USAAAO 2020, I кръг — Задача 12

USAAAO National Astronomy Olympiad First Round 02/10/2020-02/16/2020 · 10 февруари 2020 г. · 1 т.

Указания

This exam contains 8 pages and 30 questions. Each question is worth 1 point, so there are 30 points total. Students MUST take the exam between 02/10/2020-02/16/2020. Proctors must scan students’ responses by 11:59 pm PST on 02/16/2020.

PHYSICAL AND ASTRONOMICAL CONSTANTS
cSpeed of light in vacuo2.998×108m s−12.998 \times 10^{8} \mathrm{m\ s^{-1}}
eElementary charge1.602×10−19 C1.602 \times 10^{-19}\ \mathrm{C}
mn\mathrm{m}_nNeutron rest mass1.675×10−27 kg1.675 \times 10^{-27}\ \mathrm{kg}
mp\mathrm{m}_pProton rest mass1.673×10−27 kg1.673 \times 10^{-27}\ \mathrm{kg}
me\mathrm{m}_eElectron rest mass9.110×10−31 kg9.110 \times 10^{-31}\ \mathrm{kg}
hPlanck’s constant6.626×10−34 J s6.626 \times 10^{-34}\ \mathrm{J\ s}
H0\mathrm{H}_0Hubble’s constant70 (km/s)/Mpc
kBoltzmann’s constant1.381×10−23 J K−11.381 \times 10^{-23}\ \mathrm{J\ K^{-1}}
bWien’s constant2.898×10−3 m K2.898 \times 10^{-3}\ \mathrm{m\ K}
GGravitational constant6.673×10−11 N m2 kg−26.673 \times 10^{-11}\ \mathrm{N\ m^{2}\ kg^{-2}}
σ\sigmaStefan-Boltzmann constant5.670×10−8 J m−2 K−4 s−15.670 \times 10^{-8}\ \mathrm{J\ m^{-2}\ K^{-4}\ s^{-1}}
c1\mathrm{c}_1First Radiation Constant (=2πhc2)(= 2\pi hc^2)3.742×10−16 J m2 s−13.742 \times 10^{-16}\ \mathrm{J\ m^{2}\ s^{-1}}
c2\mathrm{c}_2Second Radiation Constant (=hc/k)(= hc/k)1.439×10−2 m K1.439 \times 10^{-2}\ \mathrm{m\ K}
NA\mathrm{N}_AAvogadro constant6.022×1023 mol−16.022 \times 10^{23}\ \mathrm{mol^{-1}}
RGas constant8.314 J K−1 mol−18.314\ \mathrm{J\ K^{-1}\ mol^{-1}}
a0\mathrm{a}_0Bohr radius5.292×10−11 m5.292 \times 10^{-11}\ \mathrm{m}
μB\mu_BBohr magneton9.274×10−24 J T−19.274 \times 10^{-24}\ \mathrm{J\ T^{-1}}
M⊙\mathrm{M}_{\odot}Solar mass1.989×1030 kg1.989 \times 10^{30}\ \mathrm{kg}
R⊙\mathrm{R}_{\odot}Solar radius6.96×108 m6.96 \times 10^{8}\ \mathrm{m}
L⊙\mathrm{L}_{\odot}Solar luminosity3.827×1026 J s−13.827 \times 10^{26}\ \mathrm{J\ s^{-1}}
T⊙\mathrm{T}_{\odot}Solar temperature5770 K
M⊕\mathrm{M}_{\oplus}Earth mass5.976×1024 kg5.976 \times 10^{24}\ \mathrm{kg}
R⊕\mathrm{R}_{\oplus}Mean Earth radius6.371×106 m6.371 \times 10^{6}\ \mathrm{m}
I⊕\mathrm{I}_{\oplus}Earth moment of Inertia8.04×1037 kg m28.04 \times 10^{37}\ \mathrm{kg}\ m^{2}
R☾Mean Moon radius1.737×106 m1.737 \times 10^{6}\ \mathrm{m}
M♃Mean Jupiter mass1.9×1027 kg1.9 \times 10^{27}\ \mathrm{kg}
R♃Mean Jupiter radius7.1492×107 m7.1492 \times 10^{7}\ \mathrm{m}
a♃Mean orbital radius of Jupiter5.2 AU
a☾Mean semimajor axis Moon orbit3.84399×108 m3.84399 \times 10^{8}\ \mathrm{m}
1 light year9.461×1015 m9.461 \times 10^{15}\ \mathrm{m}
1 AUAstronomical Unit1.496×1011 m1.496 \times 10^{11}\ \mathrm{m}
1 pcParsec3.086×1016 m3.086 \times 10^{16}\ \mathrm{m}
1 year3.156×107 s3.156 \times 10^{7}\ \mathrm{s}
1 erg1×10−7 J1 \times 10^{-7}\ \mathrm{J}

ENERGY CONVERSION : 1 joule (J) = 6.2415×10186.2415 \times 10^{18} electronvolts (eV)

Условие

Knowing that the distance between the Sun and Uranus is 2.87×1092.87 \times 10^9 km and Uranus’ revolution period is 17h 14 min, determine the approximate amount of time that the Sun is above the horizon for an observer on the Uranus in the following situations:

I. At the South pole

II. At latitude 30∘30^{\circ}5’N when the declination of the Sun is 10∘10^{\circ}N

A. I = 84 years and II = 17h 14 min

B. I = 21 years and II = 12h 47 min

C. I = 42 years and II = 9h 28 min

D. I = 21 years and II = 8h 37 min

E. I = 42 years and II = 14h 53 min

Отговори

Решение

Оригинал в Архива: 2020_usaaao_first_round.pdf · официални решения: usaaao_first_round_answer_key_2020.pdf