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Our Sun is moving in a prograde orbit around the galactic center with a distance of about 8 kpc. This paper says there are many retrograde stars in the galactic halo 10-20 kpc from the galactic center. Do any of these retrograde stars have an extremely eccentric orbit that would cause them to pass closer to the galactic center than our Sun?

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There's a whole stream of them: https://iopscience.iop.org/article/10.3847/1538-4357/aadba3

Named Phlegethon, this is a stellar stream that covers about 75⁰ of the sky, and is probably the remnants of a disrupted globular cluster.

It orbits the galaxy retrograde on orbits that take it between 4.9 and 19.8 kpc from the galactic centre. The orbits are highly non-Keplarian. The image shows the orbits with the sun marked as a yellow dot.

enter image description here

Other streams exist and may have similar shaped orbits.

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