Final answer:
The imaginary line through the center of Earth from pole to pole is Earth's axis, which extends to the north celestial pole and the south celestial pole in the sky. These celestial points, along with the celestial equator, create a coordinate system for celestial navigation and observation.
Step-by-step explanation:
The imaginary line that runs through the center of Earth from the North Pole to the South Pole is called Earth's axis. Earth rotates about this axis. Extending this line outward to the celestial sphere gives us two important points: the north celestial pole and the south celestial pole. These are the points in the sky directly above Earth's North and South Poles. Along with the celestial equator, which is an extension of Earth's equator onto the celestial sphere, these points form the basis for the system of celestial coordinates used in astronomical navigation and observation.
Imagine standing at the North Pole; the sky would appear to rotate around the north celestial pole, which would remain stationary directly overhead. The celestial equator would run along the horizon, and the entire northern half of the celestial sphere would be visible over time, with stars never rising or setting. The same phenomenon occurs at the South Pole with the south celestial pole. These celestial markers help us orient ourselves in the cosmos, much like the terrestrial poles and equator help us navigate the Earth.