 The celestial sphere can be considered to be centered at the Earth's center, the Sun's center, or any other convenient location, and offsets from positions referred to these centers can be calculated.In this way, astronomers can predict geocentric or heliocentric positions of objects on the celestial sphere, without the need to calculate the individual geometry of any particular observer, and the utility of the celestial sphere is maintained.Individual observers can work out their own small offsets from the mean positions, if necessary.