**You are invited to participate in
the 5th Canadian Astronomical Olympiad!**

**Check the Problems:**

1.
*Satellite*** .** Phobos has a radius of 11 km while Mars has a radius
of 3390 km. Phobos has a circular orbit around Mars which is inclined at 0° to
Mars’s equator. The period of Phobos is 7

^{h}40

^{m}, while the time it takes for Mars to complete a full rotation around its axis is 24

^{h}37

^{m}.

a)
How
many times in a Martian day does Phobos rise above the horizon?

b)
Where
on the horizon does Phobos rise?

c)
Suppose
Mars was inhabited by Martians. Would it be practical for them to create a
calendar using Phobos analogous to the lunar calendars we have on earth? There
is no single correct answer, but please justify your opinion with three reasons
backed up with calculations.

2.
*Seasons*** .** A common misconception is that summer and winter are
caused by the changing distance between Earth and the Sun. In reality, however,
the seasons are caused by Earth’s tilt. For an observer at a latitude of 55°,
find the ratio of the solar irradiance at noon of summer solstice to the irradiance
at noon of winter solstice due to Earth’s tilt (without considering the changing
distance). Find the ratio of the irradiances due to Earth’s changing distance
from the sun (without considering Earth’s tilt). Compare the two ratios. What
can you conclude?

3.
** Polar
night.** A city has a
latitude of 68° 58’. Find the length of the polar night in this city.

**Galaxy M96 in Leo has an angular size of 11’ by 8’ and an apparent magnitude of 10**

*Galaxy.*^{m}. The wavelength of light emitted in the H and K bands is shifted by 10.3 Å. Given that the wavelengths of ionized calcium are 3968 Å (H) and 3934 Å (K), find the galaxy’s

b) distance to Earth,

c) linear dimensions,

d) absolute magnitude, and

e) luminosity.

5.

**The photo below shows a picture of the moon taken at the prime focus of a telescope with a CCD chip with dimensions 22.2 by 14.8 mm. The ratio of the sides of the photo is the same as the ratio of the sides of the CCD chip. Find the focal length of the objective lens of the telescope.**

*Telescope.***An amateur astronomer (**

*Beginner Astronomer.**φ*= +45°) is observing a galaxy in upper culmination at solar midnight on June 21

^{st}(summer solstice). They leave for a late-night snack but end up watching 3 hours of TV instead. When they come back 3 hours later, they look at the galaxy again without repositioning their telescope and of course cannot find it. Not knowing that they should reposition their telescope, they think, “Since Earth moves around the Sun and rotates around its axis, is it possible that an increased distance to the galaxy caused it to become too dim to see?”

Prove
this astronomer wrong by calculating the change in apparent magnitude of the
galaxy during the time they were watching TV. Also calculate the actual
apparent magnitude and find the ratio of the two values. Assume Earth’s orbit
is circular and the galaxy is stationary relative to the Sun. You may use the
following data about the galaxy:

Distance to the Sun (*d*)
= 810 kpc

Surface brightness (*μ*)
= 23.65 mag/arcsec^{2}

Radius (*r*) = 12
kpc

**You think you can
solve them? If so, send your answers to ****info@astroclub.ca**** by May 17, 2021. You
might be one of the lucky winners who will be selected to represent Canada
at ****International Olympiad on Astronomy and Astrophysics 2021****!**

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