IAO 2017, Практически тур, Група α — Задача 7. Extinction in terrestrial atmosphere.

XXII International Astronomy Olympiad · Practical round. Problems to solve · 27 октомври 2017 г.

Условие

Extinction is a term used in astronomy to describe light attenuation due to its absorption and scattering.

A star ($\alpha = 22^{\mathrm{h}}02^{\mathrm{m}}40^{\mathrm{s}}$, $\delta = +42^{\circ}14'41''$) was observed at different zenith distances on October 26, 2017 (after its upper culmination at 11:34:20 UT), at the Weihai Observatory (WHO) of Shandong University. Astronomers use parameter $F(z)$, air mass, as an extinction characteristic, $F(z) \approx 1/\cos(z)$ if the zenith distance ($z$) is smaller than 60°. The atmospheric extinction equation can be written as: $m_{\mathrm{V}} = m_0 + K\cdot F(z)$, where $m_0$ is the magnitude of the star without atmospheric extinction, $K$ is the atmospheric extinction coefficient. Table 7 (see separate sheet) gives the observing times (UT, in units of hour) and the measured magnitudes ($m_{\mathrm{V}}$) of the star.

7.1. Draw the table (similar to that you see below) in your answer book. Calculate zenith distances, $z$, in unit of degrees (°), for given observing times in 1$^{\mathrm{st}}$ column, and write the result into the 2$^{\mathrm{nd}}$ column. Calculate the air mass ($F(z)$) for different zenith distances, and write the result into the 3$^{\mathrm{rd}}$ column.

7.2. Plot the scatter diagram between magnitudes ($m_{\mathrm{V}}$) vs. air mass ($F(z)$). Draw a straight dashed line on the plot to indicate the linear relation between $m_{\mathrm{V}}$ vs. $F(z)$.

7.3. Estimate the atmospheric extinction coefficient ($K$) and the magnitude of this star without atmospheric extinction ($m_0$) with help of graphical method, and write results in forms of «$K = \ldots$», «$m_0 = \ldots$».

7.4. Determine the magnitude ($m_{\mathrm{Z}}$) of this star as it was observed in zenith, and write result in form of «$m_{\mathrm{Z}} = \ldots$».

Таблица к задаче 7.

Table for problem 7.

Решение

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Оригинал в Архива: alphapract.pdf · официални решения: practalphasol.xlsx