Technically you could try some clever gravity assists with Jupiter to greatly reduce the ∆v requirements. But that's still a very expensive way of solving a non-problem. We know how to deal with nuclear waste. The problem is with people being scared out of proportion by it.

It isn't sufficient to launch in the general direction of the sun, using the minimum energy required to escape earth's gravity?

The reason the Earth doesn't fall into the sun is that it's moving quickly enough that the centripetal force balances the Sun's gravity. If you escape the Earth's gravity well and give it a small push it would still have nearly as much orbital energy as the Earth and way more than Venus, which hadn't fallen into the sun either.

To slow down enough that you could fall into the sun you need to kill 30 km/s of velocity. To go fast enough to escape the solar system you only need about 15 km/s. And crashing into Jupiter is even cheaper than that.

No. For an entertaining explanation why, see https://www.youtube.com/watch?v=uNS6VKNXY6s

Obligatory xkcd: https://xkcd.com/1244/ (explanation and more details https://explainxkcd.com/1244/ )

Why not do an elliptical orbit that takes you close enough to the sun to burn up? That seems like less energy than dropping to zero no?

You'd still need an Earth-Sun transfer orbit, which is still a lot of deltaV.

http://i.imgur.com/SqdzxzF.png

Close to the sun still takes more energy than leaving the solar system, similar to how it's just as hard to charge a capacitor to -9V as to 9V. And in what sense would it "burn up"?

Bring it up does not change the fact that there is now radioactive material on an orbit which still potential overlaps the earth. Out of the solar system is a much better solution.

On the other hand it's not like the Sun isn't spewing out way more radioactive material continuously than we're talking about adding here.

EDIT: To give some orders of magnitude, the back of the envelope tells me that the sun inflicts about 700 TBq of carbon-14 on us every year. For comparison, countries like the USSR and UK have dumped 85,000 TBq of radioactive waste into the ocean (and Fukushima added another 15,000). I don't know how to judge how much of the vaporized waste would end up back on Earth so it's quite possible I'm wrong in the above.

An elliptical orbit that gets close to the sun is nearly the same as an orbit that goes through the sun.

Besides, exposing radioactive materials to heat does not affect their radioactivity.

That's only true up to a point. I suspect that if you exposed just about anything to 100,000 kelvin it ceased to look like any kind of matter we know anything about.

This experiment was performed thousands of times back in the 1950s and 1960s. A nuclear weapon's fireball is way hotter than 100,000K, and the exploding weapon contains lots of fissionable material and fission byproducts. The extreme temperatures don't destroy them, they just help spread it around.

Yup, you got me there. Speculating wildly ends poorly.

> I suspect that if you exposed just about anything to 100,000 kelvin it ceased to look like any kind of matter we know anything about.

1e5 K? You're missing a couple orders of magnitude, there.

The hottest parts of the Sun's surface go up to 20 million Kelvin, and that doesn't "cease to look like any kind of matter we know anything about".

Yes, but there is SOME temperature at which heating things up does start to cause things to act weirdly. You know, like in a fusion reactor. That definitely changes the radioactivity of certain elements.