Съдържание

IAO 2007, Теория, Група α, английски — Задача 4. Photo.

Оригинал на условието (изображение)Съобщи за грешка

Всички материали от IAO 2007

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

In the photo given to you there is an airplane with the Moon in the background. Let us suppose that the photo was taken in Simeiz at the day of a solar eclipse (or at one of the days closest to a solar eclipse). Estimate how long later is (or how long time ago was) the solar eclipse. (Note: The answer «Будет-Will be» or «Было-Was» has to be written in English or Russian.) Will it be (or was it) possible to observe this eclipse in Simeiz? (Note: the answer «Да-Yes», «Может быть-May be» or «Нет-No» has to be written in English or Russian and a picture explaining your answer has to be included.)

Решение

Внимание: Непълно решение

The official solution photograph clips some initial letters/words at the left edge. All legible content is retained and ellipses mark the genuine source loss.

At first, the character of illumination of the exhaust trail from an airplane shows us that the photo was …ken around the sunrise or sunset.

Second, we see the illuminated area on the right side of moon. For the northern hemisphere it means that the phase … Moon is rising, i.e. the image was shot around sunset. Also it means that the new moon was a short time ago (and not to be during the next few days). That is, the solar eclipse already took place. (Answer «Было-Was».)

We see the illuminated area on the moon with relative size b/R about 2 mm / 52 mm (measurement of author).

b/R=1-\cos\varphi,\quad\varphi=\arccos(1-b/R)\approx15.9^\circ.

…r (easier to calculate without calculator):

\varphi\approx(2b/R)^{1/2}=(0.077)^{1/2}\approx0.277\ \mathrm{rad}\approx15.9^\circ.

…aking into account that the relative angular speed of the moon relative to the sun is

360^\circ/29.53^{\mathrm d},\quad\text{i.e. }\approx12.2^\circ\text{ per day}

…e may estimate the period since the new moon (solar eclipse) as

15.9^\circ/12.2^\circ\approx1.30^{\mathrm d}\approx31^{\mathrm h}.

One should take into account that the main inaccuracy in the solution is due to the inaccuracy in measuring the …ize of the illuminate area. While taking it 25% narrower or 25% wider (the real inaccuracy while using the picture) …he calculations result to $28^{\mathrm h}$ or $34^{\mathrm h}$ respectively. Nevertheless, since the photo has been shot near sunset, this interval …llows us to say that the solar eclipse definitely took place in daytime ([midday plus 2 – minus 4] hours) on the …revious day. So it was seen in Simeiz in the case the eclipse zone covered Simeiz. (Answer «Может быть-…May be».)

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