IOAA 2013, Теория, кратки задачи — Задача 5

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

The optical spectrum of a galaxy, whose distance had been measured to be 41.67 Mpc, showed the Balmer Hα line ($\lambda_o=656.3$ nm) redshifted to $\lambda=662.9$ nm.

a Use this distance to calculate a value of the Hubble constant, $H_o$.

b Using your results, estimate the Hubble time of the Universe.

Решение

Теми и трудност

Трудност: неоценена.

Галактики и космология · Разширение на Вселената

Предпоставки: Разширена олимпиадна подготовка

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