USAAAO 2021, I кръг — Задача 15

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

An interesting phenomena that happens in the Solar System is the capture of comets in the interstellar medium. Assume that a comet with a mass of 7.15∗10167.15 * 10^{16} kg is captured by the solar system. The perihelion of this comet’s orbit after it is captured is equal to 4.64 AU, and its velocity with respect to the Sun before being captured by the Solar System was very small. Calculate the velocity of the comet at the perihelion.

(a) 87.1 km/s

(b) 45.9 km/s

(c) 5.67 km/s

(d) 105.4 km/s

(e) 19.6 km/s

Отговори

Решение

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