To fix the position of any astronomical object, we must have a frame of reference, or coordinate system, which assigns a different pair of numbers to every point in the sky. The two numbers, or coordinates, usually refer to ‘how far round’ and ‘how far up’, just as do the longitude and latitude of an object on the Earth's surface. There are several such coordinate systems which you may meet, and we shall be concerned with four of these, namely the horizon system, the equatorial system, the ecliptic system and the galactic system. Each system takes its name from the fundamental plane which it uses as a reference; for instance, the ecliptic coordinate system makes all its measurements with respect to the plane of the ecliptic, the plane of the Earth's orbit about the Sun. In the next few sections, we shall find how to convert any position given in one system into the equivalent coordinates of another system. We shall also find how to describe positions on the surfaces of the Sun and Moon, how to deal with the problems of calculating the time of rising and setting, and with the effects of the Earth's precession, nutation, aberration, atmospheric refraction, and parallax on the apparent position of a celestial body.