Of course it would be prohibitively expensive, but the OP specifically said "If we neglect the danger of unsuccessful lift-off of the rocket and the cost". Also, I don't see why it's necessary to "protect" the nuclear waste. Does it have to be in pristine condition when it impacts the sun?

@James Read again my first sentence. I don't think the public opinion would agree with sending a rocket full of nuclear waste which could be blown up by solar winds near the Earth, or more probably explode during launch!

"Early conceptual designs for the Solar Probe mission used a gravity assist maneuver at Jupiter to cancel the orbital speed of the probe launched from Earth, in order to drop onto a trajectory close to the Sun. The Solar Probe Plus mission design simplifies this trajectory by using repeated gravity assists at Venus" en.wikipedia.org/wiki/Solar_Probe_Plus

@Spirine: Sorry, I forgot about the first half of your first sentence.

Basically the arguments laid out by me in this mostly-unrelated post

@MatthewWhited, yes, yes they are. But they generally Don't effect us here on are pretty little planet because of things like the magnetosphere and ozone and atmosphere and ect... Nuclear waste rockets blown apart by a strong solar storm would be much heavier, i.e. like an asteroid or a comet, and have the ability to pass through those things, and burn up in our atmosphere or crash back on earth, causing lots of radioactive contamination. That's the difference. They do occasionally though, like back in the 1850's when they knocked out the Telegraph.

the radiation wouldn't be into the atmosphere. The materials may but that's pretty unlikely. The of the objects would just be too dense and have too much velocity to be effected enough by solar winds alone.

Can't we slow down the barrel a little less? Wouldn't setting its speed to 15 km/s in the heliocentric frame (i.e. "only" -15 km/s in earth frame) be enough to let the sun trap it into its gravity field? Also, you say it would be a cost of 4 M$ / kg; do you know how this compares to "standard" underground storage for long-term radioactive waste?

@Spirine Hmm why does the rocket need to be fueled by liquid hydrogen and oxygen? I mean, if we're not too concerned about sending nuclear waste in space, we can use nuclear energy for the rocket as well, right?

@atlaste You suggesting using an electrically powered rocket, but there are two main concerns: is still needs to expell a lot of propellant, and the thrust provided by such engines is to weak to allow a launch from Earth's surface.

@Spirine Actually there have been a lot of proposals, like using small nuclear explosions to propel te space craft. See: en.wikipedia.org/wiki/Nuclear_propulsion .

@atlaste I challenge you to find any government which agree with using nuclear explosions for a launch from Earth surface! Remember how Orion project died.

@Spirine You can launch it into orbit the usual way, and then use nuclear fuel for the long trip to the sun. And by the ways, governments wouldn't launch anything filled with nuclear waste, because of the chance the thing will blow... I would hardly consider that an argument. :-)

@atlaste This may be a good idea, yet you should provide me some figures ;)

but why does it need to consume fuel in its way to Sun ? won't it just "drop" toward Sun attracted to its gravity ?

@BudaFlorin No, because that's not how orbits work. Think of gravity like a centripetal force.

@Evariste Similar thing here. The sun doesn't have a 'gravity field', all objects with mass attract each other. Since we are moving at ~30 km/s around the sun, our tangential speed is moving away from the sun fast enough that we stay a relatively constant distance from the sun.

@Ryan Why would solar winds impact a spacecraft so catastrophically so close to earth