The sky appears as a half-sphere to the human eye, even though it is infinite in expanse. This is convenient since we can map the Earth's coordinate system (north/south pole, equator) onto the sky. Depending on where you live on the Earth's surface, the tilt of the celestial sphere as you view it with your zenith and horizon, will differ.
Problem 1: Imagine that you cut the celestial sphere in half at the horizon to form a half-sphere, then you pass a plane through the zenith, north celestial pole and you. You will get a half-circle, called the meridian (shown below). Label you, the south point, the north point, the north celestial pole, zenith and the celestial equator. Assume you live at 50 degrees north latitude, mark the angles.
