Съдържание

USAAAO 2026, III кръг — Задача 4. Sky Map Attack 2!

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Всички материали от USAAAO 2026

2026 USAAAO Third Exam (Data Analysis + Observation) · 54 т.

Instructions (Please Read Carefully)

The test must be completed within 2 hours (120 minutes) and the maximum number of points is 230 points. The point breakdown per problem is as follows.

Problem	P1	P2	P3	P4	Total
Points	55	75	46	54	230

Please solve each problem on a blank piece of paper and mark the number of the problem at the top of the page. Some problems may require a designated answer sheet; these will be provided. The contestant's full name in capital letters should appear at the top of each solution page. If the contestant uses scratch papers, those should be labeled with the contestant's name as well and marked as “scratch paper” at the top of the page. Scratch paper will not be graded. Partial credit will be available given that correct and legible work was displayed in the solution.

This is a written exam. Contestants can only use a scientific calculator (non-programmable and non-graphing) for this exam. A table of physical constants will be provided. Discussing the problems with other people is strictly prohibited in any way until the end of the examination period on June 25, 2026. Receiving any external help during the exam is strictly prohibited. This means that the only allowed items are: a calculator, the provided table of constants, a pencil (or pen), an eraser, blank sheets of papers, and the exam. No books or notes are allowed during the exam. Students must be proctored during the entire duration of the exam.

This exam sheet and your answer sheets (including scratch papers) should be returned to your proctors once the exam ended. Your proctors should upload your answer sheets to the Google Form provided to them.

We acknowledge the following people for their contributions to this year's practical exam:

Ferdinand, Vincent Bian

After reading the instructions, please make sure to sign, affirming that:

All work on this exam has been completed by me.
I took this exam under the supervision of a proctor.
I did not receive any external help beyond the materials provided.
I will not discuss the contents of this exam with anyone until June 24, 2026.
Failure to follow these rules will result in disqualification from the exam.

Student Signature: ____________ Date: ____________

Условие

Please answer this question in the provided Question 4 Answer Sheet

After your first experience stargazing in a deserted island, you and your friends decided to go on another vacation to another island to practice your observation skills for IOAA 2026. One night, you looked up at the sky and it looked like the image below.

As the sky was bright, you and your friends gave each other quizzes about the sky.

Circular all-sky map (azimuthal equidistant projection) with black dots for stars of various sizes on a white background; no labels, grid or cardinal points are drawn.

(a) List out 6 constellations above the Horizon. [12 т.]

(b) Mark and label two out of three poles (North/South, whichever is above the Horizon): Celestial, Ecliptic, or Galactic (pick two). [8 т.]

(c) What is the estimated latitude of the island? Hint: the projection is azimuthal equidistant [10 т.]

(d) Mark and label the four cardinal points. [8 т.]

(e) Draw and label two out of three planes: Celestial Equator, Ecliptic, or Galactic (pick two). [8 т.]

(f) Are there any planets seen in the sky? If yes, mark and label the planets. [3 т.]

(g) Mark and label: M4 or M13 (pick one). [5 т.]

Отговори

Решение

Solution: Please refer to these two images below for the sky map. The first image is the inverted image, while the second image is the screenshot from Stellarium.

The sky map inverted, with constellation lines and annotations: cardinal points N, NE, E, SE, S, SW, W, NW around the rim with red tick marks at N, E, S and W; the celestial equator (blue, between light-blue tolerance lines), the ecliptic (dark red, between red lines) and the galactic equator (green, between black lines); NEP, SCP and SGP marked with red and orange circles; M13 and M4 circled in red; Saturn labelled near the East point.

Stellarium screenshot of the same sky on a dark background with an alt-azimuth grid, constellation lines, the celestial equator and the ecliptic of date, cardinal points, NEP, SCP, SGP and Saturn labelled; the status bar reads Earth, -15, 105, 0 m; FOV 207°; 2026-07-12 00:10:00 UTC+07:00.

(a) Each correct constellation is 2 points. Available constellations are: Draco, Lacerta, Pisces, Andromeda, Pegasus, Lyra, Cygnus, Hercules, Cepheus, Corona Borealis, Bootes, Serpens, Ophiuchus, Vulpecula, Sagitta, Delphinus, Scutum, Equuleus, Aquila, Aquarius, Capricornus, Virgo, Libra, Scorpius, Sagittarius, Crux, Corona Australis, Centaurus, Apus, Cetus, Piscis Austrinus, Grus, Phoenix, Sculptor, Tucana, Indus, Octans, Lupus, Norma, Ara, Pavo, Musca, Chamaleon, Hydrus, Triangulum Australe, Eridanus

(b) Each pole is 4 points. Minus 1 point for mark correctly but labeled wrong. If marked within the red circle, it's full 4 points. If marked within the orange circle, it's 2 points. Outside is 0 points.

(c) In the sky, we can see Rigil Kentaurus and Crux constellation. We can make a rough isosceles triangle with Rigil Kent and Acrux as the base and the side is around 4 times the length of Acrux and Gacrux. We can estimate that the South Celestial Pole (SCP) altitude is around $a_{\mathrm{SCP}} = 1$ cm and the distance to Zenith is around $R = 6$ cm. As it is azimuthal equidistant, we can get the latitude of the island:

\varphi = a_{\mathrm{SCP}} = \frac{1}{6} \times 90^{\circ} = 15^{\circ}\ \mathrm{S}

In this subpart, $11^{\circ}\ \mathrm{S} - 20^{\circ}\ \mathrm{S}$ gets full 10 points; $5^{\circ}\ \mathrm{S} - 10^{\circ}\ \mathrm{S}$ or $10^{\circ}\ \mathrm{S} - 25^{\circ}\ \mathrm{S}$ gets 4 points; and outside that range gets no points. If you didn't explain your thoughts, you'd only get 2.5 points if it's within $10^{\circ}\ \mathrm{S} - 20^{\circ}\ \mathrm{S}$ and no points outside that.

(d) Each cardinal point is 2 points. Full points within the red line.

(e) Give full points if drawn and labeled correctly within the lines (90%-100% within). Half of the correct points if partially (50%-90%) within the lines. Zero otherwise

(f) There is only Saturn near the East cardinal point. If the answer is yes, but not labeled planet as Saturn, give 2 points. If the answer is yes, but Saturn/label is not marked correctly, give 1 point. No points given to labeling Saturn in a wrong star.

(g) Give full points as long as it's within the red circles.

Оригинал в Архива: practical.pdf · официални решения: practical_solutions.pdf