Final answer:
To see the largest fraction of the celestial sphere over the course of a year, a telescope should ideally be built on the equator where the celestial equator passes overhead, enabling the observation of the entire celestial sphere.
Step-by-step explanation:
If you wanted to build a telescope that could see as large a fraction of the celestial sphere as possible over the course of a year, the ideal location would be on the equator. At the equator, the celestial equator passes directly overhead at the zenith, allowing an observer to potentially see the entire sky over a year as the Earth orbits the Sun.
Furthermore, the celestial poles are situated on the northern and southern horizons, which enables visibility of the entirety of the celestial sphere up to the horizon, with all stars rising and setting.
While high elevations are preferred for observatories due to reduced atmospheric interference and increased clarity, the capacity to view the largest fraction of the night sky depends more on latitude than altitude. Erecting a telescope at the Earth's equator brings the advantage of being able to observe all the constellations throughout the year, maximizing sky coverage.