USAAAO 2021, I кръг — Задача 16

USAAAO 2021 - First Round · 30 януари 2021 г.

PHYSICAL AND ASTRONOMICAL CONSTANTS
cSpeed of light in vacuum2.998×108m 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 mass1.6725×10−27 kg1.6725 \times 10^{-27}\ \mathrm{kg}
me_eElectron rest mass9.110×10−31 kg9.110 \times 10^{-31}\ \mathrm{kg}
mHe_{He}Helium-4 rest mass6.644×10−27 kg6.644 \times 10^{-27}\ \mathrm{kg}
hPlanck’s constant6.626×10−34 J s6.626 \times 10^{-34}\ \mathrm{J\ s}
H0_0Hubble’s constant70 (km/s)/Mpc
kB_BBoltzmann’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_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}
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}}
M⊙_\odotSolar mass1.989×1030 kg1.989 \times 10^{30}\ \mathrm{kg}
R⊙_\odotSolar radius6.96×108 m6.96 \times 10^{8}\ \mathrm{m}
L⊙_\odotSolar luminosity3.827×1026 J s−13.827 \times 10^{26}\ \mathrm{J\ s^{-1}}
T⊙_\odotSolar temperature5770 K
M⊕_\oplusEarth mass5.976×1024 kg5.976 \times 10^{24}\ \mathrm{kg}
R⊕_\oplusMean Earth radius6.371×106 m6.371 \times 10^{6}\ \mathrm{m}
I⊕_\oplusEarth 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 sidereal day86164 s
1 erg1×10−7 J1 \times 10^{-7}\ \mathrm{J}
1 bar105 N m−210^{5}\ \mathrm{N}\ m^{-2}

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

Условие

In a certain day, when it is 0h UT, the sidereal time of Prime Meridian is 5h 56min 9.4s. For this day, with start and end based on UT, find the civil time of Chicago, whose longitude and time zone are respectively, 87.65004722o^{o} W and UT-6, when the sidereal time there is 20h. The difference between solar time and sidereal time SHOULD be accounted for.

(a) 14h 1min 32s

(b) 13h 26min 17s

(c) 14h 36min 47s

(d) 14h 0min 43s

(e) 13h 51min 11s

Отговори

Решение

Оригинал в Архива: usaaao2021_exam1.pdf · официални решения: usaaao2021_exam1_solutions.pdf