Съдържание

IAO 2021, Практически тур — Задача 13. Observations at the INAF – Abruzzo Astronomical Observatory (OAAB)

Оригинал на условието (PDF)Съобщи за грешка

Всички материали от IAO 2021

IAO 2021 — Practical round (IRAO, α/β/γ) · 12 т.

Practical round. Problems to solve

International Remote Astronomy Olympiad. Milan, Italy, 5–13 XI 2021. Task 12: groups α, γ (β crossed out); task 13: α, β, γ; task 14: β, γ. The question pages carry the round label M&I. The text and matching solution/criteria identify the practical round.

Printed source details

The introduction calls the objects in task 13 open clusters, while question 13.1 says “globular cluster”; both wordings are retained. Table 14.a prints “rm” for Europa and has handwritten “km” for Ganymede and Callisto. The official solution retains “Sun-Eart”, the table-13.b heading refers to questions 12.1–12.3, and the final diagram prints “12th Nov, 021”. These are source defects, not transcription corrections.

Practical Round - Sketches for solutions. For jury job ONLY

These solutions are written for jury members, so they contain some explanations in the form of text. Students are instructed to use only formulas, calculations, drawings, graphs and filling tables. Writing texts is not allowed in the solutions.

Reference inventory

The separately archived constants sheet is labelled Theo (Russian/English). It was inspected as reference context; it supplies no additional practical task or requested answer form. The protractor sheet contains three identical copies; one complete copy is reproduced with task 12.

Условие

The observation nights of December 23, 2021, January 24, 2022 and November 25, 2022 are made available at the “TNT” telescope (on photo 13.1.) of the OAAb (geographical coordinates: $\lambda=13^\circ44^\prime$ , $\varphi=42^\circ39^\prime$ ).

The TNT has a Ritchey-Chretien optical design (two mirrors with hyperbolic curvature), with a primary diameter of 720 mm and a secondary of 185 mm. The overall focal length is 9800 mm.

At the focal plane is mounted a back-illuminated E2V CCD47 with $2048\times2048$ square pixels of $20\times20$ micron size each.

You are the scientific manager of a project that aims to study the optical bands of open stellar clusters of our galaxy listed in Table 13.a. In such table you find:

Column 1: cluster name.
Columns 2 & 3: right ascension and declination of the cluster.
Column 4: angular diameter of the cluster.
Column 5: distance of the cluster in parsecs.

Write in Table 13.b the answers to the following questions:

13.1 Choose for each of the three available dates listed in column 1 the globular cluster that at 00:00 Local Time is the nearest at culmination and write its name in column 2.

13.2 For each of the three selected clusters infer if it can fit entirely into the field of view of the CCD (i.e. if you can get an image of it with one single acquisition) and write the answer as YES or NO in column 3.

13.3 Calculate the radius in light years of the three selected clusters and write them in column 4.

13.1.

13.a

1 · Cluster	2 · RA (2021)	3 · DEC (2021)	4 · Diameter	5 · Distance (pc)
NGC 1039	02h 42m	42°45′	25.2′	470
NGC 1342	03h 31m	37°22′	15.0′	665
NGC 1444	03h 49m	52°38′	4.1′	1000
NGC 1502	04h 08m	62°20′	7.1′	821
NGC 1746	05h 04m	23°46′	45.2′	760
NGC 2129	06h 01m	23°19′	6.1′	2036
NGC 2323	07h 03m	−08°20′	15.3′	998
NGC 2548	08h 14m	−05°45′	30.2′	775

13.b

1 · Date	2 · Cluster	3 · Image with a single acquisition (Yes/Not)	4 · Radius (ly)
23 December 2021
24 January 2022
25 November 2022

Решение

13.1

On Dec 23 the mean Sun has a RA of about $18^{\mathrm h}$ . Hence at local midnight the stars closest to culmination have $\mathrm{RA}\simeq6^{\mathrm h}$ .

Each day the RA of the mean Sun increase of about $3.93^{\mathrm m}$ ; from Dec 23 to Jan 24 lasted 32 days, while from 25 Nov to Dec 23 lasted 28 days.

The RA of the mean Sun on 24 Jan is of about $18^{\mathrm h}+32\cdot3.93\simeq20^{\mathrm h}6^{\mathrm m}$ hence at local midnight the stars closest to culmination have $\mathrm{RA}\simeq8^{\mathrm h}6^{\mathrm m}$ .

The RA of the mean Sun on 25 Nov is of about $18^{\mathrm h}-28\cdot3.93\simeq16^{\mathrm h}10^{\mathrm m}$ hence at local midnight the stars closest to culmination have $\mathrm{RA}\simeq4^{\mathrm h}10^{\mathrm m}$ .

13.2

The length of each CCD side is $2048\cdot20\cdot10^{-6}\,\mathrm m\simeq41\,\mathrm{mm}$ . Taking into account the focal length of the telescope the FoV is a square with a side of $\alpha=\arctan\frac{41\,\mathrm{mm}}{9800\,\mathrm{mm}}\simeq14^\prime$

13.3

Given the angular diameter $\beta$ and the distance $D$ of the clusters, the radius $R$ , after transforming the distance in ly can be computed using the formula:

R=D\cdot\tan\frac{\beta}{2}

13.b – Answers to questions 12.1, 12.2 and 12.3

1 · Date	2 · Cluster	3 · Image with a single acquisition (Yes/Not)	4 · Radius (ly)
23 December 2021	NGC 2129	Yes	5.9
24 January 2022	NGC 2548	Not	11.1
25 November 2022	NGC 1502	Yes	2.8

Practical Round - Basic criteria. For work of Jury

Note. Everywhere terms as “positioning” means “correct positioning”, “values” means “correct values”, “identification” means “correct identification”, etc., ...

N	Description	Points (up to)
1	Identification of the first cluster	2
2	Identification of the second cluster	2
3	Identification of the third cluster	2
4	Indication if the first cluster can be observed with a single acquisition	1
5	Indication if the second cluster can be observed with a single acquisition	1
6	Indication if the third cluster can be observed with a single acquisition	1
7	Estimation of first cluster radius in light years (0.5 points max if the values is not provided in light years)	1
8	Estimation of second cluster radius in light years (0.5 points max if the values is not provided in light years)	1
9	Estimation of third cluster radius in light years (0.5 points max if the values is not provided in light years)	1

Теми и трудност

Трудност: неоценена.

Уреди и наблюдения · Светлина и астрономически измервания · Планиране на наблюдения · Ъглов размер

Предпоставки: Разширена олимпиадна подготовка

Оригинал в Архива: prac-EN.pdf · официални решения: Practical_Round_IRAO_2021_Solutions.pdf · допълнителни данни: Practical_Round_IRAO_2021_Criteria.pdf · допълнителни данни: protractor.pdf · допълнителни данни: Ia21_TABLE_Constants.pdf