Historically, many cultures and societies believed the sun travelled around the earth; this idea is called the geocentric model of the solar system. Today, however, we know the earth travels around the sun, a concept called the heliocentric model.
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In 1543 a European academic named Nicolaus Copernicus proposed in a famous treatise that the earth orbited the sun. Most universities at that time, however, taught that the sun orbited the earth, in keeping with the ideas of the Greek philosopher Aristotle, so Copernicus' treatise was greeted with hostility by Church authorities. Another famous philosopher and scientist named Galileo Galilei found more evidence to support Copernicus' views; although Galileo was forced to recant, the heliocentric model became more popular as additional evidence emerged to favour it over geocentrism.
The earth orbits around the sun; it takes roughly 365 days or one year to complete a full orbit. The earth also completes a full rotation roughly once every 24 hours. This latter motion is what causes the sun to appear to move. During the night, your location on the earth is facing away from the sun and consequently receives no light.
It's important to note that when the sun "travels across the sky," it is not actually the sun that is moving. Rather, it's the rotation of the earth that causes the apparent motion of the sun. Since earth's axis is at a tilt with respect to the plane of earth's orbit, the elevation of the sun's path above the southern (or northern) horizon is different at different times of the year, unless you live at the equator, in which case the sun always traverses the same path and the length of a day does not vary throughout the year.
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