The Orbit of the Minor Planet (7) Iris

ACTA ASTRONOMICA Vol. 43 (1993) pp. 177–181 The Orbit of the Minor Planet (7) Iris by I. W ł o d a r c z y k Astronomical Observatory of the Chorzo´w Planetarium, 41-501 Chorzo´w 1, P.O. box 10, Poland. Received December 17, 1992, final version received in May 1993 ABSTRACT 30 precise positions from the Chorzo´w 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 fits better to all the observations. Key words: Minor planets – Astrometry <ul style="display: flex;"><li style="flex:1">1. The Chorzow Observations </li><li style="flex:1">´</li></ul>The photographic observations of (7) Iris were made with the photographic camera 200 1000 mm attached to the refractor 300 4500 mm. The geographical s<ul style="display: flex;"><li style="flex:1">coordinates of this refractor are </li><li style="flex:1">1h15m58.52, </li><li style="flex:1">50 17 31. 8, </li><li style="flex:1">328 m. </li></ul>The ORWO plates ZU-21 16 16 cm were measured with the coordinate measuring instrument Ascorecord E-2. For the reduction of these plates the Turner method with the complete secondorder 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 1950 0 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. T a b l e 1 Observations of the minor planet Iris in Aug. 1991. <ul style="display: flex;"><li style="flex:1">No </li><li style="flex:1">UT </li><li style="flex:1">Code </li></ul><ul style="display: flex;"><li style="flex:1">1950 0 </li><li style="flex:1">1950 </li></ul>12 7d.46545 23h11m08.s01 + 4 50 52. 2 675 7.48229 23 11 07.64 8.43003 23 10 48.77 8.46441 23 10 48.04 10.41771 23 10 04.12 10.46597 23 10 02.85 3.88476 22 53 07.70 3.89888 22 53 06.79 3.91522 22 53 06.03 3.93281 22 53 05.04 3.95307 22 53 03.89 3.97135 22 53 02.81 7.30868 22 50 01.92 7.35069 22 49 59.59 9.27049 22 48 14.91 9.29896 22 48 13.37 + 4 50 55.0 + 4 53 21.0 + 4 53 25.1 + 4 57 46.1 + 4 57 51.4 + 4 34 44.9 + 4 34 40.8 + 4 34 39.2 + 4 34 36.4 + 4 34 32.6 + 4 34 27.4 + 4 20 37.5 + 4 20 25.7 + 4 11 27.2 + 4 11 21.2 + 4 03 20.2 + 4 03 16.5 + 4 03 09.9 + 3 53 04.7 + 3 52 59.1 + 3 52 50.6 + 3 47 37.7 + 3 47 29.4 + 3 47 21.4 + 3 45 02.7 + 2 22 48.2 + 2 22 39.9 + 1 39 50.1 + 1 39 42.3 + 1 39 33.5 + 1 39 32.7 + 1 39 25.3 + 1 39 18.9 + 1 27 43.9 + 1 27 35.9 + 1 27 28.3 + 1 22 01.8 + 1 21 53.6 + 1 21 49.3 + 1 16 37.1 + 1 16 28.6 + 1 16 17.1 + 1 03 44.1 + 1 03 24.3 675 675 675 675 675 46 34567<ul style="display: flex;"><li style="flex:1">8</li><li style="flex:1">46 </li></ul><ul style="display: flex;"><li style="flex:1">9</li><li style="flex:1">553 </li></ul>553 553 553 675 675 675 675 553 553 553 553 553 553 553 553 553 657 553 553 553 553 553 553 553 553 553 553 553 553 553 553 553 553 553 657 657 10 11 12 13 14 15 16 17 10.89784 22 46 46.16 18 10.91398 22 46 45.27 19 10.93742 22 46 43.86 20 12.85366 22 45 00.64 21 12.87582 22 44 59.42 22 12.89928 22 44 58.14 23 13.85363 22 44 07.29 24 13.87933 22 44 05.83 25 13.90363 22 44 04.55 26 14.32500 22 43 42.02 27 27.84074 22 33 14.35 28 27.86227 22 33 13.49 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 4.80912 22 29 33.94 4.82995 22 29 33.35 4.85079 22 29 32.75 4.85495 22 29 32.70 4.87579 22 29 32.08 4.89697 22 29 31.57 6.86810 22 28 46.10 6.89032 22 28 45.72 6.91116 22 28 45.23 7.85862 22 28 26.43 7.88223 22 28 25.99 7.89433 22 28 25.74 8.82050 22 28 09.21 8.84549 22 28 08.76 8.87917 22 28 08.07 44 14.22639 22 29 42.15 45 14.29236 22 29 41.70 Two last observations are for the epoch 2000.0 positions in Table 1 made in Chorzo´w Observatory (code 553) are reduced from the SAO Catalogue. Vol. 43 179 Let us define standard deviation of position of (7) Iris reduced with Turner method as 2<ul style="display: flex;"><li style="flex:1">1</li><li style="flex:1">2</li></ul>1 6<ul style="display: flex;"><li style="flex:1">where </li><li style="flex:1">is a difference between the catalogue star position and the position </li></ul>obtained from the measured coordinates , using 12 plate constants from Turner’s formulae, and 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 <ul style="display: flex;"><li style="flex:1">0. 77 </li><li style="flex:1">2</li></ul>and those from PPM Catalogue is PPM <ul style="display: flex;"><li style="flex:1">0. 54 </li><li style="flex:1">3</li></ul>It seems, that the positions of (7) Iris which were reduced from the PPM Catalogue are more precise. In both calculations of the reference stars were identical. 2. The Residuals O-C from the Starting Orbital Elements <ul style="display: flex;"><li style="flex:1">To calculate </li><li style="flex:1">residuals from the observations the Bielicki and Ziołkowski </li></ul>algorithm for the astrometric positions was used (Bielicki and Ziołkowski 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). T a b l e 2 Starting elements from EMP 1991. Epoch: 1991 Dec. 10.0 E.T. 1992 Jan. 30.67034 E.T. 1 83996119 0 22895700 144 79637 259 32553 1950.0 5 51309 <ul style="display: flex;"><li style="flex:1">Table 3 contains: numberofobservation (see Table 1), </li><li style="flex:1">in rightascension </li></ul>and declination for the SAO and the PPM position respectively. 180 A. A. T a b l e 3 for the observations from Table 1. <ul style="display: flex;"><li style="flex:1">No </li><li style="flex:1">SAO </li><li style="flex:1">PPM </li></ul>in R.A in D. in R.A. in D. <ul style="display: flex;"><li style="flex:1">+ 0. 6 + 0. 2 + 0. 6 + 0. 2 </li><li style="flex:1">1</li></ul><ul style="display: flex;"><li style="flex:1">2</li><li style="flex:1">+ 0.5 </li></ul>– 0.6 + 0.4 + 0.7 + 1.0 + 2.1 + 0.3 + 3.0 + 2.9 + 2.7 + 1.8 + 1.6 + 2.9 + 1.8 + 3.3 + 0.8 + 1.2 – 0.1 + 1.0 + 1.3 + 1.7 + 1.8 + 1.3 + 2.3 + 0.4 – 0.1 – 0.1 + 0.3 – 0.0 – 0.5 + 0.5 – 0.3 + 0.7 – 1.2 + 0.9 + 0.7 + 1.0 + 1.8 + 1.9 + 0.9 + 1.4 + 0.7 + 1.1 + 1.6 + 0.3 + 0.8 – 0.1 + 0.7 + 0.3 – 2.4 – 3.3 – 1.0 + 0.2 + 1.0 + 0.0 + 0.7 + 0.3 – 1.1 + 1.1 – 1.3 – 0.1 + 0.5 – 1.9 – 0.3 – 1.2 – 2.1 – 1.9 – 1.9 – 0.6 – 0.3 – 0.4 + 1.2 + 0.9 – 0.5 + 0.2 + 0.3 + 1.4 + 1.2 + 0.9 + 0.5 – 0.2 – 0.3 – 0.5 + 0.0 – 0.1 – 0.3 + 1.2 + 0.6 + 0.5 – 0.6 + 0.4 + 0.6 + 1.0 + 2.1 + 0.2 + 2.5 + 2.4 + 2.0 + 1.3 + 1.6 + 2.9 + 1.8 + 3.3 + 0.4 + 0.7 – 0.5 + 1.0 + 1.1 + 1.8 + 2.4 + 1.5 + 2.1 + 0.4 + 0.6 + 1.3 + 0.5 + 0.6 – 0.2 + 0.9 + 0.0 + 0.8 – 1.0 + 0.5 + 0.5 – 0.1 + 1.1 + 1.0 + 0.8 + 1.2 + 0.2 + 1.1 + 1.6 + 0.2 + 0.8 – 0.1 + 0.7 + 0.3 – 2.4 – 3.3 – 1.3 – 0.0 + 0.7 – 0.1 + 0.7 + 0.3 – 1.1 + 1.1 – 1.3 + 0.1 + 0.6 – 1.3 + 0.3 – 0.6 – 0.5 – 0.3 – 0.2 – 0.6 – 0.1 – 0.3 + 0.7 + 0.5 – 0.5 + 0.3 + 0.0 – 0.3 + 0.2 – 0.0 – 0.5 – 0.2 – 0.3 – 0.2 + 0.2 – 0.0 – 0.1 + 1.2 + 0.6 345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 2Let us define the mean residual from EMP 1991 as: of (7) Iris position using starting elements 2<ul style="display: flex;"><li style="flex:1">1</li><li style="flex:1">2</li></ul>4 6Vol. 43 181 <ul style="display: flex;"><li style="flex:1">where </li><li style="flex:1">is a difference between the observed minor planet position and </li></ul>the calculated right ascension and declination, and is the number of observation. Then, if we only use SAO Catalogue for the reduction of the observations, 1. 22. For PPM Catalogue this figure 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 first orbit of (7) Iris was calculated by using SAO reduced observations from Chorzo´w 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 <ul style="display: flex;"><li style="flex:1">PPM Catalogue, is better adjusted to all the observations. </li><li style="flex:1">is the mean error. </li></ul>T a b l e 4 The calculated orbits. Epoch 1991 Dec.10.0 E.T. <ul style="display: flex;"><li style="flex:1">The SAO orbit </li><li style="flex:1">The PPM orbit </li></ul>1992 Jan. 30.71626 E.T. 1992 Jan. 30.70346 E.T. <ul style="display: flex;"><li style="flex:1">.01912 E.T. </li><li style="flex:1">.01706 E.T. </li></ul>1.84000448 0.00008917 1.83992340 0.00007961 0.22903730 0.00004664 0.22904175 0.00004164 144.81150 0.00402 144.81410 0.00801 259.32604 0.00285 259.32228 1950.0 0.00255 5.51349 0.00026 5.51324 0.00023 <ul style="display: flex;"><li style="flex:1">0. 98 </li><li style="flex:1">0. 87 </li></ul>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 Ziołkowski, K. 1976, Acta Astron., 26, 371. Everhart, E. 1974, Cel. Mech., 10, 35. Sitarski, G. 1979, Acta Astron., 29, 401.

The Orbit of the Minor Planet (7) Iris

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