IAO 2017, Практически тур, Група α — Задача 6. Transiting extra-solar planet.

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

Условие

The transit of an extra-solar planet (TrES-3b) across a star (TrES-3) was observed by the 1-m telescope of Weihai Observatory (WHO) on April 16, 2009, using the broad-band V filter and a PI CCD. The photometric data (selected part from the original one) are given in the Table 6 (see separate sheet), the time is in Julian days, and $m_{\mathrm{V}}$ is the V-band magnitude.

6.1. Plot the transit light curve (magnitude vs time), determine the moment of mid-transit (the deepest transit) and write result (in Julian days) in form of «$T_{\mathrm{mid}} = \ldots$», estimate the duration of the transit (in days) in form of «$T_{\mathrm{d}} = \ldots$», determine the depth of the transit (in magnitudes) in form of «$D = \ldots$» .

6.2. Give the formula and calculate the radius of the extra-solar planet TrES-3b $R_{\mathrm{p}}$ (in units of the radius of Jupiter: $R_{\mathrm{Jupiter}}$, write the answer in form of «$R_{\mathrm{p}} = \ldots$»). The radius of the star (TrES-3) is known to be 0.813 radius of the Sun, $R_{\mathrm{s}} = 0.813\,R_{\mathrm{sun}}$.

6.3. Estimate the approximate value of the angle $i$, in unit of degrees (°) between the axis of this planet’s orbiting and the line of sight of the observer. Write the answer in form of «$i \approx \ldots$».

6.4. The next mid-transit moment after the above transit event was: JD = 2454939.578. The mass of the star (TrES-3) is known to be 0.924 mass of the Sun, $M_{\mathrm{s}} = 0.924\,M_{\mathrm{sun}}$. Calculate the orbital period of TrES-3b (in units of days, in form of «$P = \ldots$»), and the semi-major axis of the orbit (in units of au, in form of «$a = \ldots$»).

Таблица к задаче 6.

Table for problem 6.

Элементы орбит и физические характеристики Солнца, Земли, Луны и Юпитера

Parameters of orbits and physical characteristics of Sun, Earth, Moon and Jupiter

**) В среднем противостоянии.

**) In mean opposition.

Решение

Теми и трудност

Трудност: неоценена.

Екзопланети и среди · Небесна механика · Светлина и астрономически измервания · Откриване на екзопланети · Закони на Кеплер · Звездни величини

Предпоставки: Гимназиална подготовка, Разширена олимпиадна подготовка

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