The Orbit of the Minor Planet (7) Iris

ACTA ASTRONOMICA Vol. 43 (1993) pp. 177±181

by I. Wøodarczyk

Astronomical Observatory of the ChorzÂow Planetarium, 41-501 Chorz Âow 1, P.O. box 10, Poland.

Received December 17, 1992, ®nal version received in May 1993

ABSTRACT

30 precise positions from the ChorzÂow Observatory and 15 observations from 3 others observatories of (7) Iris made in 1991 are used to determine the orbit of this minor planet. The orbit was determined using once the SAO Catalogue and once the PPM Catalogue. The latter orbit ®ts better to all the observations. Key words: Minor planets ± Astrometry

1. TheChorzowÂ Observations

The photographic observations of (7) Iris were made with the photographic

camera 200 1000 mm attached to the refractor 300 4500 mm. The geographical

0 00

h m s

= = h = coordinates of this refractor are 1 15 58.52, 50 17 31. 8, 328 m.

The ORWO plates ZU-21 16 16 cm were measured with the coordinate measur- ing instrument Ascorecord E-2. For the reduction of these plates the Turner method with the complete second- order polynomial was used. On every plate 10 to 14 reference stars were chosen (together 50 stars were considered). The coordinates and the proper motions of

all stars were taken once from the SAO Catalogue for the epoch 19500 and once from the PPM Catalogue for the epoch 2000.0. Our positions of (7) Iris obtained with the SAO Catalogue are given in Table 1. There are observations made in 1991 during the opposition of (7) Iris in Nov. 15th, and published in the Marsden's Minor Planet Circulars (MPC) till 1992 Aug. 13th. There are 30 observations made in our observatory (Marsden code 553) and 15 observations from others observatories. The codes are: 46-Klet Observatory, 657-Climenhage Observatory, Victoria and

675-Palomar Mountain Observatory. Table 1 contains: number of observation, date of observation in UT, observed topocentric position and , referred to the mean epoch 1950.0, and the Marsden code of the observatory (MPC 19 348). All 178 A. A.

Table1

Observations of the minor planet Iris in Aug. 1991.

No UT 1950:0 1950 Code

0 00 1 7.d46545 23h11m08.s01 + 4 50 52. 2 675 2 7.48229 23 11 07.64 + 4 50 55.0 675 3 8.43003 23 10 48.77 + 4 53 21.0 675 4 8.46441 23 10 48.04 + 4 53 25.1 675 5 10.41771 23 10 04.12 + 4 57 46.1 675 6 10.46597 23 10 02.85 + 4 57 51.4 675 7 3.88476 22 53 07.70 + 4 34 44.9 46 8 3.89888 22 53 06.79 + 4 34 40.8 46 9 3.91522 22 53 06.03 + 4 34 39.2 553 10 3.93281 22 53 05.04 + 4 34 36.4 553 11 3.95307 22 53 03.89 + 4 34 32.6 553 12 3.97135 22 53 02.81 + 4 34 27.4 553 13 7.30868 22 50 01.92 + 4 20 37.5 675 14 7.35069 22 49 59.59 + 4 20 25.7 675 15 9.27049 22 48 14.91 + 4 11 27.2 675 16 9.29896 22 48 13.37 + 4 11 21.2 675 17 10.89784 22 46 46.16 + 4 03 20.2 553 18 10.91398 22 46 45.27 + 4 03 16.5 553 19 10.93742 22 46 43.86 + 4 03 09.9 553 20 12.85366 22 45 00.64 + 3 53 04.7 553 21 12.87582 22 44 59.42 + 3 52 59.1 553 22 12.89928 22 44 58.14 + 3 52 50.6 553 23 13.85363 22 44 07.29 + 3 47 37.7 553 24 13.87933 22 44 05.83 + 3 47 29.4 553 25 13.90363 22 44 04.55 + 3 47 21.4 553 26 14.32500 22 43 42.02 + 3 45 02.7 657 27 27.84074 22 33 14.35 + 2 22 48.2 553 28 27.86227 22 33 13.49 + 2 22 39.9 553 29 4.80912 22 29 33.94 + 1 39 50.1 553 30 4.82995 22 29 33.35 + 1 39 42.3 553 31 4.85079 22 29 32.75 + 1 39 33.5 553 32 4.85495 22 29 32.70 + 1 39 32.7 553 33 4.87579 22 29 32.08 + 1 39 25.3 553 34 4.89697 22 29 31.57 + 1 39 18.9 553 35 6.86810 22 28 46.10 + 1 27 43.9 553 36 6.89032 22 28 45.72 + 1 27 35.9 553 37 6.91116 22 28 45.23 + 1 27 28.3 553 38 7.85862 22 28 26.43 + 1 22 01.8 553 39 7.88223 22 28 25.99 + 1 21 53.6 553 40 7.89433 22 28 25.74 + 1 21 49.3 553 41 8.82050 22 28 09.21 + 1 16 37.1 553 42 8.84549 22 28 08.76 + 1 16 28.6 553 43 8.87917 22 28 08.07 + 1 16 17.1 553 44 14.22639 22 29 42.15 + 1 03 44.1 657 45 14.29236 22 29 41.70 + 1 03 24.3 657

Two last observations are for the epoch 2000.0 positions in Table 1 made in ChorzowÂ Observatory (code 553) are reduced from the SAO Catalogue. Vol. 43 179

Let us de®ne standard deviation of position of (7) Iris reduced with Turner

method as n

P 2

(O C )

i =

2 i 1

) (

= 1

n )

( 6

where O is a difference between the catalogue star position and the position y obtained from the measured coordinates x , using 12 plate constants from Turner's

formulae, and n is the number of the stars used in Turner method (usually 10 to 12). The average of the residuals for 30 positions of (7) Iris made in our observatory and reduced from the SAO Catalogue is

SAO 00

= ( )

0. 77 2 T and those from PPM Catalogue is

PPM 00

= ( )

0. 54 3 T

It seems, that the positions of (7) Iris which were reduced from the PPM Catalogue

are more precise. In both calculations of T the reference stars were identical.

2. The Residuals O-C from the Starting Orbital Elements

C To calculate O residuals from the observations the Bielicki and Zioøkowski algorithm for the astrometric positions was used (Bielicki and Zioøkowski 1976). The equations of motion of (7) Iris were integrated numerically by recurrent power series method (Sitarski 1979) and by Everhart method (Everhart 1974). As starting point the elements of (7) Iris published in Efemeridy Malykh Planet 1991 (EMP 1991) were used (Table 2).

Table2 Starting elements from EMP 1991.

Epoch: 1991 Dec. 10.0 E.T.

= =

T 1992 Jan. 30.67034 E.T. 144 79637

= =

q 1 83996119 259 32553 1950.0

= i =

e 0 22895700 5 51309

C Table3contains: numberofobservation(seeTable1), O in rightascension and declination for the SAO and the PPM position respectively. 180 A. A.

Table3

O for the observations from Table 1.

O C ) (O C ) No ( SAO PPM

in R.A in D. in R.A. in D.

00 00 00 1 + 0.00 6 + 0. 2 + 0. 6 + 0. 2 2 + 0.5 + 0.3 + 0.5 + 0.2 3 ± 0.6 + 0.8 ± 0.6 + 0.8 4 + 0.4 ± 0.1 + 0.4 ± 0.1 5 + 0.7 + 0.7 + 0.6 + 0.7 6 + 1.0 + 0.3 + 1.0 + 0.3 7 + 2.1 ± 2.4 + 2.1 ± 2.4 8 + 0.3 ± 3.3 + 0.2 ± 3.3 9 + 3.0 ± 1.0 + 2.5 ± 1.3 10 + 2.9 + 0.2 + 2.4 ± 0.0 11 + 2.7 + 1.0 + 2.0 + 0.7 12 + 1.8 + 0.0 + 1.3 ± 0.1 13 + 1.6 + 0.7 + 1.6 + 0.7 14 + 2.9 + 0.3 + 2.9 + 0.3 15 + 1.8 ± 1.1 + 1.8 ± 1.1 16 + 3.3 + 1.1 + 3.3 + 1.1 17 + 0.8 ± 1.3 + 0.4 ± 1.3 18 + 1.2 ± 0.1 + 0.7 + 0.1 19 ± 0.1 + 0.5 ± 0.5 + 0.6 20 + 1.0 ± 1.9 + 1.0 ± 1.3 21 + 1.3 ± 0.3 + 1.1 + 0.3 22 + 1.7 ± 1.2 + 1.8 ± 0.6 23 + 1.8 ± 2.1 + 2.4 ± 0.5 24 + 1.3 ± 1.9 + 1.5 ± 0.3 25 + 2.3 ± 1.9 + 2.1 ± 0.2 26 + 0.4 ± 0.6 + 0.4 ± 0.6 27 ± 0.1 ± 0.3 + 0.6 ± 0.1 28 ± 0.1 ± 0.4 + 1.3 ± 0.3 29 + 0.3 + 1.2 + 0.5 + 0.7 30 ± 0.0 + 0.9 + 0.6 + 0.5 31 ± 0.5 ± 0.5 ± 0.2 ± 0.5 32 + 0.5 + 0.2 + 0.9 + 0.3 33 ± 0.3 + 0.3 + 0.0 + 0.0 34 + 0.7 + 1.4 + 0.8 ± 0.3 35 ± 1.2 + 1.2 ± 1.0 + 0.2 36 + 0.9 + 0.9 + 0.5 ± 0.0 37 + 0.7 + 0.5 + 0.5 ± 0.5 38 + 1.0 ± 0.2 ± 0.1 ± 0.2 39 + 1.8 ± 0.3 + 1.1 ± 0.3 40 + 1.9 ± 0.5 + 1.0 ± 0.2 41 + 0.9 + 0.0 + 0.8 + 0.2 42 + 1.4 ± 0.1 + 1.2 ± 0.0 43 + 0.7 ± 0.3 + 0.2 ± 0.1 44 + 1.1 + 1.2 + 1.1 + 1.2 45 + 1.6 + 0.6 + 1.6 + 0.6

Let us de®ne the mean residual of (7) Iris position using starting elements s

from EMP 1991 as: n

P 2

(O C )

i =

2 i 1

( )

= 4

s n 6

Vol. 43 181

C where O is a difference between the observed minor planet position and

the calculated right ascension and declination, and n is the number of observa-

tion. Then, if we only use SAO Catalogue for the reduction of the observations,

00 00

s 1. 22. For PPM Catalogue this ®gure is 0. 96 (Table 1). In this case the results for the PPM Catalogue are better then for the SAO Catalogue.

3. Orbital Calculations

Using the Sitarski's procedure of improvement the two following corrected elements were obtained. The ®rst orbit of (7) Iris was calculated by using SAO reduced observations from ChorzowÂ and the observations from others observatories ± it is the SAO orbit. The second one ± the PPM orbit ± was calculated for PPM reduced observations. The result is shown in Table 4. The second orbit, with the

PPM Catalogue, is better adjusted to all the observations. is the mean error.

Table4 The calculated orbits.

Epoch 1991 Dec.10.0 E.T. The SAO orbit The PPM orbit

T 1992 Jan. 30.71626 E.T. 1992 Jan. 30.70346 E.T. .01912 E.T. .01706 E.T.

q 1.84000448 1.83992340 0.00008917 0.00007961

e 0.22903730 0.22904175 0.00004664 0.00004164

144.81150 144.81410 0.00402 0.00801

259.32604 259.32228 1950.0 0.00285 0.00255

i 5.51349 5.51324

0.00026 0.00023

0. 98 0. 87

Acknowledgements. The author wishes to thank prof. Grzegorz Sitarski for his help in preparing this paper and for his calculations of the improved orbits of (7) Iris.

REFERENCES

Bielicki, M., and Zioøkowski, K. 1976, Acta Astron., 26, 371. Everhart, E. 1974, Cel. Mech., 10, 35. Sitarski, G. 1979, Acta Astron., 29, 401.