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Summary Assumptions ...... 2

Initial data ...... 2

Analysis ...... 13

Conclusion ...... 22

Assumptions Discovered 08/03/1888 at Pola observatory by Semi-major axis: 2.3951 A : 0.16026 : 20 .440 ° Diameter: 29.27 Km

This is reported on Lightcurve database with period = 23.928 hours, amplitude = 0.65 Mag. and quality code 2. Do the period very near to the Earth rotation the light curve coverage is at maximum 75%. On October 2 nd 2012 Frederick Pilcher invited Bassano Bresciano and other Observatories worldwide spreaded to a collaborative observation finalized to a full light curve coverage.

Initial data 273 Atropos was observed between 03/09/2012 and 24/12/2012. Observations cover 85 days span. These sessions was included

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Sessions from Frederick Pilcher (Organ Mesa Observatory)

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Session from Andrea Ferrero (Bigmuskie Observatory)

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Sessions from Julian Oey (Kingsgrove Observatory)

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Sessions from Eduardo M. Alvarez (Observatorio Los Algarrobos Salto Uruguay)

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Session from Raguli Ya. Inasaridze and Otar I. (Kvaratskhelia (Abastumani Astrophysical Observatory)

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Sessions from Yurij N. Krugly (Institute of Astronomy of Kharkiv National University)

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Sessions from Bassano Bresciano Observatory

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Analysis A first check was done with all raw values.

Because sessions comes from different observatory are very different level. These delta comp. was preliminary assigned: 1 12.0 2 12.0 3 12.0 4 0.0 5 0.0 6 0.0 7 0.0 8 0.0 9 0.0 10 0.0 11 0.0 12 0.0 13 0.0 14 0.0 15 0.0 16 0.0 17 0.0 18 0.0 19 0.0 20 0.0 21 4.5 22 4.5 23 3.0 24 3.0 Bassano Bresciano Observatory Jan 2013 273 Atropos rotation time find out Pag.14 ______

After that raw data have this shape.

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A first analysis was done in the range between 10 and 30 hours with step 0.01. This is period spectrum.

It show possible rotation time at: 11.9, 23.9, 35.9 Bassano Bresciano Observatory Jan 2013 273 Atropos rotation time find out Pag.16 ______

An analysis in the range between 11.5 and 12.5 hours with step 0.001 shows this phase diagram.

Good correlation but amplitude don’t match with monomodal lightcurve Bassano Bresciano Observatory Jan 2013 273 Atropos rotation time find out Pag.17 ______

An analysis in the range between 23.5 and 24.5 hours with step 0.001 shows this phase diagram.

Good correlation Bassano Bresciano Observatory Jan 2013 273 Atropos rotation time find out Pag.18 ______

An analysis in the range between 35.5 and 36.5 hours with step 0.001 shows this phase diagram.

Good correlation but 3 minimums and 3 maximums Bassano Bresciano Observatory Jan 2013 273 Atropos rotation time find out Pag.19 ______

The only possible solution is 23.919 hours. Because 24 sessions are too many for a manual alignment a preliminary job was done selecting some session. Session have been selected in order to have a full phase coverage, low noise and long time. Session selected was 1,4,6,10,12,20.23. Delta comps have been adjusted assuming as reference the sessions 1. Others sessions was adjusted running many time period finding trying different delta comp. values util RMS decrease. These was done for all sessions. Each time was found a value minimizing RMS the operation was replied on all other sessions. Process was stopped when any change in any session would make RMS greater.

After that all others session have added in the game. Delta comps have been adjusted assuming as reference the sessions 1. Others sessions (even if already adjusted by step befor) was adjusted running many time period finding trying different delta comp. values util RMS decrease. Each time was found a value minimizing RMS the operation was replied on all other sessions. Process was stopped when any change in any session would make RMS greater. At the end delta comp sessions is 1 12.000 2 12.050 3 12.010 4 -0.060 5 -0.010 6 -0.100 7 -0.060 Bassano Bresciano Observatory Jan 2013 273 Atropos rotation time find out Pag.20 ______

8 -0.060 9 -0.010 10 -0.080 11 -0.050 12 -0.110 13 -0.210 14 -0.030 15 -0.050 16 -0.110 17 -0.130 18 0.000 19 -0.030 20 -0.050 21 4.600 22 4.620 23 3.530 24 3.300

This is the new period spectrum.

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With this phased plot.

Diagram shows 23.924 hours period corresponding to 23h 55m 26 s only 38 s. less than sidereal rotation. Bassano Bresciano Observatory Jan 2013 273 Atropos rotation time find out Pag.22 ______

Conclusion 273 Atropos. It is reported on Lightcurve database with period = 23.928 hours, amplitude = 0.65 Mag. and quality code 2. It was observed to have a full lightcurve coverage an period confirmation. Due the period is very near to the Earth rotation a worldwide collaborative observation was needed. This collaboration full matched the target. Now lightcurve is totally know and period is confirmed without dubt. P = 23.924 ± 0.001 hours with amplitude A = 0.50 ± 0.02 Mag.