How long would it take for something to fall from one light year away into the sun

I'm imagining something without an existing orbital trajectory, but instead is very slowly commencing a straight-line trajectory towards the Sun. How long would it take to get there - or would it be compelled into an orbit and perhaps never get there?

I imagine we are talking hundreds of thousands of years so the proper motion of the Sun would be an issue, so I am also assuming there's an appreciable gravity well at one light year out that would not only keep a hold of the object but also accelerate it inwards? The object would be very small (grain of rice say). Thanks

How long would it take for something to fall from one light year away into the sun

One major issue would be the gravitational attraction of other bodies. But if you can hypothesize a universe with only two bodies, and you start them off with absolutely no velocity relative to each other, then yes, it would fall in. I don’t know how to do the math, but I’m pretty sure it’s just a fairly simple calculus problem.

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