USAAAO 2019, I кръг — Задача 17

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

The Sun’s differential rotation can be estimated with the equation ω=X+Ysin2(ϕ)+Zsin4(ϕ)\omega = X + Ysin^2(\phi) + Zsin^4(\phi), where ω\omega is the angular velocity in degrees per day, ϕ\phi is solar latitude, and XX, YY, and ZZ are constants (equal to 15, -2.5, and -2 degrees per day respectively). Two sunspots are spotted along the same solar meridian, one at 0∘0^{\circ} and the other at 40∘40^{\circ}. Assuming that the sunspots do not disappear or change latitude and move with the same velocity as the surface of the sun, after how many days will the sunspots be aligned once again? Round your answer to the nearest day.

A. 142

B. 202

C. 262

D. 312

E. 372

Отговори

Решение

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