The apparent movements of the stars in the night sky can be influenced by several factors related to the Earth-Sun system. Based on your model, the three factors that might cause changes in the apparent movements of the stars are:
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Earth's rotation on its axis - This daily rotation causes the stars to appear to move across the sky from east to west.
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The tilt of Earth's axis - The axial tilt affects the position of the stars in the sky throughout the year, leading to seasonal changes in the visibility and path of certain stars.
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Earth's revolution around the Sun - As the Earth orbits the Sun over the course of a year, the perspective from which we view the stars changes, resulting in different stars being visible at different times of the year.
Note: While "Earth's changing distance from the Sun" can affect the strength of sunlight and seasons, it does not directly impact the apparent movement of stars in the night sky in the same way as the other three factors mentioned.