IOAA 2017, Теория — Задача 1. The Large Magellanic Cloud in Phuket

IOAA 2017 — Theoretical Examination · 10 т.

Original Examination Instructions

  1. The theoretical examination lasts for 5 hours and is worth a total of 300 marks.

  2. Dedicated IOAA Summary Answer Sheets are provided for writing your answers. Enter the final answers into the appropriate boxes in the corresponding Summary Answer Sheet. On each Summary Answer Sheet, please fill in

    • Student Code (Country Code and 1 digit)

  3. There are Answer Sheets for carrying out detailed work/rough work. On each Answer Sheet, please fill in

    • Student Code (Country Code and 1 digit)
    • Question no.
    • Page no. and total number of pages.

  4. Start each problem on a separate Answer Sheet. Please write only on the printed side of the sheet. Do not use the reverse side. If you have written something on any sheet which you do not want to be evaluated, cross it out.

  5. Use as many mathematical expressions as you think may help the evaluator to better understand your solutions. The evaluator may not understand your language. If it is necessary to explain something in words, please use short phrases (if possible in English).

  6. You are not allowed to leave your work desk without permission. If you need any assistance (malfunctioning calculator, need to visit a restroom, need more Answer Sheets, etc.), please draw the attention of the proctor using the Help card.

  7. The beginning and end of the examination will be indicated by a long sound signal. Additionally, there will be a buzzer sound, fifteen minutes before the end of the examination (before the final sound signal).

  8. At the end of the examination you must stop writing immediately. Sort and put your sheets in separate stacks, a) Stack 1: Summary Answer Sheets, Answer Sheets of part 1
    b) Stack 2: Summary Answer Sheets, Answer Sheets of part 2
    c) Stack 3: Summary Answer Sheets, Answer Sheets of part 3
    d) Stack 4: question papers and paper sheets you do not want to be graded.

  9. Wait at your table until your envelope is collected. Once all envelopes are collected, your student guide will escort you out of the examination room.

  10. A list of constants and a table of the mark distribution for this exam are given on the next two pages.

Original List of Constants

Earth

QuantityValue
Mass (M⊕M_\oplus)5.98×10245.98\times10^{24} kg
Radius (R⊕R_\oplus)6.38×1066.38\times10^6 m
Acceleration of gravity (gg)9.8m⋅s−19.8 \mathrm{m\cdot s^{-1}}
Obliquity of Ecliptic23∘27′23^\circ27'
Length of Tropical Year365.2422 mean solar days
Length of Sidereal Year365.2564 mean solar days
Albedo0.39

Moon

QuantityValue
Mass (M with subscript ☾)7.35×10227.35\times10^{22} kg
Radius (R with subscript ☾)1.74×1061.74\times10^6 m
Mean distance from Earth3.84×1083.84\times10^8 m
Orbital inclination with the Ecliptic5.14∘5.14^\circ
Albedo0.14
Apparent magnitude (mean full moon)−12.74

Sun

QuantityValue
Mass (M⊙M_\odot)1.99×10301.99\times10^{30} kg
Radius (R⊙R_\odot)6.96×1086.96\times10^8 m
Luminosity (L⊙L_\odot)3.83×10263.83\times10^{26} W
Absolute Magnitude (M⊙\mathcal M_\odot)4.80 mag
Angular diameter0.5 degrees
Rotational velocity in the Galaxy220km s−1220 \mathrm{km\,s^{-1}}
Distance from Galactic centre8.5 kpc

Jupiter

QuantityValue
Mass1.89×10271.89\times10^{27} kg
Orbital semi-major axis5.20 au
Orbital period11.86 year

Saturn

QuantityValue
Mass5.68×10265.68\times10^{26} kg
Orbital semi-major axis9.58 au
Orbital period29.45 year

Physical constants

QuantityValue
1 au1.50×10111.50\times10^{11} m
1 pc206,265 au
Gravitational constant (GG)6.67×10−11N⋅m2⋅kg−26.67\times10^{-11} \mathrm{N\cdot m^2\cdot kg^{-2}}
Planck constant (hh)6.62×10−34J⋅s6.62\times10^{-34} \mathrm{J\cdot s}
Boltzmann constant (kBk_B)1.38×10−23J⋅K−11.38\times10^{-23} \mathrm{J\cdot K^{-1}}
Stefan-Boltzmann constant (σ\sigma)5.67×10−8W⋅m−2⋅K−45.67\times10^{-8} \mathrm{W\cdot m^{-2}\cdot K^{-4}}
Hubble constant (H0H_0)67.8km s−1 Mpc−167.8 \mathrm{km\,s^{-1}\,Mpc^{-1}}
Speed of light in vacuum (cc)299,792,458m⋅s−1299,792,458 \mathrm{m\cdot s^{-1}}
Proton mass938.27MeV⋅c−2938.27 \mathrm{MeV\cdot c^{-2}}
Deuterium mass1875.60MeV⋅c−21875.60 \mathrm{MeV\cdot c^{-2}}
Neutron mass939.56MeV⋅c−2939.56 \mathrm{MeV\cdot c^{-2}}
Helium-3 mass2808.30MeV⋅c−22808.30 \mathrm{MeV\cdot c^{-2}}
Helium-4 mass3727.40MeV⋅c−23727.40 \mathrm{MeV\cdot c^{-2}}
Original Mark Distribution
Problem numberMarks
T110
T210
T310
T410
T510
T615
T720
T820
T920
T1025
T1150
T1240
T1360
Total300

Условие

The coordinates of the Large Magellanic Cloud (LMC) are R.A. = 5h 24min and Dec = −70∘00′-70^\circ00'. The latitude and longitude of Phuket are 7∘53′7^\circ53' N and 98∘24′98^\circ24' E, respectively. What is the date when the LMC culminates at 9pm as seen from Phuket in the same year? You may note that the Greenwich Sidereal Time, GST, at 00h UT 1st January is about 6h 43min, and Phuket is in the UT+7 time zone.

Решение

Бележки за изданието

The original question and key contain several differing expressions. The Galactic-arm question uses a flat curve beyond 5 kpc and its worked key uses 2 kpc. The HI survey key prints differing flux-threshold exponents and an unusual Hubble-constant unit. The Bethlehem key has differing multiplication and remainder values. The Galactic Outflow key heading says T2 while its full prompt matches T9. GOTO assigns a different pair of marks to parts a) and d) in the question and key. The Shipwreck key prints differing sidereal-time values in its main and alternative methods. Visible missing-font glyph squares and the Exomoon key’s grading dependency are preserved. The original constants table prints the acceleration unit as m·s^-1. These printed forms remain literal.

Оригинал в Архива: Theory.pdf · официални решения: Theory_Solution.pdf