IOAA 2013, Теория, кратки задачи — Задача 13

7th International Olympiad on Astronomy & Astrophysics — Theoretical Exam - Short Questions

Table of Constants

Group	Quantity	Value
Earth	Mass ($M_\oplus$)	$5.98\times10^{24}$ kg
Earth	Radius ($R_\oplus$)	$6.38\times10^6$ m
Earth	Acceleration of gravity	9.8 m/s²
Earth	Obliquity of Ecliptic	$23°27^{\prime}$
Earth	Length of Tropical Year	365.2422 mean solar days
Earth	Length of Sidereal Year	365.2564 mean solar days
Earth	Albedo ($a$)	0.39
Moon	Mass	$7.35\times10^{22}$ kg
Moon	Radius	$1.74\times10^6$ m
Moon	Mean distance from Earth	$3.84\times10^8$ m
Moon	Orbital inclination with the Ecliptic	$5.14°$
Moon	Albedo	0.14
Moon	Apparent magnitude (mean full moon)	−12.74
Sun	Mass ($M_\odot$)	$1.99\times10^{30}$ kg
Sun	Luminosity ($L_\odot$)	$3.83\times10^{26}$ W
Sun	Absolute Magnitude ($\mathcal M_\odot$)	4.72 mag
Sun	Angular diameter	0.5 degrees
Sun	Effective Surface Temperature	5800 K
Jupiter	Jupiter’s orbit semi-major axis	5.204 AU
Jupiter	Jupiter’s orbital period	11.8618 yr
Distances and sizes	Diameter of human pupil	6 mm
Distances and sizes	1 AU	$1.50\times10^{11}$ 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 ($G$)	$6.67\times10^{-11}$ N·m²·kg⁻²
Physical constants	Planck constant ($h$)	$6.62\times10^{-34}$ J·s
Physical constants	Boltzmann constant ($k_B$)	$1.38\times10^{-23}$ J·K⁻²
Physical constants	Stefan-Boltzmann constant ($\sigma$)	$5.67\times10^{-8}$ W·m⁻²·K⁻⁴
Physical constants	Hubble constant ($H_0$)	72 km s⁻¹ Mpc⁻¹
Physical constants	Speed of light ($c$)	299,792,458 m/s
Physical constants	Proton mass	938.27 MeV·c⁻²
Physical constants	Deuterium mass	1875.60 MeV·c⁻²
Physical constants	Neutron mass	939.56 MeV·c⁻²
Physical constants	Helium-3 mass	2808.30 MeV·c⁻²
Physical constants	Helium-4 mass	3727.40 MeV·c⁻²

The brightest stars visible from Greece

Star	Designation	α (2000), h m	δ (2000), ° ′	m(V), mag	M(V), mag	B−V	Spectral Type
Alpheratz	α And	00 08	+29 05	2.03	‒0.9	‒0.10	A0 p
Caph	β Cas	00 09	+59 09	2.26	+1.5	+0.34	F2 IV
Schedar	α Cas	00 40	+21 26	2.22	‒1.0	+1.17	K0 II
Diphda	β Cet	00 44	‒17 59	2.04	+0.2	+1.04	K0 III
Mirach	β And	01 10	+35 37	2.06	‒0.4	+1.62	M0 III
Achernar	α Eri	01 38	‒57 15	0.48	‒1.6	‒0.18	B5 IV
Almach	γ And	02 04	+42 20	2.13	‒0.1	+1.20	K2 III
Hamal	α Ari	02 07	+23 28	2.00	+0.2	+1.15	K2 III
Mira	ο Cet	02 19	‒02 59	2.0	‒1.0	+1.42	M6 e
Polaris	α UMi	02 32	+89 16	2.02	‒4.6	+ 0.6	F8 Ib
Algol	β Per	03 08	+40 57	2.2	‒0.3	‒0.1	B8 V
Mirfak	α Per	03 24	+49 51	1.80	‒4.3	+0.48	F5 Ib
Aldebaran	α Tau	04 36	+16 30	0.85	‒0.3	+1.54	K5 III
Rigel	β Ori	05 15	‒08 12	0.11	‒7.0	‒0.03	B8 Ια
Capella	α Aur	05 17	+46 00	0.08	+0.3	+0.80	G8 III
Bellalrix	γ Ori	05 25	+06 21	1.63	‒3.3	‒0.22	B2 III
EINath	β Tau	05 26	+28 36	1.65	‒1.6	‒0.13	B7 III
Mintaka	δ Ori	05 32	‒00 18	2.19	‒6.1	‒0.21	O9.5II
Alnilam	ε Ori	05 36	‒01 12	1.70	‒6.2	‒0.19	B0 Ια
Alnitak	ζ Ori	05 41	‒01 57	1.79	‒5.9	‒0.21	O9.5 Ib
Saiph	κ Ori	05 48	‒09 40	2.05	‒6.8	‒0.18	B0.5 Ια
Betelgeuse	α Ori	05 55	+07 24	0.50	‒5.6	+1.86	M2 Ιab
Menkalinan	β Aur	06 00	+44 57	1.90	+0.6	+0.03	A2 IV
Mirzam	β CMa	06 23	‒17 57	1.98	‒4.5	‒0.24	Bl II
Canopus	α Car	06 24	‒52 42	‒0.73	‒4.7	+0.16	F0 Ib
Alhena	γ Gem	06 38	+16 24	1.93	+0.0	+0.00	A0 IV
Sirius	α CMa	06 45	‒16 43	‒1.45	+1.4	+0.00	Al V
Adhara	ε CMa	06 59	‒28 58	1.50	‒5.0	‒0.22	B2 II
Wezen	δ CMa	07 08	‒26 24	1.84	‒7.3	+0.67	F8 Ιa
Castor	α Gem	07 35	+31 53	1.58	+0.8	+0.04	Al V
Procyon	α CMi	07 39	+05 14	0.35	+2.7	+0.41	F5 IV
Pollux	β Gem	07 45	+28 01	1.15	+1.0	+1.00	K0 III
Naos	ζ Pup	08 04	‒40 00	2.25	‒7.0	‒0.27	Ο5.8
―	γ Vel	08 10	‒47 20	1.83	‒4.0	‒0.26	WC 7
Avior	ε Car	08 23	‒59 30	1.87	‒2.1	+1.30	K0 II
―	δ Vel	08 45	‒54 43	1.95	+0.1	+0.0	A0 V4
Suhail	λ Vel	09 08	‒43 26	2.26	‒4.5	+1.69	K5 Ib
Miaplacidus	β Car	09 13	‒69 43	1.68	‒0.4	+0.00	A0 III

The brightest stars visible from Greece (cont.)

Star	Designation	α (2000), h m	δ (2000), ° ′	m(V), mag	M(V), mag	B−V	Spectral Type
Scutulum	ι Car	09 17	‒59 16	2.24	‒4.5	+0.18	F0 Ib
Alphard	α Hya	09 28	‒08 40	1.99	‒0.4	+1.43	K3 III
Regulus	α Leo	10 08	+11 58	1.35	‒0.6	‒0.11	B7 V
Algeiba	γ Leo	10 20	+19 51	2.1	‒0.5	+1.12	K0 III
Dubhe	α UMa	11 03	+61 45	1.79	‒0.7	+1.06	K0 III
Denebola	β Leo	11 49	+14 34	2.14	+1.6	+0.09	A3 V
Acrux	α Cru	12 27	‒63 06	0.9	‒3.5	‒0.26	Bl IV
Gacrux	γ Cru	12 31	‒57 07	1.64	‒2.5	+1.60	M3 III
Muhlifain	γ Cen	12 42	‒48 58	2.16	‒0.5	‒0.02	A0 III
Mimosa	β Cru	12 48	‒59 41	1.26	‒4.7	‒0.24	B0 III
Alioth	ε UMa	12 54	+55 57	1.78	‒0.2	‒0.02	A0 p
Mizar	ζ UMa	13 24	+54 56	2.09	+0.0	+0.03	A2 V
Spica	α Vir	13 25	‒11 09	0.96	‒3.4	‒0.23	Bl V
―	ε Cen	13 40	‒53 28	2.30	‒3.6	‒0.23	Bl V
Alkaid	η UMa	13 48	+49 19	1.86	‒1.9	‒0.19	B3 V
Hadar	β Cen	14 04	‒60 22	0.60	‒5.0	‒0.23	Bl II
Menkent	θ Cen	14 07	‒36 22	2.06	+1.0	+1.02	K0 III
Arcturus	α Boo	14 16	+19 11	‒0.06	‒0.2	+1.23	K2 IIIp
Rigil Kent	α Cen	14 40	‒60 50	‒0.1	+4.3	+0.7	G2 V
Kochab	β UMi	14 50	+74 09	2.07	‒0.5	+1.46	K4 III
Alphecca	α CrB	15 35	+26 43	2.23	+0.5	‒0.02	A0 V
Antares	α Sco	16 29	‒26 26	1.0	‒4.7	+1.81	Ml Ib
Atria	α TrA	16 49	‒69 02	1.93	‒0.3	+1.43	K4 III
―	ε Sco	16 5O	‒34 18	2.29	+0.7	+1.15	Κ2 ΙΙΙ
Shaula	λ Sco	17 34	‒37 06	1.62	‒3.4	‒0.22	Bl IV
Ras‒Alhague	α Oph	17 35	+12 34	2.07	+0.8	+0.15	A5 III
―	θ Sco	17 37	‒43 00	1.87	‒4.5	+0.40	FO Ι
Eltanin	γ Dra	17 57	+51 29	2.22	‒0.6	+1.52	K5 III
Kaus Australis	ε Sgr	18 24	‒34 23	1.83	‒1.5	‒0.02	B9 IV
Vega	α Lyr	18 37	+38 47	0.04	+0.5	+0.00	AO V
Nunki	σ Sgr	18 55	‒26 18	2.08	‒2.5	‒0.20	B2 V
Altair	α Aql	19 51	+08 52	0.77	+2.3	+0.22	A7 IV
Sadir	γ Cyg	20 22	+40 15	2.23	‒4.7	+0.67	F8 Ib
Peacock	α Pav	20 26	‒56 44	1.93	‒2.9	‒0.20	B3 IV
Deneb	α Cyg	20 41	+45 17	1.25	‒7.3	+0.09	A2 Ia
Al Na' ir	α Gru	22 08	‒46 58	1.74	+0.2	‒0.14	B5 V
―	β Gru	22 42	‒46 53	2.20	–1.5	+ 1.6	M3 II
Fomalhaut	α PsA	22 58	‒29 37	1.16	+1.9	+0.09	A3 V

The brightest stars of the sky with m(V) ≤ 1.00

Star	Designation	α (2000), h m	δ (2000), ° ′	m(V), mag	M(V), mag	B−V	Spectral Type
Sirius	α CMa	06 45	‒16 43	‒1.45	+1.4	+0.00	Al V
Canopus	α Car	06 24	‒52 42	‒0.73	‒4.7	+0.16	F0 Ib
Rigil Kent	α Cen	14 40	‒60 50	‒0.10	+4.3	+0.7	G2 V
Arcturus	α Boo	14 16	+19 11	‒0.06	‒0.2	+1.23	K2 IIIp
Vega	α Lyr	18 37	+38 47	0.04	+0.5	+0.00	AO V
Capella	α Aur	05 17	+46 00	0.08	+0.3	+0.80	G8 III
Rigel	β Ori	05 15	‒08 12	0.11	‒7.0	‒0.03	B8 Ια
Procyon	α CMi	07 39	+05 14	0.35	+2.7	+0.41	F5 IV
Achernar	α Eri	01 38	‒57 15	0.48	‒1.6	‒0.18	B5 IV
Betelgeuse	α Ori	05 55	+07 24	0.50	‒5.6	+1.86	M2 Ιab
Hadar	β Cen	14 04	‒60 22	0.60	‒5.0	‒0.23	Bl II
Altair	α Aql	19 51	+08 52	0.77	+2.3	+0.22	A7 IV
Aldebaran	α Tau	04 36	+16 30	0.85	‒0.3	+1.54	K5 III
Acrux	α Cru	12 27	‒63 06	0.90	‒3.5	‒0.26	Bl IV
Spica	α Vir	13 25	‒11 09	0.96	‒3.4	‒0.23	Bl V
Antares	α Sco	16 29	‒26 26	1.00	‒4.7	+ 1.81	Ml Ib

Условие

Recently in London, because of a very thick layer of fog, the visual magnitude of the Sun, became equal to the (usual – as observed during cloudless nights) magnitude of the full Moon. Assuming that the reduction of the intensity of light due to the fog is given by an exponential equation, calculate the exponential coefficient, $\tau$, which is usually called optical depth.

Решение

Теми и трудност

Трудност: неоценена.

Светлина и астрономически измервания · Междузвездно поглъщане

Предпоставки: Разширена олимпиадна подготовка

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Оригинал в Архива: ShortQuestions.pdf · допълнителни данни: IOAA7-Constants.doc · допълнителни данни: IOAA7-BrightStars-list.docx