USAAAO 2019, I кръг — Задача 8

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

Suppose a spacecraft were orbiting in a low Earth orbit at an altitude of 400 km. The spacecraft makes a single orbital maneuver to place it into a Mars transfer orbit. Delta-v (Δv\Delta v) refers to the change in velocity during an orbital maneuver. What is the Δv\Delta v required for this trans-Mars injection? The semimajor axes of the orbits of Earth and Mars are 1.496×1081.496 \times 10^8 km and 2.279×1082.279 \times 10^8 km, respectively.

A. 2.94 km/s

B. 3.57 km/s

C. 6.12 km/s

D. 10.85 km/s

E. 11.24 km/s

Отговори

Решение

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