SOLUTIONS TO EXERCISE 17

Remember that the convex side of a crescent moon is always facing toward
the Sun, between 0 and 90 degrees away.  (If it were 0 degrees it'd be a new
moon; 90 degrees away, it's a quarter moon.) The concave side of a crescent
moon always faces away from the Sun.  A waxing moon always has its lit side 
toward the western horizon; a waning moon always has its lit side toward the
eastern horizon.

(a) a crescent moon near the eastern horizon, with concave side up, means the
Sun is just below the eastern horizon; so it's just before sunrise.  This is
a waning crescent, because the lit side faces toward the east. 

(b) a crescent moon near the western horizon, with concave side up, means the
Sun is just below the western horizon; so it's just after sunset.  This is a
waxing crescent, because the lit side faces toward the west.  In this case and
the one above, the Moon looks like a smile.

(c) a crescent moon near the eastern horizon, with concave side down, means 
the Sun is in the eastern sky, so it's about mid-morning, and it's a waxing 
crescent.

(d) a crescent moon near the western horizon, with concave side down, means
the Sun is in the western sky, so it's about mid-afternoon, and it's a waning 
crescent. In this case and the one above, the Moon looks like a frown.

(e) a crescent moon straight up - that is, transiting - with concave edge 
facing east means that the Sun is in the western sky, so it's about 
mid-afternoon, and it's a waxing crescent.

(f) a crescent moon transiting with concave edge facing west means that 
the Sun is in the eastern sky, so it's about mid-morning, and it's a waning
crescent.

All of these phases are clearly possible.  But are they visible?  It's
pretty hard to see a crescent moon when the Sun is high in the sky.
So phases (c) - (f) may not be visible, depending on the exact point
in the crescent phase and the exact time you choose.  But (a) and (b)
phases are usually visible, and are the so-called "Cheshire Cat" moons.