2021USAAAO预赛选择题

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 * 10²⁶ W and radius of 8.51 * 10⁸ 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