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. $\endgroup$– HeoppsMay 21 '20 at 9:34
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1$\begingroup$ 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. $\endgroup$– GdDMay 21 '20 at 10:15
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1$\begingroup$ Assuming same mass as that of Voyager 1 $\endgroup$– AuberronMay 21 '20 at 11:50
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1$\begingroup$ @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. $\endgroup$– TonyKMay 21 '20 at 20:52
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3$\begingroup$ Randal Munroe actually answered that in what-if.xkcd.com/38 (and quite entertaining to read) $\endgroup$– SpeedphoenixMay 22 '20 at 1:58
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With reasonably current technology there are basically three options, I think:
- 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.
- 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
- 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.
answered May 21 '20 at 11:22
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2$\begingroup$ Agree with options 1-3, but what is "nuclear shotgun"? Is it a railgun? $\endgroup$– HeoppsMay 21 '20 at 11:30
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$\begingroup$ fyi I've just asked What exactly is a solar gravity well manouver and in what cases would it be helpful? $\endgroup$– uhohMay 21 '20 at 11:58
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$\begingroup$ 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? $\endgroup$ May 21 '20 at 13:50
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$\begingroup$ @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. $\endgroup$ May 21 '20 at 15:47
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1$\begingroup$ @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. $\endgroup$– MarkMay 21 '20 at 21:01