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Not literally in a sense that it must go in same direction as they went, but in distance to Earth.

I understand that this question may be a bit vague (is the budget 500M or 5B?) so feel free to assume: large budget: tens of billions.

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  • $\begingroup$ Voyager-1 didn't get from gravity assists as much delta-V as it could potentially. The purpose of Jupiter gravity assist was targeting to Saturn, and Saturn flyby was designed to fly close to its satellite Titan. Gravity assist is most effective when they are closer to the planet's centre. So, with existing technologies it's not so difficult to design a spacecraft to overcome Voyager-1 just by purpose-designed close Jupiter flyby gravity assist. If it would be the only purpose of the spacecraft, of course. $\endgroup$ – Heopps May 21 at 9:34
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    $\begingroup$ How heavy? Without payload weight there's no possible answer to this question. We could send a small rock to overtake very quickly, or a heavy probe may never catch up at all. $\endgroup$ – GdD May 21 at 10:15
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    $\begingroup$ Assuming same mass as that of Voyager 1 $\endgroup$ – Auberron May 21 at 11:50
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    $\begingroup$ @GdD: How do you accelerate your "small rock"? Even if our new probe had no payload at all, but it would still need a means of propulsion. I think the question is good as it stands. $\endgroup$ – TonyK May 21 at 20:52
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    $\begingroup$ Randal Munroe actually answered that in what-if.xkcd.com/38 (and quite entertaining to read) $\endgroup$ – Speedphoenix May 22 at 1:58
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With reasonably current technology there are basically three options, I think:

  1. A Jupiter gravity assist similar to how the Voyagers themselves got most of their velocity. This could do a bit more by going closer to Jupiter (we know more about the environment there now, and our navigation is better); or by actively boosting at closest approach (how much you can do this depends on your budget and your payload mass). We can save some fuel for a boost at Jupiter by using multiple Earth and Venus flybys in the way that is now standard.
  2. A solar gravity well manouver: use Jupiter to drop us in close to the Sun and then use as much boost as we can possibly manage at closest approach. If you can manage to get to Jupiter with a big enough delta-V reserve, this is better than using it at Jupiter
  3. Long duration low thrust systems like ion engines. A nuclear powered ion drive vehicle with a big tank of xenon and few spare thrusters to switch to when the first ones run out could eventually build up a very high velocity.

In all cases, I think, the answer would be a few decades.

If you are really in a hurry you could consider the "nuclear shotgun", perhaps on the Moon. That could launch a reasonably large, very tough payload at a very high initial velocity.

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    $\begingroup$ Agree with options 1-3, but what is "nuclear shotgun"? Is it a railgun? $\endgroup$ – Heopps May 21 at 11:30
  • $\begingroup$ fyi I've just asked What exactly is a solar gravity well manouver and in what cases would it be helpful? $\endgroup$ – uhoh May 21 at 11:58
  • $\begingroup$ How about calculating the max delta-V achievable with, say, the BFR and no other payload, or perhaps maximize payload in the form of an additional engine& fuel to be used exoatmospherically? $\endgroup$ – Carl Witthoft May 21 at 13:50
  • $\begingroup$ @Heopps Dig a deep hole about as wide as your payload and open out a chamber at the bottom. Put a nuke and some ice or water in the chamber then your payload at the base of the straight hole. Detonate the nuke. Your payload heads off very quickly. $\endgroup$ – Steve Linton May 21 at 15:47
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    $\begingroup$ @Heopps, the Pascal-B test of Operation Plumbbob accidentally used a nuclear explosion at the bottom of a hole to launch a one-ton steel plate at very high velocity; if it survived passing through the atmosphere, it was going fast enough to beat the Voyagers and Pioneers into interstellar space. Better planning will let you do that deliberately, and get an even higher velocity. $\endgroup$ – Mark May 21 at 21:01
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Propulsion technology would require a massive leap forward. There are a few methods for overtaking Voyager

  1. Build a finished, fueled large rocket in orbit and fire it into the direction, the speed boost without having to achieve escape velocity.
  2. Exotic high energy propulsion system with enough fuel to cover the distance
  3. Magnetic accelerator or mass driver that can accelerate a standing projectile into space from orbit at high speed. At 100 km per second, it would take six years to match Voyager 2's distance of 11 billion miles away.
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    $\begingroup$ "Exotic high energy propulsion system with enough fuel to cover the distance" You dont need enough fuel to cover the distance, you need enough fuel to accelerate to the neccessary speed. $\endgroup$ – Uwe May 21 at 20:53
  • $\begingroup$ To reach 100 km/s at reasonal acceleration, you need a pretty long distance. $\endgroup$ – Uwe May 21 at 21:07
  • $\begingroup$ They could use the Alameda-Weehauken Burrito Tunnel. $\endgroup$ – Harper - Reinstate Monica May 22 at 0:02
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There is a 2011 MIT PhD thesis by Daniel B. White, Jr., that discusses nuclear reactors driving high-power electric propulsion devices. These propulsion devices seem like technologies that did not yet exist in 2011 but that aren't drastic leaps beyond the current state of the art. He models a list of missions, including one that he calls the Interstellar Precursor, which would fly to 250 AU from the sun in 10 years, with a 6.5 ton burnout mass and a very small payload. To get an idea of the scale of the effort required, he tosses around ideas like basically taking over the ISS in order to develop space-based reactors and propulsion systems.

With current state of technology if we wanted how long would it take for newly launched probe to overtake Voyagers?

So with considerable R&D and investment, it sounds like the answer might be 10 years, starting from a launch date maybe 10-20 years in the future. But with strictly off-the-shelf current technology, the flight time is probably much longer.

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  • $\begingroup$ Could the downvoter explain the reason for the downvote? $\endgroup$ – Ben Crowell May 23 at 0:01
  • $\begingroup$ The question requested "current technology". I interpret that as meaning "Technology readiness level 7" (prototype demonstrated in a space environment) or higher. A PhD thesis is TRL 1, just one step above science fiction. $\endgroup$ – Mark May 30 at 22:12

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