2020USAAAO预赛选择题 - 版本历史

Dg1200：清空页面

2022-04-03T02:32:12Z

清空页面

2022年4月3日 (日) 02:29 Dg1200

2022-04-03T02:29:34Z

2022年4月3日 (日) 02:05 Dg1200

2022-04-03T02:05:57Z

Dg1200：创建页面，内容为“==题目== 1. On December 21, 2020, Jupiter was at $$(\alpha,\delta)=(20^{h}10^{m},-20°34′)$$. Which constellation was Saturn in? (a) Capricornus (b) Aquarius…”

2022-04-03T01:56:11Z

创建页面，内容为“==题目== 1. On December 21, 2020, Jupiter was at $$(\alpha,\delta)=(20^{h}10^{m},-20°34′)$$. Which constellation was Saturn in? (a) Capricornus (b) Aquarius…”

新页面

==题目==

1. On December 21, 2020, Jupiter was at $$(\alpha,\delta)=(20^{h}10^{m},-20°34′)$$. Which constellation was Saturn in?

(a) Capricornus

(b) Aquarius

(c) Pisces

(d) Aquila

2. What is the spectral type of a star with a luminosity of 5.86 * 10<sup>26</sup> W and radius of 8.51 * 10<sup>8</sup> m?

(a) A

(b) F

(c) G

(d) K

(e) M

3. The exoplanet HD 209458b has a mass of 0.71 Jupiter masses and orbits HD 209458 with an orbital period of 3.53 days. HD 209458 has a mass of 1.15 Solar masses. Assuming that the orbit of HD 209458b is circular (which is a good approximation here) and that its orbit lies perfectly in our line of sight, what is the radial velocity semi-amplitude of HD 209458 due to the orbital motion of HD 209458b, in m/s?

(a) 69.6 m/s

(b) 85.9 m/s

(c) 94.2 m/s

(d) 120.8 m/s

4. The photon number density of a blackbody depends on temperature as $$nd = a(\frac{k_{B}T}{\hbar_{c}})^{n}$$ where $$k_{B}$$ is the Boltzman constant, $$\hbar$$ is the reduced Planck’s constant, $$c$$ is the speed of light and $$T$$ is the blackbody temperature. Here, $$a$$ is a dimensionless numerical constant. What is the value of $$n$$?

(a) 1

(b) 2

(c) 3

(d) 4

5. HD 209458b has a radius of 1.35 Jupiter radii, while the radius of HD 209458 is 1.20 Solar radii. What is the transit depth of HD 209458b, in percent?

(a) 0.013%

(b) 0.13%

(c) 1.3%

(d) 13%

←上一版本		2022年4月3日 (日) 02:32的版本
第1行：		第1行：
−	~~==题目==~~

−	~~1. On December 21, 2020, Jupiter was at $$(\alpha,\delta)=(20^{h}10^{m},-20°34′)$$. Which constellation was Saturn in?~~
−
−	~~(a) Capricornus~~
−
−	~~(b) Aquarius~~
−
−	~~(c) Pisces~~
−
−	~~(d) Aquila~~
−
−	~~2. What is the spectral type of a star with a luminosity of 5.86 * 10<sup>26</sup> W and radius of 8.51 * 10<sup>8</sup> m?~~
−
−	~~(a) A~~
−
−	~~(b) F~~
−
−	~~(c) G~~
−
−	~~(d) K~~
−
−	~~(e) M~~
−
−	3. The exoplanet HD 209458b has a mass of 0.71 Jupiter masses and orbits HD 209458 with an orbital period of 3.53 days. HD 209458 has a mass of 1.15 Solar masses. Assuming that the orbit of HD 209458b is circular (which is a good approximation here) and that its orbit lies perfectly in our line of sight, what is the radial velocity semi-amplitude of HD 209458 due to the orbital motion of HD 209458b, in m/s?
−
−	~~(a) 69.6 m/s~~
−
−	~~(b) 85.9 m/s~~
−
−	~~(c) 94.2 m/s~~
−
−	~~(d) 120.8 m/s~~
−
−	4. The photon number density of a blackbody depends on temperature as $$nd = a(\frac{k_{B}T}{\hbar_{c}})^{n}$$ where $$k_{B}$$ is the Boltzman constant, $$\hbar$$ is the reduced Planck’s constant, $$c$$ is the speed of light and $$T$$ is the blackbody temperature. Here, $$a$$ is a dimensionless numerical constant. What is the value of $$n$$?
−
−	~~(a) 1~~
−
−	~~(b) 2~~
−
−	~~(c) 3~~
−
−	~~(d) 4~~
−
−	~~5. HD 209458b has a radius of 1.35 Jupiter radii, while the radius of HD 209458 is 1.20 Solar radii. What is the transit depth of HD 209458b, in percent?~~
−
−	~~(a) 0.013%~~
−
−	~~(b) 0.13%~~
−
−	~~(c) 1.3%~~
−
−	~~(d) 13%~~
−
−	~~6. Which of the following is a problem of the conventional Big Bang theory that is resolved by the theory of inflation?~~
−
−	~~(a) Under the conventional Big Bang theory, it is extremely unlikely for our universe to be flat or nearly flat today, contrary to observation.~~
−
−	(b) Under the conventional Big Bang theory, it is impossible for the Cosmic Microwave Background to have come into thermal equilibrium by the time of recombination, despite its observed uniform temperature.
−
−	~~(c) The conventional Big Bang theory predicts a huge abundance of magnetic monopoles, while no magnetic monopoles have ever been discovered.~~
−
−	~~(d) All of the above~~
−
−	7. Comet C/2020 F3 (NEOWISE) last reached perihelion on July 3, 2020. Comet NEOWISE has an orbital period of ≈ 4400 years and its eccentricity is 0.99921. What is the perihelion distance of Comet NEOWISE, in AU?
−
−	~~(a) 0.0123 AU~~
−
−	~~(b) 0.212 AU~~
−
−	~~(c) 2.69 AU~~
−
−	~~(d) 26.8 AU~~
−
−	8. An astronomer detected a galaxy and decided to analyze its different parts and physical aspects. The frequency generated by a “spin-flip” transition of atomic hydrogen is $$v_{0} = 1420.406MHz$$, however it was detected on the galaxy as $$v = 1422.73$$. He finds that:
−
−	~~1. Population I stars are (1) and are metal-(2).~~
−
−	~~2. The galaxy is (3) from us with a speed of (4) $$km * s^{-1}$$.~~
−
−	~~Choose the alternative that correctly completes sentences above.~~
−
−	~~(a) (1) young; (2) poor; (3) distancing; (4) 245~~
−
−	~~(b) (1) old; (2) rich; (3) approaching; (4) 490~~
−
−	~~(c) (1)old; (2) poor; (3) distancing; (4) 490~~
−
−	~~(d) (1) young; (2) rich; (3) approaching; (4) 490~~
−
−	~~(e) (1) young; (2) rich; (3) approaching; (4) 245~~
−
−	9. A stable open cluster of about $$N = 1000$$ sun-like stars has an angulardiameter of $$\theta$$ = 30 arc minutes and distance of $$d$$ = 500 pc. Assuming the cluster can be approximated by a sphere of uniform density, estimate the average velocities of stars in the cluster. The gravitational potential energy of a sphere of uniform density and radius $$r$$ is
−
−	~~$$U_{sphere} = -\frac{3}{5}\frac{GM^{2}_{sphere}}{r}$$~~
−
−	~~(a) 507 m/s~~
−
−	~~(b) 643 m/s~~
−
−	~~(c) 894 m/s~~
−
−	~~(d) 1021 m/s~~
−
−	~~(e) 771 m/s~~
−
−	~~10. What would happen to the analemma of the Sun if the obliquity of the Earth’s orbit suddenly went to zero degrees and its eccentricity remained unchanged?~~
−
−	~~(a) The anallema would be perfectly symmetric in both axes and would have the shape of an“8”.~~
−
−	~~(b) The analemma would look like a dot.~~
−
−	~~(c) The analemma would be the arc of a great circle.~~
−
−	~~(d) The analemma would look like a circle.~~
−
−	~~(e) The analemma would be a spherical triangle.~~
−
−	11. Let $$T_{{\odot},C}$$ and $$T_{{\odot},S}$$ be the temperatures at the core and the surface of the sun, respectively. Similarly, let $$T_{A,C}$$ and $$T_{A,S}$$ be the temperatures at the core and surface of the red giant Arcturus, and let $$T_{S,C}$$ and $$T_{S,S}$$ be the temperatures at the core and surface of the white dwarf Sirius B. Which of the following inequalities is true?
−
−	~~(a) $$\frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{A,C}}{T_{A,S}} < \frac{T_{S,C}}{T_{S,S}}$$~~
−
−	~~(b) $$\frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{S,C}}{T_{S,S}} < \frac{T_{A,C}}{T_{A,S}}$$~~
−
−	~~(c) $$\frac{T_{A,C}}{T_{A,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{S,C}}{T_{S,S}}$$~~
−
−	~~(d) $$\frac{T_{S,C}}{T_{S,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{A,C}}{T_{A,S}}$$~~
−
−	~~(e) $$\frac{T_{S,C}}{T_{S,S}} < \frac{T_{A,C}}{T_{A,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}}$$~~
−
−	12. The spectral line $$H_{\alpha}$$ in the spectrum of a star is recorded as having displacement of $${\Delta}{\lambda} = 0.043 {\times} 10^{-10}$$ m. At rest, the spectral line has a wavelength of $${\lambda}_{0} = 6.536 {\times} 10^{-7}$$ m. Calculate the period of rotation for this star, if it is observed from its equatorial plane. We also know: $$R_{star} = 8 {\times} 10^{5}$$ km.
−
−	~~(a) 29.59 days~~
−
−	~~(b) 14.63 days~~
−
−	~~(c) 21.15 days~~
−
−	~~(d) 34.39 days~~
−
−	13. The reflector telescope built by Sir Issac Newton was a f{5 telescope and had a primary mirror of diameter 30mm. He used an eyepiece with a focal length of 5mm. What is the focal length and magnification obtained by this telescope?
−
−	~~(a) 150mm, 30ˆ~~
−
−	~~(b) 300mm, 15ˆ~~
−
−	~~(c) 300mm, 30ˆ~~
−
−	~~(d) 150mm, 15ˆ~~

←上一版本		2022年4月3日 (日) 02:29的版本
第104行：		第104行：

	(e) 771 m/s		(e) 771 m/s
		+
		+	10. What would happen to the analemma of the Sun if the obliquity of the Earth’s orbit suddenly went to zero degrees and its eccentricity remained unchanged?
		+
		+	(a) The anallema would be perfectly symmetric in both axes and would have the shape of an“8”.
		+
		+	(b) The analemma would look like a dot.
		+
		+	(c) The analemma would be the arc of a great circle.
		+
		+	(d) The analemma would look like a circle.
		+
		+	(e) The analemma would be a spherical triangle.
		+
		+	11. Let $$T_{{\odot},C}$$ and $$T_{{\odot},S}$$ be the temperatures at the core and the surface of the sun, respectively. Similarly, let $$T_{A,C}$$ and $$T_{A,S}$$ be the temperatures at the core and surface of the red giant Arcturus, and let $$T_{S,C}$$ and $$T_{S,S}$$ be the temperatures at the core and surface of the white dwarf Sirius B. Which of the following inequalities is true?
		+
		+	(a) $$\frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{A,C}}{T_{A,S}} < \frac{T_{S,C}}{T_{S,S}}$$
		+
		+	(b) $$\frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{S,C}}{T_{S,S}} < \frac{T_{A,C}}{T_{A,S}}$$
		+
		+	(c) $$\frac{T_{A,C}}{T_{A,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{S,C}}{T_{S,S}}$$
		+
		+	(d) $$\frac{T_{S,C}}{T_{S,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{A,C}}{T_{A,S}}$$
		+
		+	(e) $$\frac{T_{S,C}}{T_{S,S}} < \frac{T_{A,C}}{T_{A,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}}$$
		+
		+	12. The spectral line $$H_{\alpha}$$ in the spectrum of a star is recorded as having displacement of $${\Delta}{\lambda} = 0.043 {\times} 10^{-10}$$ m. At rest, the spectral line has a wavelength of $${\lambda}_{0} = 6.536 {\times} 10^{-7}$$ m. Calculate the period of rotation for this star, if it is observed from its equatorial plane. We also know: $$R_{star} = 8 {\times} 10^{5}$$ km.
		+
		+	(a) 29.59 days
		+
		+	(b) 14.63 days
		+
		+	(c) 21.15 days
		+
		+	(d) 34.39 days
		+
		+	13. The reflector telescope built by Sir Issac Newton was a f{5 telescope and had a primary mirror of diameter 30mm. He used an eyepiece with a focal length of 5mm. What is the focal length and magnification obtained by this telescope?
		+
		+	(a) 150mm, 30ˆ
		+
		+	(b) 300mm, 15ˆ
		+
		+	(c) 300mm, 30ˆ
		+
		+	(d) 150mm, 15ˆ

←上一版本		2022年4月3日 (日) 02:05的版本
第52行：		第52行：

	(d) 13%		(d) 13%
		+
		+	6. Which of the following is a problem of the conventional Big Bang theory that is resolved by the theory of inflation?
		+
		+	(a) Under the conventional Big Bang theory, it is extremely unlikely for our universe to be flat or nearly flat today, contrary to observation.
		+
		+	(b) Under the conventional Big Bang theory, it is impossible for the Cosmic Microwave Background to have come into thermal equilibrium by the time of recombination, despite its observed uniform temperature.
		+
		+	(c) The conventional Big Bang theory predicts a huge abundance of magnetic monopoles, while no magnetic monopoles have ever been discovered.
		+
		+	(d) All of the above
		+
		+	7. Comet C/2020 F3 (NEOWISE) last reached perihelion on July 3, 2020. Comet NEOWISE has an orbital period of ≈ 4400 years and its eccentricity is 0.99921. What is the perihelion distance of Comet NEOWISE, in AU?
		+
		+	(a) 0.0123 AU
		+
		+	(b) 0.212 AU
		+
		+	(c) 2.69 AU
		+
		+	(d) 26.8 AU
		+
		+	8. An astronomer detected a galaxy and decided to analyze its different parts and physical aspects. The frequency generated by a “spin-flip” transition of atomic hydrogen is $$v_{0} = 1420.406MHz$$, however it was detected on the galaxy as $$v = 1422.73$$. He finds that:
		+
		+	1. Population I stars are (1) and are metal-(2).
		+
		+	2. The galaxy is (3) from us with a speed of (4) $$km * s^{-1}$$.
		+
		+	Choose the alternative that correctly completes sentences above.
		+
		+	(a) (1) young; (2) poor; (3) distancing; (4) 245
		+
		+	(b) (1) old; (2) rich; (3) approaching; (4) 490
		+
		+	(c) (1)old; (2) poor; (3) distancing; (4) 490
		+
		+	(d) (1) young; (2) rich; (3) approaching; (4) 490
		+
		+	(e) (1) young; (2) rich; (3) approaching; (4) 245
		+
		+	9. A stable open cluster of about $$N = 1000$$ sun-like stars has an angulardiameter of $$\theta$$ = 30 arc minutes and distance of $$d$$ = 500 pc. Assuming the cluster can be approximated by a sphere of uniform density, estimate the average velocities of stars in the cluster. The gravitational potential energy of a sphere of uniform density and radius $$r$$ is
		+
		+	$$U_{sphere} = -\frac{3}{5}\frac{GM^{2}_{sphere}}{r}$$
		+
		+	(a) 507 m/s
		+
		+	(b) 643 m/s
		+
		+	(c) 894 m/s
		+
		+	(d) 1021 m/s
		+
		+	(e) 771 m/s