I would like know if our Solar System is moving independently through our galaxy or is stuck on the Orion Arm which is revolving around our galaxy? Is our solar system an onboard passenger of the Orion Arm?
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The arms of a spiral galaxy are "gravity waves" Stars orbiting the galaxy are pulled towards them and speed up as they approach, and then are slowed down as they leave. So an arm of the galaxy is not composed of the same stars. The arm is, in some ways, like a fountain, because it can maintain its shape even though the stars in it are constantly changing.
So the sun will move in its orbit out of the arm and into another, just the same as other stars.
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$\begingroup$ Then why do milky way look the same in the sky since several centuries even though our solar system are moving? Night sky galaxy appearance supposed to be changed while we travelling is it? $\endgroup$ Commented May 15, 2021 at 13:24
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2$\begingroup$ @user1844933 The Sun orbits the center of the galaxy at a distance of aobut 27,000 light years with a period of about 225 million years. So the relative posiitons of stars, star clusters, and nebulae changes very slowly by human standards. Thus it takes a very long time by human standards for the visible sky to change. $\endgroup$ Commented May 15, 2021 at 14:58
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1$\begingroup$ See youtube.com/watch?v=nUnKDPk60gU for an animation of how the stars will move over 5 million years $\endgroup$– James KCommented May 15, 2021 at 16:22