"The Sun's Movement in the Solar System: Unraveling Space Mysteries"

TL;DR Summary
The sun does move within the solar system, orbiting the center of the Milky Way and exhibiting a small wobble due to gravitational interactions with the planets. This wobble, detectable through the Doppler effect, allows scientists to infer the presence and properties of exoplanets in distant star systems. While the sun's apparent daily and yearly movements are due to Earth's rotation and orbit, respectively, the sun and each planet orbit a point of mutual gravity called a "barycenter," with the sun's massive size resulting in these barycenters being located deep within the sun.
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