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In the context of whether or not nearby stars were created from the same nebula, this answer states:

imagine two stars with very similar orbits, one with a period of 200 million years and the other with a period of 210 million years. If they start off right next to each other, then after 2 billion years, the first star has made 10 complete orbits, while the second has made about 9.5 -- meaning it will now be on the other side of the galaxy from the first star.

How close would the two stars have originally been to have such different orbital periods?

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  • $\begingroup$ If the only information provided is the orbital period, there is no minimum distance constraint. It's always possible to find two orbits with any two orbital periods such that the orbits intersect. $\endgroup$
    – notovny
    Commented Feb 13, 2021 at 14:10

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The rotation curve of the Milky Way is quite flat in the vicinity of the Sun. That means that the average velocity tangential to the Galactic centre is constant.

If we assume one star is at 8 kpc from the galactic centre, then to orbit in 200 million years means the tangential speed is 259 km/s.

To have a period of 210 million years and a tangential velocity of 259 km/s, the other object would have originated at a radial distance of 8.4 kpc from the galactic centre.

Of course this doesn't define a separation, just a likely birth galactocentric radius. Even that can't be definitive because stars are born with a small dispersion in velocities. It also assumes both orbits are close to circular. If you allow quite eccentric (and unusual) orbits then almost anything is possible.

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  • $\begingroup$ In addition, radial migration can potentially shift orbits in radius while still keeping them approximately circular. $\endgroup$
    – Peter Erwin
    Commented Dec 20, 2022 at 0:44

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