USAAAO 2026, III кръг — Задача 3. Stars in the Telescope
2026 USAAAO Third Exam (Data Analysis + Observation) · 46 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 3 Answer Sheet
Berwyn, an amateur astronomer, is observing at a random star in the night sky through his telescope. He first positioned the star in the center of his telescope's field of view (FoV) and labeled some of the stars as seen in Figure 5a. Since the telescope is not tracking the sky, the star slowly drifts across the telescope's FoV due to Earth's rotation. After 81.0 seconds, the telescope FoV looks like Figure 5b.
Berwyn then consults with his friends on his observations and gains additional information:
- Star 1 has magnitude 7.70.
- Star 2 has magnitude 9.8.
- Star 4 has magnitude 10.25 and coordinates
However, Berwyn wants to find out more information and you, as one of his friends, want to help him. Please help him find:
(a) Orientation (cardinal points) of the telescope (mark and label them in the answer sheet), [16 т.]
(b) Estimated magnitude of Star 3, and [10 т.]
(c) Telescope's FoV in degrees, please answer in 3 significant figures! [20 т.]
Отговори
(b) 8.4
Official estimate 8.40; answers between 8.20 and 8.60 get full points.
(c) 0.6736 °
Official value FoV ≈ 0.6736° (360° cos δ / 23h56m4s × 81 s × 2).
Решение
Solution:
(a) Stars always go from East to West, so the direction Star 2, 3, and 4 heading is West. In a sky map, the north is always 90 degrees clockwise of the east. More specifically, the orientation can be seen below. Each correct orientation is 4 points. Give full points if the cardinal point is within the blue line.
(b) An educated guess from the size of Star 1, Star 2, and Star 3, Star 3's magnitude is around 8.40. Answer between 8.20 and 8.60 is full 10 points, answer between 8.00 and 8.20 and between 8.60 and 8.80 is 5 points, else is 0.
(c) Star 4 essentially drifts from the center of the FoV to the edge of the FoV. This means Star 4 traverses half the FoV in 81 seconds. Hence, the whole FoV is:
Rubric:
- point for using units other than degrees
- point for using 24 hours instead of
- point for not using
- points for not multiplying by 2
Оригинал в Архива: practical.pdf · официални решения: practical_solutions.pdf