(Not that we're anywhere near having a rocket factory on the moon... but maybe one could be assembled and fueled in orbit?)
I believe that this is wrong.
The Earth weighs 5.96e+24 kg and has radius 3.37e6 meters. The Sun weighs 1.98e30 kg and our orbit has radius 1.496e11 meters. That means that the potential well for getting away from Earth is about 11,800,000 joules/kg while for getting out of the Sun's gravity well is about 882,800,000 joules/kg. Assuming that I did the math right, that's about 7.5 times as hard.
It therefore takes a lot more energy to climb out of the Solar System than it does to climb out of Earth's gravity well. Voyager got a LOT of energy from those gravitational slingshots.
A probe has to launch from the surface of the earth. But counterintuitively the probes start out already in solar orbit, even before they're launched -- because the earth is in solar orbit. More than half the energy required to achieve escape velocity is needed just to get into a roughly circular relatively low orbit around the gravitating body you're trying to escape from, and by virtue of being launched from the earth the probes get that velocity for free. Furthermore, the earth's orbit isn't really "low" with respect to the sun. We're fairly far out there, so the fraction of the energy needed to go from earth orbit to a solar escape trajectory is even less.
Put another way: a probe launched from the earth gets no help leaving earth's gravity well. But once it does it gets a huge automatic gravity assist from the earth itself as it enters solar orbit.
It takes a lot of energy to escape Earth's gravity well. It takes a comparatively tiny amount to escape the Sun's, as a sibling poster pointed out. It would be actually harder to visit, say, Mercury, as you now have to shed all the energy Earth has given you for free, in order to "fall" into the Sun's well.
Voyager wanted to visit multiple planetary bodies – changing orbital parameters is not cheap. But if all it wanted was to get out of the system, burning straight out would probably be cheaper (in Delta-V terms). The closer to Earth the better, for the Oberth effect.
https://www.nasa.gov/mission_pages/station/expeditions/exped...
It would be cheaper in fuel terms, and require less thrust, but it'd also require us to manufacture propellant on the lunar surface and fly everything we can't build there from Earth (and landing on the Moon is purely propulsive).
Which you can't. So that's a no for the moon, but something from orbit could make sense.
Have a staging area and just accumulate tons of fuel from multiple launches.
Of course you can.
> By atomic composition, the most abundant element found on the Moon is oxygen. It composes 60% of the Moon's crust by weight, followed by 16-17% silicon, 6-10% aluminum, 4-6% calcium, 3-6% magnesium, 2-5% iron, and 1-2% titanium.
You have oxygen. You have aluminum. You can now make a solid rocket. There's some magnesium there too if you want to use that instead.
Not exactly. You have aluminium oxide, which you could split into aluminium and oxygen using huge amounts of energy, like we do on earth.
Helium-3 could be interesting, though.