Съдържание

IOAA 2013, Анализ на данни — Задача 3. Question 3

Оригинал на условието (PDF)Съобщи за грешка

Всички материали от IOAA 2013

7th International Olympiad on Astronomy & Astrophysics — Data analysis

Table of Constants

Group	Quantity	Value
Earth	Mass	$5.98\times10^{24}\ \mathrm{kg}$
Earth	Radius	$6.38\times10^6\ \mathrm{m}$
Earth	Acceleration of gravity	$9.8\ \mathrm{m/s^2}$
Earth	Obliquity of Ecliptic	$23^\circ27^\prime$
Earth	Length of Tropical Year	365.2422 mean solar days
Earth	Length of Sidereal Year	365.2564 mean solar days
Earth	Albedo	0.39
Moon	Mass	$7.35\times10^{22}\ \mathrm{kg}$
Moon	Radius	$1.74\times10^6\ \mathrm{m}$
Moon	Mean distance from Earth	$3.84\times10^8\ \mathrm{m}$
Moon	Orbital inclination with the Ecliptic	$5.14^\circ$
Moon	Albedo	0.14
Moon	Apparent magnitude (mean full moon)	−12.74
Sun	Mass	$1.99\times10^{30}\ \mathrm{kg}$
Sun	Luminosity	$3.83\times10^{26}\ \mathrm{W}$
Sun	Absolute Magnitude	4.72 mag
Sun	Angular diameter	0.5 degrees
Sun	Effective Surface Temperature	5800 K
Jupiter	Orbit semi-major axis	5.204 AU
Jupiter	Orbital period	11.8618 yr
Distances and sizes	Diameter of human pupil	6 mm
Distances and sizes	1 AU	$1.50\times10^{11}\ \mathrm{m}$
Distances and sizes	1 pc	206,265 AU
Distances and sizes	Distance from Sun to Barnard’s Star	1.83 pc
Distances and sizes	Mars orbit semi-major axis	1.52 AU
Physical constants	Gravitational constant (G)	$6.67\times10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$
Physical constants	Planck constant (h)	$6.62\times10^{-34}\ \mathrm{J\,s}$
Physical constants	Boltzmann constant	$1.38\times10^{-23}\ \mathrm{J\,K^{-2}}$
Physical constants	Stefan-Boltzmann constant	$5.67\times10^{-8}\ \mathrm{W\,m^{-2}\,K^{-4}}$
Physical constants	Hubble constant	$72\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$
Physical constants	Speed of light	299,792,458 m/s
Physical constants	Proton mass	$938.27\ \mathrm{MeV}\,c^{-2}$
Physical constants	Deuterium mass	$1875.60\ \mathrm{MeV}\,c^{-2}$
Physical constants	Neutron mass	$939.56\ \mathrm{MeV}\,c^{-2}$
Physical constants	Helium-3 mass	$2808.30\ \mathrm{MeV}\,c^{-2}$
Physical constants	Helium-4 mass	$3727.40\ \mathrm{MeV}\,c^{-2}$

Бележки за изданието

The archive PDF contains questions and inline official answers. The Hyades photograph is already annotated; no unannotated version or Hyades-stars.txt is present in the complete 19-entry year catalogue. All 35 input rows are printed in Question 4 and also supplied in DataHyades.xlsx. Source formula/numbering defects are retained: duplicate solution step 4 in Question 1, Figure 2/Figure 5 references, missing range dash for star 10, and incorrect right-ascension conversion in Question 4 and workbook. The workbook filters differences less than 10 rather than absolute differences. The reference star list also has printed value differences between its tables.

Условие

Figure 2 shows a photograph of the sky in the vicinity of the Hyades open cluster. The V-filter in the Johnson’s photometric system was used. Figure 3 is a chart of the region with known V-magnitudes $(m_V)$ of several stars (note that in order to avoid confusion with the stars, no decimal point is used, i.e. a magnitude $m_V=8.1$ is noted as “81”). Hint: some of the stars may not be in the chart.

Figure 2. Photograph of the sky in the vicinity of the Hyades open cluster — source already annotated.

Figure 3. Sky chart of the region in the vicinity of the Hyades open cluster

(a) Identify as many of the stars shown with a number and an arrow in Figure 3 and mark them on Figure 2.

(b) Comparing the V-magnitudes of the known stars in Figure 2, estimate the V-magnitudes of the stars shown with a number and an arrow in Figure 3.

Решение

The human eye can easily recognize differences of the order of $\Delta m_V=0.1-0.2\ \mathrm{mag}$ . The student should first align the photograph with the chart, which has a different scale and orientation. Then the magnitudes of the stars can easily be recognized. Note: not all arrowed stars can be found in the photograph. (0.5 Point for each star that has been correctly identified and 0.5 point for every correct magnitude within $\pm0.3$ magnitude (18 Points)

Star	3	4	5	6	7	8	9	10	11
m	7.3–7.9	5.3–5.9	5.2–5.8	4.6–5.2	5.2–5.8	4.5–5.1	4.3–4.9	4.9 5.5	5.3–5.9

Stars 1, 2 and 12 are outside the boundaries of the photograph

Теми и трудност

Трудност: неоценена.

Светлина и астрономически измервания · Звездни величини

Предпоставки: Разширена олимпиадна подготовка

Оригинал в Архива: Data-Analysis.pdf · допълнителни данни: IOAA7-BrightStars-list.docx · допълнителни данни: IOAA7-Constants.doc · допълнителни данни: DataHyades.xlsx · допълнителни данни: 130501_P-24.11_B-4.17-rot.jpg · допълнителни данни: 130503_P-23.74_B-3.97_rot.jpg · допълнителни данни: 130505_P-23.34_B-3.76-rot.jpg · допълнителни данни: 130507_P-22.92_B-3.55-rot.jpg · допълнителни данни: 130509_P-22.46_B-3.33_rot.jpg · допълнителни данни: Stonyhurst.3 for Nov 09 to Nov 17 & Dec 28 to Jan 05 & June 28 to July 06 & May 07 to May 15_14cm.jpg · допълнителни данни: Stonyhurst.4 for Jan 06 to Jan 14 & Apr 28 to May 06 & July 07 to July 16 & Oct 31 to Nov 08_14cm.jpg