USAAAO 2014, Национална олимпиада (NAO) — Задача 3. Section B: Long Questions, 2

National Astronomy Olympiad 2013-2014 · 12 т.

Указания

Duration: 2 hours 30 minutes

Maximum Points: 66 (Multiple Choice: 32 points, Long Questions: 34 points)

This test is designed to be taken with an answer sheet and scantron sheet on which the student records his or her responses. All answers are to be marked on these sheets, not written in the booklet. Anything written in the test booklet will not be scored. Students must begin each Long Answer on a new sheet, clearly indicating the question number. Each student should be provided with an answer sheet and scratch paper, both of which must be turned in with the test booklet at the end of the examination.

The full examination consists of 16 multiple-choice questions and 3 Long Answer questions representing a fairly wide range of difficulty. Students should be permitted to use scientific calculators. A table of physical constants other useful information are provided as an attached booklet.

Do not discuss this examination with anyone after its completion. Your results will be emailed to you by March 20th.

Declaration

I hereby affirm that all work on this exam is mine, and that I took this test under a proctor's supervision, with no outside aids beyond the materials provided and allowed. Furthermore, I also affirm to not discuss the test with others or provide any sort of aid to other examiners through the course of the examination. I understand that failure to do so may result in your disqualification from the exam.

Signature: ____________ Date: ____________

Long Answers

Please note that there are other possible methods of solving these questions. Points were awarded for any method with correct reasoning. Points were also given for partially correct solutions and errors carried forward, however one point was deducted for an incorrect final answer.

Условие

Circumpolar stars are stars that never set below the horizon. Consider such a star with declination δ\delta, as seen by a northern observer at latitude Φ\Phi.

(a) Draw a figure that illustrates the motion of such a star in the sky. Label all relevant angles. [3] [3 т.]

(b) Find the condition δ\delta and Φ\Phi must fulfill for the star to be circumpolar. [3] [3 т.]

(c) Write an expression (in terms of δ\delta and Φ\Phi) for the maximum azimuth of a circumpolar star that cannot reach 180 degrees. (The azimuth of a star is its angle from north) [6] [6 т.]

Отговори

Решение

Оригинал в Архива: 2014-nao-exam.pdf · официални решения: 2014-nao-solutions.pdf