USAAAO 2019, I кръг — Задача 24

USAAAO National Astronomy Olympiad First Round 01/26/2019-02/01/2019 · 26 януари 2019 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 01/26/2019-02/01/2019. Proctors must scan students’ responses by 11:59 pm PST on 02/01/2019.

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_nNeutron rest mass1.675×10−27 kg1.675 \times 10^{-27}\ \mathrm{kg}
mp_pProton rest mass1.673×10−27 kg1.673 \times 10^{-27}\ \mathrm{kg}
me_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}
ℏ\hbarDirac’s constant (=h/2π= h/2\pi)1.055×10−34 J s1.055 \times 10^{-34}\ \mathrm{J\ s}
kBoltzmann’s constant1.381×10−23 J K−11.381 \times 10^{-23}\ \mathrm{J\ K^{-1}}
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_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_2Second Radiation Constant (=hc/k= hc/k)1.439×10−2 m K1.439 \times 10^{-2}\ \mathrm{m\ K}
εo\varepsilon_oPermittivity of free space8.854×10−12 C2 N−1 m−28.854 \times 10^{-12}\ \mathrm{C^{2}\ N^{-1}\ m^{-2}}
μo\mu_oPermeability of free space4π×10−7 H m−14\pi \times 10^{-7}\ \mathrm{H\ m^{-1}}
NA_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_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}}
α\alphaFine structure constant (=1/137.0= 1/137.0)7.297×10−37.297 \times 10^{-3}
M⊙_{\odot}Solar mass1.989×1030 kg1.989 \times 10^{30}\ \mathrm{kg}
R⊙_{\odot}Solar radius6.96×108 m6.96 \times 10^{8}\ \mathrm{m}
L⊙_{\odot}Solar luminosity3.827×1026 J s−13.827 \times 10^{26}\ \mathrm{J\ s^{-1}}
T⊙_{\odot}Solar temperature5770 K
M⊕_{\oplus}Earth mass5.976×1024 kg5.976 \times 10^{24}\ \mathrm{kg}
R⊕_{\oplus}Mean Earth radius6.371×106 m6.371 \times 10^{6}\ \mathrm{m}
RMean Mars radius3.390×106 m3.390 \times 10^{6}\ \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

Two amateur astronomers A and B living in Ecuador are standing on the Equator at the Galapagos Islands (height 0 m, longitude 91∘91^{\circ} W) and Volcan Cayambe (height 5790 m, longitude 78∘78^{\circ} W) respectively. What are the differences (in degrees) of the altitudes from the horizon and zenith distances of the Sun measured by these two astronomers on March 20, 2019 when it is local noon for observer B? Neglect refraction and give your answer to the nearest degree.

A. Difference in altitudes: 15, Difference in zenith distances: 13.

B. Difference in altitudes: 13, Difference in zenith distances: 13.

C. Difference in altitudes: 13, Difference in zenith distances: 15.

D. Difference in altitudes: 11, Difference in zenith distances: 13.

Отговори

Решение

Оригинал в Архива: 2019_usaaao_first_round.pdf · официални решения: usaaao_first_round_answer_key.pdf