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What are the possibilities of the sun orbiting the black hole Sagittarius A* at a very close distance? Is there anything that could possibly alter the solar system's orbit, bringing it much closer to the center of the milky way and thereby threatening all life on Earth?

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    $\begingroup$ The black hole at the centre of Sgr A* is simply too far from the Sun (or the Sun, too far from it) to be of any concern. While the Sun’s orbit around the centre of the Milky Way is not exactly an ellipse (due to perturbations by surrounding stars), it is reasonably “regular” to continue along a similar path even in the distant future. Orbits don’t decay so easily. $\endgroup$ Feb 8, 2023 at 4:50
  • $\begingroup$ By orbit, do you mean the innermost circular stable orbit or ISCO? $\endgroup$
    – user47732
    Feb 8, 2023 at 5:24
  • $\begingroup$ Or a binary system $\endgroup$
    – user47732
    Feb 8, 2023 at 5:33
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    $\begingroup$ I suspect this question is motivated by the widely held misunderstanding that black holes are giant vacuum cleaners in space that suck in anything and everything. They aren't, but that's how pop-sci and sci-fi misportray them. $\endgroup$ Feb 9, 2023 at 8:56
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    $\begingroup$ @PierrePaquette that's why I said it depends on what you mean. $\endgroup$ Feb 9, 2023 at 16:22

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Pretty much none whatsoever. The radial migration of stars within the galaxy is a slow process and not completely understood. The radial positions of stars with respect to the centre of the galaxy can change by thousands of light years over the course of their lives (billions of years). The Sun probably started off a few thousand light years closer to the Galactic centre because it is more metal-rich than most of the stars around us.

However, it would need something pretty drastic to change the Sun's orbital energy and angular momentum by enough to send it anywhere near the Galactic centre - probably a very close encounter with another massive object, which is very unlikely.

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In order to get close to Sag* the sun needs to change its fairly circular orbit for one with a very high eccentricity (or a very small semimajor axis). That is not something that happens due to any normal orbital decay (e.g. due to emission of gravitational waves or resistance from some medium) since it would need to change the energy or angular momentum a lot.

What in principle could happen is a close passage near another star, causing a gravitational slingshot that changes the orbit. This is still unlikely to work, since the typical relative velocities between nearby stars is some tens of km/s: the change is unlikely to be big enough to cancel the entire orbital velocity of the sun, about 230 km/s. There would have to be a sequence of very carefully aligned encounters to achieve a trajectory to the center of the galaxy. More importantly, the probability of a very close encounter is on the order of $10^{-15}$ per year, so we should not expect it to happen anytime soon.

Obviously any close encounter with another star that could change the sun's orbit significantly would also threaten the stability of the solar system. Even a 100 AU encounter might be bad news, but for the big changes in velocity you need encounters measured in an AU or less... which would be pretty guaranteed to threaten the biosphere directly.

Even if the sun got into a core-ward trajectory it would take a long time to get there. It would take about 113 million years.

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