See you next July! I look forward to reading this story every year for the next 50 years or so. Maybe I'll pass it in some spaceship and be reading stories about how it's leaving the solar system.
However, for humor's sake, I also had thoughts pretty much along the line of yours when I read the headline.
Also, if you plan to wait it to live the Oort Cloud, you'd beter invest some time pushing up cryogenics or imortality.
Just being reminded about Voyager and the vastness and other miracles of space helps put that daily to-do list in perspective. For me anyway. Your mileage may vary, no pun intended.
And bringing Voyager I to a full stop is currently impossible. It doesn't have the fuel and is traveling at incredible speed. Although, technically the velocity is relative to our own. It very well may BE stopped relative to some other object in space.
If it were pointing at Proxima Centauri, the nearest star system to ours, it would take 75,000 years, give or take, to get there.
For the equation, you should put the mass of the sun in for m and the mass of the galactic core in for M and see what you get.
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There is no cut-off point. What's special about that distance?
His distance is awful close to 1e16 meters. Figure an atom of H weights 6e-23 (ha ha we'll ignore isotopes) (edited note, well, thats embarassing, but no one else will notice, not here on HN anyway, and it doesn't change the result, so I'm not redoing the arithmetic in my head again). Guess the mass of the sun at 2e30
So the Hill radius would be 1e16 (6e-23 / (3 * 2e30) ) ^ 1/3 and that works out to like 3e-38 meters or so? And if an atomic bond is like "hundreds of picometers" that means that there's no real possible way for two hydrogen atoms to stably orbit each other gravitationally without influence from the sun at 100000 AU. They could get into a chemical bond, sure, which would gravity gradient stabilize... eventually. But the sun is going to be a part of the party.
If you tossed the earth out there, this close in right now our hill sphere is like 1.5e6 meters, but way out there it would be like 3e9 meters which is pretty big, ridiculous close (well, to one sig fig) to neptune's orbit. So assuming he didn't pick a random number, that does work out that if you tossed the earth that far away from the sun, the earth's little "solar system" of junk orbiting it without interference from the far away sun, would be about the size of the solar system. Which I guess means something, although not much.