How fast is Voyager travelling? Could we send out a Voyage X at a faster speed and with better tech to catch up and surpass it?
If you give yourself 10 years to design the probe and something to get it going that fast, then the speed you actually need jumps up to 19.5 AU/year. The longer it takes you to design your fast rocket, the faster it has to go in order to catch Voyager 1 in the same amount of time.
Realistically, unless something exotic happens in space propulsion technology, we will never catch Voyager 1 within our lifetime. If we launched today at twice the speed of Voyager 1, then we could catch it in around 50 years, but that's not going to happen.
The question you're asking is hard to answer: When do you want to catch up? If we send a new object to space today, which travels 5% faster, is that good enough? It won't pass Voyager 1 for a looooong time, but will eventually.
Is that what you're aiming for? Why? Or are you asking for a magical way to cross that distance (35 years of traveling) 'instantly'?
1: http://www.wolframalpha.com/input/?i=3.595+AU+per+year&d...
http://en.wikipedia.org/wiki/Helios_probes (70 km/s)
http://en.wikipedia.org/wiki/Solar_Probe%2B (theoretical 200 km/s)
Accelerating to ludicrous speed on the way out of the solar system is much more difficult.
My understanding (though I'm no astrophysicist) is that gravity boost from a planet works because of the relative velocities between the planet and the sun, whereas trying to use the sun's gravity to boost your solar system escape velocity would fail since gravity would be fighting you on the way out just as much as it was helping you on the way in.
A gravity assist works by robbing orbital momentum from the planet, transferring it to the spacecraft. (I once saw a calculation that Voyager's slingshot slowed Jupiter's motion by one foot per trillion years.) Jupiter has orbital momentum around the Sun, but the Sun has no orbital momentum around itself.
Flying past the Sun could give you velocity relative to the galactic center, making use of the Sun's orbit around that. But that velocity doesn't help you leave the Sun's neighborhood or travel within the Solar System, because the gained velocity is in the same direction as the Sun and Solar System are already moving.
Yes, this is basically correct. What a gravity boost from a planet does is transfer a very small amount of the planet's orbital kinetic energy to the spacecraft; it puts the planet into a slightly smaller orbit, and boosts the spacecraft to a higher speed on its way out. Since the Sun is what the planets are orbiting, this trick obviously won't work the same way with the Sun.
(Technically, the Sun itself, or more precisely the center of mass of the Solar System, is orbiting the center of the galaxy; so I suppose it would be theoretically possible to fly a spacecraft by the Sun in such a way as to transfer a very small amount of its orbital kinetic energy with respect to the center of the galaxy to the spacecraft, so it would fly outward faster than it went in, even after taking into account the slowdown climbing out of the Sun's gravity well. But I doubt we're going to be in any practical position to try this any time soon.)
In the reference frame of the planet you will travel in a hyperbola as you go by. The incoming branch is from the front of the planet, the outgoing branch is also in the front of the planet. So you go from moving backwards to moving forwards.
However the planet is moving in the reference frame of the Sun. The initial "moving backwards" is actually more like "sitting there". The ending "moving forwards" is actually something like, "moving up to 2x as fast as the planet".
So a gravity boost only looks like a gravity boost in a reference frame that is moving relative to the object. Furthermore the gravity boost also does nothing to help you to escape from the object you're getting the gravity boost from.
Therefore we cannot get a gravity boost from the Sun to leave the Solar System. And a gravity boost from the Sun does not look like a gravity boost to us, in orbit around the Sun.
(Feel free to correct me, physicists!)
The bigger issue is convincing someone to hand you millions of dollars to literally throw away faster than anything in prior human history.
No. The gravity assist is because of the motion of the planets around the sun. The sun isn't moving relative to itself. There are some other things you can do where the sun can help, but not a slingshot.
Provided it survives that far out, New Horizons is likely to follow the Voyager probes in exploring the outer heliosphere and mapping the heliosheath and heliopause. Even though it was launched far faster than any outward probe before it, New Horizons will never overtake Voyager 1 as the most distant man-made object from Earth. Close fly-bys of Saturn and Titan gave Voyager 1 an advantage with its extra gravity assist. When New Horizons reaches the distance of 100 AU, it will be travelling at about 13 km/s (29,000 mph), around 4 km/s (8,900 mph) slower than Voyager 1 at that distance.