Voyager 1 is traveling at 16.9 km/s.

New Horizons (which has the distinguishing feature of being the fastest human-made object ever launched from earth https://www.scientificamerican.com/blog/life-unbounded/the-f... ) is traveling at 12.6 km/s.

The key part there is that it got multiple gravity assists as part of the Grand Tour https://en.wikipedia.org/wiki/Grand_Tour_program . You can see the heliocentric velocity https://space.stackexchange.com/questions/10346/why-did-voya... https://www.americanscientist.org/article/the-voyagers-odyss...

The conjunction for the Grand Tour is once every 175 years. While you might be able to get a Jupiter and Saturn assist sooner, it is something that would take the right alignment and a mission to study the outer planets (rather than getting captured by Jupiter or Saturn for study of those planets and their moons).

While I would love to see a FOCAL mission https://en.wikipedia.org/wiki/FOCAL_(spacecraft) which would have reason for such a path, I doubt any such telescope would launched... this century.

175 years isn't a lot of time when we speak in humanity's time scale. We've been around 200,000 - 300,000 years.

That alignment will happen many more times in the history of humanity. That is to say, I don't know if a spacecraft to overtake Voyager will be launched on the next alignment or one 10,000 years from now, but it doesn't seem unlikely to happen.

If humans survive 1000 years I can’t see any way we haven’t populated the solar system and can build probes which travel far faster than voyager, including self sufficient asteroids

Once we leave the solar system in a self sufficient way I can’t see any event which would cause a species level extinction

I admire the confidence but a bunch of meat bags prone to bacterial and viral infection, impact damage and with limited use by dates would need some serious luck to survive a simple impact on earth let alone living in cans around the solar system. If we don’t mess our nest so much that we make it uninhabitable. We’re stuck here with short term horizon psychopaths pulling the strings remember.

A give colony would fail, but if there’s a thousand colonies and 99% fail that’s still 10 which don’t and can recover

You’ve given numbers for how fast New Horizons launched, and for how fast Voyager 1 got thanks to the 1-in-175-years boost, but is there an easy way to actually compare them?

IE either what speed Voyager 1 launched at excluding the gravity assists, or what speed New Horizons would have reached if it were launched 175 years after Voyager 1 (to take advantage of the same gravity assists)?

Not easily. The tricky part is also in the relative numbers. The Voyager 1 data (and New Horizons data now) is in heliocentric velocity. The bit with NH being the fastest was with Earth centric velocity.

Another part in this is the "the probes are slowing down over time" - and you can see that with the Voyager 1 data that while the velocity after assist is higher than before, its not a line at slope 0 but rather a curve that is slowly going down.

This is further complicated because New Horizons had a launch mass of 478 kg and voyager was a twice as massive at 815 kg.

They also had different mission profiles (Could Voyager 2 taken a redirect from Neptune to Pluto? That trajectory change would have required a perigee inside the radius of Neptune...)

Voyager was done with a Titan III-Centaur rocket (that had a misfire) https://en.wikipedia.org/wiki/Titan_IIIE

> Voyager 1's launch almost failed because Titan's second stage shut down too early, leaving 1,200 pounds (540 kg) of propellant unburned. To compensate, the Centaur's on-board computers ordered a burn that was far longer than planned. At cutoff, the Centaur was only 3.4 seconds from propellant exhaustion. If the same failure had occurred during Voyager 2's launch a few weeks earlier, the Centaur would have run out of propellant before the probe reached the correct trajectory. Jupiter was in a more favorable position vis-à-vis Earth during the launch of Voyager 1 than during the launch of Voyager 2.

Note also in there that a few weeks difference between Voyager 1 and Voyager 2 had different delta V profiles (which is why Voyager 1 is faster)

New Horizons was done with an Atlas https://en.wikipedia.org/wiki/Atlas_V

... and I don't have enough KSP background to do the orbital mechanics for this.