**You are invited to participate in the**

**3nd Canadian Astronomical Olympiad!**

**Check the Problems:**

1. About 3000 years ago, on the day of the
summer solstice, the zenith distance of the sun at midday was 26

^{о}15’ (to the south of the zenith), and, on the day of the winter solstice, at midday the sun was 16^{о}03’ above the southern horizon. Calculate the angle between the ecliptic and the celestial equator 3000 years ago.
2.
A
particular telescope is aimed such that the north pole is at the very edge of
the field of view. The telescope is not tracking the stars. Approximately how
long would Polaris be visible through the telescope (i.e. how long would it
take for Polaris to move from one edge of the FOV to the other), assuming its
path goes through the center of the telescope.

3.
An
observer on earth measured the apparent magnitude of an asteroid at (every)
opposition. The asteroid’s period is 3.9 years. Estimate the eccentricity of
the asteroid’s orbit if the difference between highest and lowest apparent
magnitudes is 2.5

4. The solar system moves at a speed of 600 km/s relative to the cosmic microwave background. How big an error in our measurements of the CMB temperature can we tolerate to still notice the solar system’s movement?

^{m}. Assume the earth’s orbit is circular.4. The solar system moves at a speed of 600 km/s relative to the cosmic microwave background. How big an error in our measurements of the CMB temperature can we tolerate to still notice the solar system’s movement?

5.
Using a certain telescope you can see
objects up to 23

^{m}. How big must an asteroid in the L_{4}Lagrange point (with respect to the earth and sun) be to be detected by this telescope? How big must it be if it’s in the L_{5}point?
6.
The hydrogen line Hα (λо=6563Å) in the spectrum of a distant
galaxy has a wavelength of λ = 7350 Å (angstroms). The galaxy’s angular
diameter is 8". How fast and in which direction is this galaxy moving? How
far away is it from us? What is its diameter in parsecs? How big is it compared
to our own galaxy?

**You think you can solve them? If so, send your answers to**

**info@astroclub.ca**

**before April 30th, 2019. You might be one of the lucky winners who will be selected to represent Canada at**

**13**

^{th}International Olympiad on Astronomy and Astrophysics**!**

*The following sources were used in preparations of these problems:*

*1.*

*Open Olympiad of Central Russia NNC on Astronomy and Space Physics (M.G.Gavrilov)*

2.

*All-Russian Olympiad of students in astronomy*
3.

*Moscow Astronomical Olympiad*
4.

*St. Petersburg Astronomical Olympiad*
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