0 < 70. 0 -50.0 y0 . 0 PROJECTED ON PLANE INCLuDING LOS son oMiaoioNi ONvid no aniDiiiOdd 0 ■ 0Z > c : d; 00191 01 0)01 Z9 # nuaci-i 6SI 160 MODEL 127 161 RZ CASS I OF^f_ IAE ; E00 TO +800 fC 70. 0 ■■ Oi t 1, . 0 n-rr-> 70, 0 -5 0 . 0 . 0 50. 0 FF F 70, P ‘'A r\ ZD < im I - 7 0 . 0 -50.0 .0 50.0 PF<0 T5 CTF:D ON PLANO INCLLDING LOO 163 RZ CASSIOPRIAC: 0 TO -300 YR Z) < 70. 01 ! ______I -50.0 • .0 50.0 PRO.TRCTRD ON FLANR INCLUDING LO 164 Fs'z CA3SiO[--F:i/\r:; 0 to 300 v t 7 e . 0 ‘L.V'.r fv tV ? \ ! 1# - * I W ê s ê é ik PF^O.TOCTOD ON PLANT INCLUDING LOO 165 F^Z CASSI0F^F:IAE; -300 to -300 TR 1 : . . a m ^ r m ZD 0 < - 1 40. -1,00. .0 1k10. PROTECTED ON PLANE INCLUDING LOS 166 RZ CASSIOPEIAFI; -500 TO - 800 YR 1 0 . Z) 0 < - 210. PROJECTED ON PLANE INCLUDING LOS 167 F^Z CASSIOPZIAZ ; -800 TO 1 1 00 YR ZD < r - 100. 00 PF^OTZCTED ON PLANE INCLUDING LOS 163 F5Z CASSIOPFIIAFI: - 1100 TO 1000 YR 1 4 0 ZD < - 1 40. - 1 0 0 . , 0 1 0 0 . FROTECTFID ON PLANE INCLUDING LOS 169 RZ CASS I OPF_ IAE i -1^00 TO - 1 700 YR 1 4 0 Z) < - 1 4 0 - 100, .0 100. PROJECTED ON PLANE INCLUDING LOS 170 RZ CASSIOPFZIAFI; 1700 TO -2000 YR 2 1 0 ZD .0 < -210 100. FROjfcCTRD ON PLANE INCLUDING LOS 171 RZ CASSIOF^CIAC: - 2000 TO 2300 Y2 ZD < - 2 G 0 . L - 2 0 ? . - ? PF^0tf:CT2D on PLANO INCLNDINC LOS LITERATURE CITED Abramowitz, M., Stegun, I. A. 1965. Handbook of mathematical functions, p. 896, New York: Dover Pub!ications. Allen, C. W. 1963. Astrophysical Quantities, 2nd ed. p. 209, London: Athlone, Batten, A. H,., van Dessel, E. L. 1975. Radial velocities of the binary 70 Ophiuchi. D.A.O., Victoria, Vol. XIV, No. 15, pp. 345-53 (December, 197^)1 Benson, G. S., Williams, J. G. 1971. Resonances in the Neptune-Pluto system. Astron. J ., Vol. 76, No. 2, pp. 167-81 (March, 1971). Chambliss, C. R. 1976. A three-color photoelectric investigation of the eclipsing binary system RZ Cassiopeiae. P.A.S.P., Vol. 88, No. 521, pp. 22-36 (February, 1976). Danby, 0. M. A. 1962. Fundamentals of Celestial Mechanics, pp. 237-9, New York: Macmillan Co. Heintz, W. D. 1969. A statistical study of binary stars. R.A.S.C. Jour., Vol. 63, No. 6, pp. 275-98. H ill, G., Barnes, J. V. 1972. A spectroscopic study of AT Pegasi. P.A.S.P., Vol. 84, pp. 430-2 (June, 1972). Horack, H. G. 1951. A spectrographic study of RZ Cassiopeiae. Ap. J ., Vol. 115, pp. 61-5. Koch, R. S., Wood, F. B. 1963. Finding lis t of eclipsing variables. Flower and Cook Ob. Lavrov, M. I. 1959. Variable Stars, Vol. 12, No. 21. Lucy, L. B., Sweeney, M. A. 1971. Spectroscopic binaries with circular orbits. A.J., Vol. 76, No. 6, pp. 544-56 (August, 1971). Margrave, T. E., Lukes, M. A., Doolittle, J. H., Evenskaas, R. S., MacDonald, J. W., Murray, N. D. 1975. Photoelectric times of minima of RZ Cassiopeiae. I.B.V.S., No. 1019 (July 8, 1975). Moore, J. H., Neubauer, F. J. 1949. Fifth catalogue of the orbital elements of spectroscopic binary stars. Lick Observatory Bulletin, No. 521, pp. 1-18. 172 173 Novotny, E. 1973. Introduction to Stellar Atmospheres and Interiors, pp. 10-1. New York: Oxford University Press. Oliver, B. M. 1972. Project Cyclops: A design study of a system for detecting extraterrestrial intelligent life . NASA CR-114445, pp. 4-15. Opik, E. 1924. Publ. Tartu, 25, part6. Pearce, J. A. 1940. Apsidal rotation of TX Ursae Majoris. P.A.S.P., Vol. 52, pp. 287-8. ------ Rossati, F. 1970. Photoelectric photometry of the binaries RZ Cas siopeiae, VW Cep, W UMa. Mem. Soc. Astron. Ita l., Vol. 41, No. 4, pp. 395-406 (1970). Roy, Archie E. 1965. The Foundations of Astrodynamics, pp. 68-90. Toronto: Macmillan Co. Sahade, J. 1945. Spectrographic observations of the eclipsing varia bles W Ursae Minoris, XZ Sagittarii, and KO Aquilae. Ap.J., Vol. 102, pp. 470-1. Savedoff, M. P. 1951. On e cos w for eclipsing binaries. A.J. , Vol. 56, No. 1, p. 3 (March, 1951). Strack, W. C. and Huff, V. N. 1963. N-body code. NASA TN D-1730, pp. 21-2. Struve, 0. 1949. Proceedings at meeting of the Royal Astronomical Society. Observatory, No. 853, pp. 203-9 (December, 1949). Suffolk, G. C. J. and Black, D. C., Concerning the planetary system of Barnard's star. Icarus (USA), Vol. 19, No. 3, p. 353-7 (July, 1973). Swihart, T. L. 1968. Astrophysics and stellar astronomy, pp. 76, 100, New York: J. Wiley & sons. Inc. Van de Kamp, P. 1962. Elements of astromechanics. IX. Perspective secular changes in radial velocity and proper motion for a star having uniform rectilinear space motion. J. Roy. Astron. Soc. Canada. Vol. 56, No. 6, p. 247-50 (December, 1962). . 1969a. Parallax, proper motion acceleration, and orbital motion of Barnard's star. Astron J. (USA), Vol. 74, No. 2, p. 238-40 (March, 1969). 1969b. Alternate dynamical analysis of Barnard's star. Astron J. (USA), Vol. 74. No. 6, p. 757-9 (August, 1969). 174 1975. Unseen astrometric companions of stars. Annual Review of Astronomy and Astrophysics. Vol. 13, pp. 295-333. Winkler, L. 1966. Blue and yellow photoelectric photometry of the eclipsing variable DO Cassiopeiae. A.J., Vol. 71, No. 1, p. 40-5 (February, 1966). Wood, Frank Bradshaw. 1950. On the change of period of eclipsing variable stars. Ap. J ., Vol. 112, pp. 196-206.