IAO 2007, Теория, Група α, английски — Задача 3. Marsset.
Theoretical round. Problems to solve · 29 септември 2007 г.
Бележка
Maybe not all problems have correct questions. Some questions (maybe the main question of the problem, maybe one of the subquestions) may have no real sense. In this case you have to write in your answer (in English or Russian): «situation is impossible – ситуация невозможна». Of course, this answer has to be explained numerically or logically.
Source availability
The numerical table of planetary data is not present in the32-file2007 archive inventory. The file bgtheo6.jpg contains only a translation of column headings, without numerical planetary rows. No table from another year has been substituted. The separately archived airplane/Moon photograph is included in full with question4.
Note for jury and team leaders
The proposed sketches are not full; the team leaders have to give more detailed explanations for students. But the correct solutions in the students’ papers (enough for8pts) may be shorter.
Source photograph damage
The second and fourth official solution photographs lose some initial letters or words at the left edge. Ellipses inside the affected solution text mark those source losses. Legible formulas, results and grading remarks are retained; missing letters have not been silently supplied. The solution for question4 contains no explanatory drawing, although the question requests one.
Printed source annotations
The supplied key’s Moon magnitude calculations and approximate values are retained. The source results and formulas are reproduced without scientific correction; punctuation and multiplication spacing are normalized only for mathematical rendering.
Условие
Estimate (at least roughly) the duration of Mars disk set for an observer at the mountain Koshka in Simeiz for Mars in Great opposition.
Решение
From the table of Solar System we may find the distance to Mars in the Great opposition
and the angular size of the disk of Mars,
in radians
in arcminutes
Mars is near the ecliptic, this part of the sky is moving with the angular speed
Taking into account that the latitude of the Simeiz is , the duration of Mars disk set is
Refraction and the height of the observer above the sea level do not affect on this value. They vary the time of the Marsset but not its duration. The speed of moving the Mars along ecliptic (of order of 1″ in minute) also almost does not affect on this value since this is too negligible in comparison with the days’ moving of the sky (15′ in minute).
Note for jury: It is proposed that the students have to know the latitude of the town-host of the Olympiad.
Data
Data from the table of planetary data may be used for solving every problem.
Оригинал в Архива: alphatheo.jpg · официални решения: theosol1.jpg · допълнителни данни: theosol2.jpg · допълнителни данни: theosol3.jpg · допълнителни данни: theosol4.jpg · допълнителни данни: photo.JPG