Съдържание

Условие Photographs of the solar photosphere Stonyhurst grids Решение

IOAA 2013, Анализ на данни — Задача 2. Question 2

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

You are given 5 recent photographs of the solar photosphere shot at exactly the same time every two days (May 1 – May 9, 2013) in equatorial coordinates. You are also given two transparent Stonyhurst grids, which display heliocentric coordinates (heliocentric longitude, $\ell_\odot$ , and heliocentric latitude, $b_\odot$ ). They cover the interval between April 28 to May 15. As the Earth does not orbit exactly around the Sun’s equator, so, through the year, the solar equator seems to move up and down a little more than 7 degrees from the centre of the solar disc. This angle, $B_0$ , varies sinusoidally through the year. Furthermore, the axis of rotation of the Sun, as seen from the Earth, does not coincide with the axis of rotation of the Earth. The angle on the plane of the sky between the two axes, $P_0$ , also varies though the year. The numerical value of these angles ( $B_0$ and $P_0$ ) are indicated on each of the 5 image of the Sun.

(1) Mark the axis of rotation of the Sun on each photograph.

(2) Choose 3 prominent sunspots that can be followed in all (or most) photographs and mark them as S1, S2 and S3 on the photos. Using the appropriate Stonyhurst grids, find their coordinates $(\ell_\odot,b_\odot)$ for every day (May 1 to May 9) and note them down in Table 1.

Table 1

Date	S1: $\ell_\odot$	S1: $b_\odot$	S2: $\ell_\odot$	S2: $b_\odot$	S3: $\ell_\odot$	S3: $b_\odot$
May 1
May 3
May 5
May 7
May 9

(3) Construct the diagrams $\Delta\ell_\odot/\Delta t$ for each sunspot.

(4) Calculate its synodic period $(P)$ of rotation in days for each sunspot. Write down the result for each sunspot, $P_{S1},P_{S2},P_{S3}$ .

(5) Calculate the average synodic period $(P_\odot)$ of rotation of the Sun in days.

Photographs of the solar photosphere

May 1, 2013 — original solar photograph with P and B angles.

May 3, 2013 — original solar photograph with P and B angles.

May 5, 2013 — original solar photograph with P and B angles.

May 7, 2013 — original solar photograph with P and B angles.

May 9, 2013 — original solar photograph with P and B angles.

Stonyhurst grids

April 28 to May 6 — Stonyhurst grid, −4°.

Решение

Five large photographs of the solar photosphere (adapted from www.spaceweather.com) and the appropriate (and on-scale) Stonyhurst grids will be given to the students (Figure 3A). The photographs given to the students, will not be annotated. Each photograph is accompanied by the angle $B_0$ and $P_0$ of the day of the observation. The student should calculate the rotation of the Sun by measuring the coordinates of at least 3 well recognized sunspots as they follow the rotation of the Sun.

1.

Correctly draw the axis of rotation of the Sun. This can be done by drawing a straight line at an angle of $P_0$ degrees anticlockwise from the vertical for each photograph (note: the photographs are given in equatorial coordinates.) (4 Points)

2.

Choose the correct Stonyhurst grid and place it on each photograph, so that the solar axis on the grid coincides with the solar axis of the photograph. Estimate the heliocentric longitude, $(\ell_\odot)$ , and heliocentric latitude $(b_\odot)$ with the help of the grid. Write down these coordinates in Table 1 for each of the 5 photographs.

Date	S1: $\ell_\odot$	S1: $b_\odot$	S2: $\ell_\odot$	S2: $b_\odot$	S3: $\ell_\odot$	S3: $b_\odot$
May 1	54	17.5	33	18.5	30.5	16
May 3	27	18	6	19	4	16
May 5	3	18.5	-19	18.5	-23	17
May 7	-24	18	-46	18	-49	16
May 9	-49.5	19	-72	18	-77	17

(12 Points)

3.

Construct the diagram $\Delta\ell_\odot/\Delta t$ for each sunspot:

Three official graphs of longitude change for sunspots S1, S2 and S3.

(2 for each graph) (6 Points)

4.

Calculate the rotation $(\Delta\ell_\odot/\Delta t)$ of the Sun for each sunspot.

P_i=8*\frac{360}{\Delta\ell_{\odot i}},\quad P_1=27.8\ \mathrm{days},\quad P_2=27.4\ \mathrm{days},\quad P_3=26.8\ \mathrm{days}.

(3 for each graph) (9 Points)

5.

Calculate the average period of the Sun

P_\odot=(P_1+P_2+P_3)/3=27.3\ \mathrm{days}.

27.3 days (1.5 Point)

Figure 3A. Five photographs of the solar photosphere (top) and the corresponding Stonyhurst grids

Теми и трудност

Трудност: неоценена.

Слънчева система · Планетни конфигурации

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