IOAA 2014, Анализ на данни · окончателна тема — Задача 3. IOAA Observer on an extrasolar planet

a)

The magnitude of the Sun as seen by observer A ($m_{\text{Sun,Planet}}$).

b)

The magnitude of Sirius star system as seen by the observer A ($m_{\text{SY,Planet}}$).

c)

The combined intrinsic luminosity of the Mizar system, $L_{\text{Mizar}}$.

d)

The average distance between gravitationally bound stars of the Mizar system and Earth.

e)

The geocentric angular distance between Mizar system and Sirius, $\Delta\theta$.

f)

The physical distance between the gravitationally bound stars of the Mizar system and the observer A ($d_{\text{Mizar,Planet}}$).

g)

The magnitude of the entire Mizar system as seen by the observer A ($m_{\text{Mizar,Planet}}$).

Also estimate amount of errors in all your answers.

Data

The following data may be used:

• $d_{\text{Sirius,Earth}}=2.6\,\mathrm{pc}$ – the Sirius–Earth distance;
• $m_{\text{Sirius,Earth}}=-1.46^{\mathrm m}$ – the apparent magnitude of Sirius measured from the Earth;
• $d_{\text{Sun,Earth}}=1\,\mathrm{AU}$ – the Sun–Earth distance;
• $m_{\text{Sun,Earth}}=-26.78^{\mathrm m}$ – the apparent magnitude of the Sun as seen from Earth;
• $d_{\text{Sirius,Planet}}=10\,\mathrm{AU}$ – distance between Sirius and its planet where the observer A is located.

In the table below information for the stars from the Mizar system as measured from the Earth is given.

The equatorial coordinates of Mizar system ($\sigma_1$) and respectively of Sirius ($\sigma_2$), located on the heliocentric map are:

Note