So, (very much ballpark, and ignoring all additional weight for fuel, etc.), would that mean this could reach three times their speed in a month, and, after that, catch up with one of them in 15 years or so?
If so, is it feasible to build one with enough fuel to accelerate for a year or so?
If so, where’s the billionaire willing to spend a few quid on a machine that goes out to photograph one of the Voyagers from close up while it zooms by, or even bring one of them back to earth before the century is over?
So, getting up to 25.5 km/s with a rocket with an exhaust velocity of 30 km/s means you need the wet weight to be 2.33 times the dry weight. Last I checked [1] you can get 77 W/kg with photovoltaics so you need you'll need 1402 kg of those in addition to the 226 kg of engine for a total of 1626 kg. Round that up to 2200 kg for structure and tankage and so on for a total we mass of 5126 kg where 2926 kg of that is fuel. You're using that at 5.4/30000=.00018 kg/s for a total of 16255555 seconds of acceleration or about six months. So six months instead of one but basically yes.
Xenon is apparently pretty expensive, like $1,200/kg. Just running it for 100 hours at 0.00018 kg/s will cost $76,800 for the propellant. Plus 10,200 kWh of electricity!
That's cheap! The launch'll set you back about $100m so another $3.5m for propellant isn't going to be worth worrying about. At some point we'll be wanting to start finding more fuel for our rockets at our destinations. There are ways we know how to do this for oxygen, hydrogen, and methane but getting more xenon on Mars or Titan just isn't doable. So at that point I expect people to switch over to Argon which doesn't ionize quite as easily but can be found all over the solar system.
For a deep space probe that fuel cost is not a showstopper. That's well down in the weeds compared to the cost of launching it to orbit and manning the tracking stations and buying airtime on the Deep Space Network.
Before doing more estimates, it's probably worth adding in the mass of a plausible payload i.e. the scientific instruments that are the purpose of the spacecraft.
So, (very much ballpark, and ignoring all additional weight for fuel, etc.), would that mean this could reach three times their speed in a month, and, after that, catch up with one of them in 15 years or so?
If so, is it feasible to build one with enough fuel to accelerate for a year or so?
If so, where’s the billionaire willing to spend a few quid on a machine that goes out to photograph one of the Voyagers from close up while it zooms by, or even bring one of them back to earth before the century is over?