Even if we had a voyager travelling the "opposite" direction, once outside the solar system they'd appear to be travelling at almost the same speed with respect to the orbit of the solar system around the milky way.
The solar system is estimated to orbit ~200km/sec around the centre of the milky way.
Even with a perfect ejection, at the estimated speed of Voyager you'd end up with one probe going ~180km and the other ~220km, which isn't a huge difference.
And that's without the fact that getting Voyager to that speed required some unique planetary alignment.
1/(2sqrt(2) - 3) ~ 5.83
times more energy to throw an object to the center of a gravity well than it does to throw it out of orbit.
It doesn’t matter how close your initial orbit it, or whether you’re orbiting around the Sun or Sagittarius A*. The ratio is always the same, though gravitational assistance from other bodies often affects the calculations in practice.
I expect we’d send a satellite outside the Milky Way long before we get one anywhere near the center of the galaxy. Not that either mission seems particularly feasible with current technology.
The key metric is that their locations would spread by ~40km/sec. Whether that is an interesting amount of distance in an interesting amount of time is debatable, but that's the number.
In the 21st century NASA has launched exactly three RTG-powered missions: New Horizons (2006), Mars Science Laboratory/Curiosity (2012), and Mars 2020/Perseverance. The next will be the (very awesome) Dragonfly mission to Titan, planned to launch in 2027. So given a cadence of roughly seven years, and one out of four missions targeting trans-Neptunian space, you could expect to launch an interstellar probe every 30 years or so, barring significant advances in power technology. The next one will most likely be a sorely-needed Uranus or Neptune flyby mission that would possibly launch in the mid to late 2030s.
There are maybe a dozen reasonable mission proposals submitted for every mission that actually ends up at the launch pad. The competition is fierce, and any proposal has to argue its return on investment incredibly convincingly to get selected for implementation. We now know many interesting Kuiper Belt objects that would definitely deserve a closer look – but we also know many other things that are much more accessible and would also deserve a closer look!
No amount of extra money would realistically allow NASA (or any space agency) to fly missions simply "because we might discover something" because there are always many, many other mission proposals in the pipeline with vastly better justification than merely "because we might discover something".
You are correct in that the Voyagers' launch window was unique.
Nit pick: gravity assist doesn't fundamentally rely on gravity. It extracts energy from planets' motion about the sun [1]. If we could somehow "bounce" a spacecraft off a planet's surface, it would impart momentum similar to that of a gravity assist. (In my opinion, it's a badly-named term.)
[1] https://science.nasa.gov/learn/basics-of-space-flight/primer...
It’s also a good illustration of why we call some forces strong and others weak.
I'm not sure how you can make that claim. If you were to bounce off the surface, that would likely not be considered a "gravity assist", no?
When my kids were little, I showed them by holding a basketball in one hand and a tennis ball in the other, with the tennis ball on top of and touching the basketball. When I dropped them simultaneously, they fell together and bounced off the driveway — and the tennis ball took off like a rocket (no pun intended).
This is a huge oversimplification by a layperson, but just as ancient seafarers had to escape the currents caused near their shore, we have to figure out how to escape our solar system first, into interstellar space. You're not safe there, but at least you've exited the wake of our sun. Just like we had to exit the graviational pull of earth to reach the moon.
For context, getting something to low earth orbit is about 9.4km/s of Delta-V. From LEO to mars is another 4.3 km/s of Delta-V. Getting from LEO to any solar escape trajectory adds is about 18km/s.
As you can see, 30km/s of fuel savings is extremely significant, and that required the 175 year Grand Tour alignment.
The closest in speed so far would be 'New Horizons'. But even then NH is going at 14.5KM/sec compared with Voyagers 18KM/sec. There are no probes currently that would catch up to Voyager.
And even more inconceivable is how slow it still is in terms of human spaceflight outside of the Solar System.
Travelling from New York to LA quicker than playing the song "From New York To LA"
The tyranny of the rocket equation is the fact that to carry more fuel to orbit, you need more fuel to get it into orbit, which itself needs more fuel. That's why gravity assists are so essential for escaping the solar system on a budget.
The planetary alignment that enabled the Voyager launch windows only occurs once every 175 years.
We should definitely be sending out more probes, but we can't just do it whenever we want, at least not without a lot more expense.
More conservative trajectories giving fewer flybyes but relying on more probes would be possible, and are in fact what we've accomplished with the Gallileo & Juno (Jupiter), Cassini-Huygens (Saturn), and New Horizons (Pluto) spacecraft. There are NASA (U.S.) and Chinese proposals for a return visit to Uranus and Neptune, though those remain in planning stages.
<https://www.space.com/nasa-uranus-orbiter-and-probe-mission-...>
The orbiter missions had a much longer time-on-station. For Gallileo, roughly 7 years 9 months, Cassini-Huygens 13 years, and Juno 7 years to date, with another 5 or more possible.
The Ulysses solar probe also flew past Jupiter, using the planet for an orbital assist to both slow it down to approach the Sun more closely and incline its orbit above and below the planetary plane so that the Sun's poles could be observed directly.
The problem with that idea is, except for a few geeks, no one wants to spend that kind of money on space probes.
We need a heavy lift platform flying for a few years before we could start making much more crude larger probes, with cheaper or even massmarket components. Then it may work.