During a night, how do the stars move? What angle does their nightly path make with respect to the horizon? How does it depend on latitude?
During the night, the path traveled by the stars through the sky represents the rotation of the Earth.
The movement of stars is illusory, in fact the Earth rotates creating the impression that the celestial sphere moves. If you need to find the paths traveled by the stars on celestial sphere, then you should know that these paths are parallel to celestial equator.
The celestial sphere is an imaginary sphere whose center is represented by the Earth.
The position of the stars on the celestial sphere is given by two coordinates that are called declination and right ascension. The point of intersection of the imaginary lines declination and right ascension represents the location of the star on celestial sphere.
Declination is the angle that the position vector of the star makes with the plane of celestial equator. For instance, the declination of a star located on the celestial equator is 0^o.
The stars found to the north of celestial equator have positive declinations, between 0^o and 90^o and the stars found to the south of celestial equator have negative declinations, between 0^o and -90^o.
Right ascensions are perpendicular lines to celestial equator and they are similar to longitude lines.
The latitude of the observer is equal to the angle of tilt made by the celestial equator with respect to the horizon.
The stars we see move because the earth is tilting while the stars are moving during the same time.