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Please correct me if I tell something wrong.

As we already know, a planet (e.g. Earth) remains on its orbit due to the gravity of the Sun.

If the Sun's gravity were not there, the Earth would be thrown into the space. Now we know, why the Earth stays there.

My question is, what is holding the Sun at its place? Why is the Sun so fixed?

Is there any force that keeps the Sun so fixed?

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If by "fixed" you mean stationary then the sun is not fixed. It is in orbit around the centre of the Milky Way, travelling at a speed of around $250$ km/s relative to the centre of the Milky Way. At this speed it travels one astronomical unit (the average distance between the earth and the sun) every seven days, and travels one light-year in about $1,190$ years. In other words, its speed relative to the centre of the Milky Way is about $0.1 \%$ of the speed of light.

The sun appears to be fixed relative to the background stars (once you take into account the earth's orbital motion around the Sun) because the stars are very far away, and also because most of the stars visible to the naked eye are also orbiting around the centre of the Milky Way in orbits that are very similar to the sun's orbit.

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    $\begingroup$ and because we live our lives in the blink of an eye so to speak $\endgroup$ – uhoh Jul 10 '20 at 12:19
  • $\begingroup$ Thanks for your answer and the explanations. My question is: whether the sun is fixed in our galaxy, I always imagined it like this, the sun has a fixed position in our galaxy and it does not move. $\endgroup$ – r_albl Jul 10 '20 at 12:20
  • $\begingroup$ Thank you guys, I understood now, as I said, I always thought differently. $\endgroup$ – r_albl Jul 10 '20 at 12:22
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    $\begingroup$ @Mr.R Also, our galaxy is moving relative to the other galaxies in our Local Group, and that group is itself moving... $\endgroup$ – PM 2Ring Jul 10 '20 at 12:32
  • $\begingroup$ @PM2Ring, thanks for this info! $\endgroup$ – r_albl Jul 10 '20 at 12:35

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