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\ft{NEW APSIDAL MOTION DETERMINATION OF THE ECCENTRIC}
\ft{ECLIPSING BINARY V1143~CYGNI}
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The eclipsing binary V1143~Cyg (HR\,7484; HD\,185912; BD+54\degr 2193;
$V_{max} = +5.86$; B$-$V = +0.46) consists of a pair of F5\,V stars 
moving in an eccentric orbit (e = 0.54) and having an orbital 
period of $P_{orb} = 7.64075$ days.  The system is detached with 
both components residing well inside their respective Roche lobes. 
The orbital and stellar properties of V1143~Cyg are very well 
determined from the careful study of Andersen {\em et al.} (1987).  
One of the interesting aspects of this binary, that apparently has 
been overlooked, is that its U, V, W space velocity components, as 
given by Andersen {\em et al.} (1987) of +31, $-$16, $-$2 km/s, are very 
close those of the Hyades cluster (+40, $-$17, $-$3) km/s (Eggen 1960; 
Eggen 1970). (Note that the U, V, W velocity components are measured 
relative to the Sun and that the Eggen system is adopted in which a 
positive U-velocity is in the direction of the Galactic anti-center.)  
Although the similarity between the space motions of the binary and 
the Hyades Moving group could be a coincidence, it is more likely 
that V1143~Cyg is a member.  If this is true, then the binary would 
be coeval with the Hyades, thus having an age of about 600 Myr.  
Knowing the age of a binary, vastly increases its importance for 
testing stellar structure, opacity laws, and evolution models 
({\em e.g.} Guinan 1993).

Because of V1143~Cyg's eccentric orbit and deep, narrow eclipses,
its apsidal motion can be accurately determined from an analysis of
the timings of primary and secondary eclipses.  The apsidal motion 
rate is determined from the change in the displacement of the 
secondary eclipse relative to the primary eclipse ({\em e.g.} 
Guinan and Maloney 1985).  Independent determinations of the apsidal 
motion of V1143~Cyg have been made by Khaliullin (1983) and Gimenez 
and Margrave (1985); they are in good agreement, Khaliullin observing an 
apsidal motion rate of 
$\dot{\omega}_{obs} = 3\fdg 49/100$yr $\pm 0\fdg 38/100$yr 
while Gimenez and Margrave observe 
$\dot{\omega}_{obs} = 3\fdg 36/100$yr $\pm 0\fdg 19/100$yr.  However, Andersen 
{\em et al.} (1987) calculate a somewhat faster theoretical apsidal motion 
of $\dot{\omega} = 4\fdg 25/100$yr $\pm 0\fdg 72/100$yr in which the expected 
relativistic and classical contributions to apsidal motion are 
$\dot{\omega}_{GR} = 1\fdg 86/100$yr and $\dot{\omega}_{cl} = 2\fdg 39/100$yr,
respectively.  The apsidal motion due to classical mechanics results from 
the component stars' departures from spherical symmetry which arises from 
the tidal and rotational deformations of the stars.  The classical term 
depends on the fractional stellar radii, stellar masses, rotation, and 
orbital period, as well as on the distribution of mass inside the stars.  
The masses, radii, and rotation velocities of the components are well known.  
The internal mass distribution of the stars is parameterized by the internal 
structure constants (k2) which are computed from stellar interior and 
evolution models ({\em e.g.} Claret and Gimenez 1992).  The relativistic 
apsidal term arises as a consequence of General Relativity as in the case 
of Mercury's 43''/100yr relativistic apsidal motion.
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Figure 1.  A plot of the primary eclipse of 19 October 1987 taken with the
Str\" omgren ``y'' filter
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Figure 2.  A plot of the displacement of secondary minimum from the half 
period point vs. epoch showing the observed apsidal motion rate
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Photoelectric photometry of V1143~Cyg was conducted with the Jenkins
38-cm reflector at Villanova University Observatory.  The observations
reported here were made on the nights of 17 and 19 October 1987 UT,
using intermediate-bandpass blue ($\lambda_{max}$ = 4530\AA) and yellow 
($\lambda_{max}$ = 5500\AA) interference filters.  These were nights on 
which the secondary and primary minima occur, respectively.  The yellow
filter has characteristics closely matched to the Str\" omgren ``y'' 
filter.  Differential photometry was carried out in the usual manner 
using HD\,185978 (F8; $m_V = +7\fm 8$).  This star had been used in 
previous photometric studies of the system and appears constant in 
light.  The observations were corrected for differential extinction and 
the times were converted to Heliocentric Julian Day Number (HJD).  The
photometry was reduced using a program developed by G. P. McCook.

For illustration, the observations of the primary minimum is presented in 
Figure 1 in which the differential magnitudes, in the sense variable minus 
comparison star (V$-$C), are plotted against HJD for the yellow observations. The mid-times of the secondary and primary eclipses were determined by 
least squares fits of the minima with parabolas and also by bisecting cords 
(see Guinan {\em et al.} 1994).  The two methods yield similar results 
for the blue and yellow data sets of each eclipse.  The measured eclipse 
timings are:

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T (Min\,I) = HJD 2447087.5669 $\pm$ 0\fd 0001
\\
T (Min\,II) = HJD 2447085.5910 $\pm$ 0\fd 0001
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These eclipse timings are very close to the times predicted using the 
light elements of Gimenez and Margrave (1985).  Thus indicating that the
ephemerides given by them are essentially correct.

We added these timings to the photoelectric eclipse timings already
available (see Koch 1977; Khaliullin 1983; Gimenez and Margrave 1985;
Guinan {\em et al.} 1987; Caton and Burns 1993; Lacy and Fox 1994).
However, the last two timings were only of primary eclipse.  We then 
recomputed the rate of apsidal motion for the system.  This was done 
following the procedure of Guinan and Maloney (1985).  Independent linear 
least squares solutions were made of the primary and secondary eclipses, 
respectively, yielding periods of P (min~I) = 7.64075095 $\pm$ 0.00000082 
days and P (min~II) = 7.64072932 $\pm$ 0.00000359 days.  The period 
determination from the primary eclipses is better determined than 
secondary eclipses because the primary eclipse has twice as many timings.  
A plot of the change of the displacement of secondary minimum from the 
half period point (D = $t_{1} + t_{2} - 0.5P$) is shown in Figure 2.  This 
slow variation in the displacement of secondary minimum is due to advance of 
the line of apsides of the orbit and the data yields an apsidal motion rate 
of $\dot{\omega}_{obs} = 3\fdg 52/100$yr $\pm 0\fdg 72/100$yr.  This value 
is nearly identical to those determined previously.  The reason for the 
relatively large error is explained in two ways.  First, there are only 
five independent timings of secondary minima and therefore the apsidal 
motion rate is still not well defined.  Also, in calculating the errors, 
we took the uncertainties in both of the periods determined from the 
analysis of primary and secondary eclipses and propagated them through the 
equations to calculate the total uncertainty in the apsidal motion rate.  
More timings, in particular of secondary eclipses, are necessary to help 
define the apsidal motion rate more precisely, so we plan to obtain 
additional photometry of V1143~Cyg.  In particular, we hope to obtain 
additional timings of the secondary minimum.
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This work was supported, in part, by NSF Grant AST 93-15365 which we
gratefully acknowledge.  This research has made use of the SIMBAD data base,
operated at CDS, Strasbourg, France.
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\beginauthors
\authorsrightcol
Joseph F. BURNS
Edward F. GUINAN
James J. MARSHALL
Dept. of Astronomy and Astrophysics
Villanova University
Villanova, PA 19085
USA
\endauthors
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\references

Andersen, J., Garcia, J. M., Gimenez, A.,  Nordstr\" om, B., 1987, 
	{\it Astron. Astrophys.}, {\bf 174}, 107

Caton, D. B. and Burns, W. C., 1993, {\it I.B.V.S.}, No.\,3900

Claret, A. and Gimenez, A., 1992, {\it Astron. Astrophys. Suppl. Ser.}, {\bf 96}, 255

Eggen, O. J., 1960, {\it M.N.R.A.S.}, {\bf 120}, 540

Eggen, O. J., 1970, {\it Vistas in Astronomy}, {\bf 12}, 367
% Original: Eggen, O. J., 1970, {\it Vistas of Astronomy}, {\bf 12}, 367
% Corrected: Mon Jul 28 17:13:40 MET DST 2003

Gimenez, A. and Margrave, T. E., 1985, {\it Astron. J.}, {\bf 90}, 358

Guinan, E. F. 1993, {\it ASP Conf. Ser.}, {\bf 38}, 1, in New Frontiers 
in Binary Star Research, eds. K.-C. Leung and I.-S. Nha
%Corrected: Wed Jun  1 16:06:43 MEST 2005

Guinan, E. F. and Maloney, F. P., 1985, {\it Astron. J.}, {\bf 90}, 1519

Guinan, E. F., Marshall, J. J., and Maloney, F. P., 1994, {\it I.B.V.S.}, No.\,4101

Guinan, E. F., Najafi, S.-I., Zamani-Noor, F., Boyd, P. T., and 
	S.M. Carroll, 1987, {\it I.B.V.S.}, No.\,3070

Khaliullin, Kh. F., 1983, {\it Astron. Tsirk.}, No.\,1262

Koch R. H., 1977, {\it Astron. J.}, {\bf 82}, 653

Lacy, C. H. and Fox, G. W., 1994, {\it I.B.V.S.},  No.\,4009

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