IOAA 2016, Теория, английски — Задача 1. True or False

Theoretical Examination · 10 т.

Внимание: Бележка към темата

Both archived English question editions print T12 AstroSat, but both 27-page English worked keys substitute T12 Exoplanets. No matching AstroSat solution was found in the inspected full year inventory. Summary Answer Sheets and Cover Sheet named by the instructions were not found in this archived source pack. Instructions specify 13 questions totalling 300 points; both question editions contain 12 questions totalling 250 points. Printed numerical/formula discrepancies are retained: T8 uses c/lambda_max for nu_max and prints 1233 pi then 3813; T9 numerical velocity denominator lacks a power of ten and the stated semimajor axis is 20933 km; T11.4 prints a direct rather than inverse mass ratio in the radius-cubed relation; T11.7 prose says 166.67 Hz while its mass calculation uses 142.86 Hz. No inferred corrections are substituted.

Instructions to the Contestants

(1) Total time duration of this examination is five hours.

(2) This examination consists of

QuestionsMarks eachTotal
Question 1 to 51010 x 5 = 50 marks
Question 6 to 102020 x 5 = 100 marks
Question 11 to 135050 x 3 = 150 marks
Total300 marks

(3) Inside the envelope you will find

a. Question paper in English

b. Question paper in your native language (if applicable)

c. Table of Constants in English

d. Table of Constants in your native language (if applicable)

e. A set of Summary Answersheets

f. Cover Sheet

(4) Use only black or blue pen for writing. For figures, you may use pencils.

(5) There is no negative marking.

(6) Some marks will be deducted if the final answer is given without detailed solution.

(7) Some marks will be deducted if the final answers have inappropriate number of significant digits, no units or wrong units.

(8) The necessary values of fundamental and astronomical constants should be taken from the Table of Constants provided to you.

(9) Instructions regarding using the answersheets

a. For each question a separate Summary Answersheet has been provided. Final answer(s) for each question / each part of the question must be written in the corresponding box in the Summary Answersheet. Write your contestant code and page number on each Summary Answersheet.

b. You should also show detailed solution in the blank space provided on each Summary Answersheet. If necessary, you can ask for extra blank sheets from the invigilators.

c. Use separate blank sheets for each question.

d. Write your contestant code, question number and page number on FRONT side of each blank sheet. Write your contestant code and page number on the BACK side of each blank sheet.

e. The page numbers should be continuous, i.e., if you use 20 sheets for the entire examination (including the Summary Answersheets), the page numbers should run from 1 to 40.

f. Write only inside the boxed area.

g. For the work that you do not want to be evaluated, cross that part out.

(10) At the end of the examination

a. On the Cover Sheet, clearly write page numbers for each question.

b. Check that you have written your contestant code on all pages.

c. Put the Cover Sheet, all Summary Answersheets, blank sheets and rough sheets inside the envelope. You may keep question paper and Table of Constants with you.

Table of Constants

Fundamental Constants

NameSymbolValue
Speed of light in vacuumcc2.998×108 m s−12.998\times10^8\ \mathrm{m\,s^{-1}}
Planck constanthh6.626×10−34 J s6.626\times10^{-34}\ \mathrm{J\,s}
Boltzmann constantkBk_B1.381×10−23 J K−11.381\times10^{-23}\ \mathrm{J\,K^{-1}}
Stefan-Boltzmann constantσ\sigma5.670×10−8 W m−2 K−45.670\times10^{-8}\ \mathrm{W\,m^{-2}\,K^{-4}}
Elementary chargeee1.602×10−19 C1.602\times10^{-19}\ \mathrm{C}
Gravitational constantGG6.674×10−11 N m2 kg−26.674\times10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}
Gas constantRR8.315 J mol−1 K−18.315\ \mathrm{J\,mol^{-1}\,K^{-1}}
Avogadro constantNAN_A6.022×1023 mol−16.022\times10^{23}\ \mathrm{mol^{-1}}
Wien's displacement constantλmT\lambda_mT2.898×10−3 m K2.898\times10^{-3}\ \mathrm{m\,K}
Mass of electronmem_e9.109×10−31 kg9.109\times10^{-31}\ \mathrm{kg}
Mass of protonmpm_p1.673×10−27 kg1.673\times10^{-27}\ \mathrm{kg}
Mass of neutronmnm_n1.675×10−27 kg1.675\times10^{-27}\ \mathrm{kg}
Atomic mass unituu1.661×10−27 kg1.661\times10^{-27}\ \mathrm{kg}

Astronomical Constants

NameSymbolValue
Parsecpc3.086×1016 m3.086\times10^{16}\ \mathrm{m}
Astronomical unita⊕a_\oplus1.496×1011 m1.496\times10^{11}\ \mathrm{m}
Mass of the SunM⊙M_\odot1.989×1030 kg1.989\times10^{30}\ \mathrm{kg}
Radius of the SunR⊙R_\odot6.955×108 m6.955\times10^8\ \mathrm{m}
Luminosity of the SunL⊙L_\odot3.826×1026 W3.826\times10^{26}\ \mathrm{W}
Apparent magnitude of the Sun at midday−26.72 mag-26.72\ \mathrm{mag}
Solar constant1366 W m−21366\ \mathrm{W\,m^{-2}}
Angular diameter of the Sun30′30'
Mass of the EarthM⊕M_\oplus5.972×1024 kg5.972\times10^{24}\ \mathrm{kg}
Radius of the EarthR⊕R_\oplus6.371×106 m6.371\times10^6\ \mathrm{m}
Tropical year365.242365.242 solar days =3.156×107 s=3.156\times10^7\ \mathrm{s}

Условие

Determine if each of the following statements is True or False. In the Summary Answersheet, tick the correct answer (TRUE / FALSE) for each statement. No justifications are necessary for this question.

T1.1 In a photograph of the clear sky on a Full Moon night with a sufficiently long exposure, the colour of the sky would appear blue as in daytime. [2 т.]

T1.2 An astronomer at Bhubaneswar marks the position of the Sun on the sky at 05:00 UT every day of the year. If the Earth's axis were perpendicular to its orbital plane, these positions would trace an arc of a great circle. [2 т.]

T1.3 If the orbital period of a certain minor body around the Sun in the ecliptic plane is less than the orbital period of Uranus, then its orbit must necessarily be fully inside the orbit of Uranus. [2 т.]

T1.4 The centre of mass of the solar system is inside the Sun at all times. [2 т.]

T1.5 A photon is moving in free space. As the Universe expands, its momentum decreases. [2 т.]

Отговори

Решение

Оригинал в Архива: theory-qp.pdf · официални решения: theory_sol.pdf · допълнителни данни: tableofconstants.pdf · допълнителни данни: tableofconstants.pdf · допълнителни данни: Instructions_theory.pdf · допълнителни данни: Instructions_theory.pdf · допълнителни данни: theory.pdf · допълнителни данни: theory.pdf