This is why you'd use gravity braking to do the work for you...
You just have to change direction, not slow yourself down, as long as your path intersects the sun you're done... we have sent spacecraft to the sun... it's not beyond our technical capabilities.
Basically, it's like flying into a banked curve... as long as you're pointed at the Sun when you exit the curve you're going to hit the sun with out needing to bleed 30km/s.
The fundamental reason why it doesn't work is because it's really expensive get stuff into space...
If it was difficult to hit things with large gravitational forces we wouldn't see very many comets in the night sky...
> Basically, it's like flying into a banked curve... as long as you're pointed at the Sun when you exit the curve you're going to hit the sun with out needing to bleed 30km/s.
That's not how it works. You're in the planet's reference frame so you inherit its orbital velocity. Exiting a slingshot in the direction of planet's retrograde (not in the direction to the Sun) you can kill off some velocity, but nowhere near enough to just drop yourself into the sun. You do need to bleed out that 30km/s to actually hit the sun.
> "If it was difficult to hit things with large gravitational forces we wouldn't see very many comets in the night sky..."
The difficulty does not come from the mass of the Sun. It comes from Earth's velocity around it. The waste starts out with that velocity as well. Basically the waste is already in a stable orbit around the sun, and getting it out of that is difficult.
If it has velocity to escape earth's gravity then it does not match earth and will eventually go somewhere else.
If it does not it will fall back.
Only at a Lagrange point will it not deviate from earth.
Given that it is not heading to earth we simply point it at an appropriate trajectory to intercept the moon and/or another planet using that planet to perform aforementioned "banked curve" which directs it to the sun at increased or decreased velocity.
The primary cost of shipping stuff to the sun is escaping earth, once you do that the additional fuel required to reach the sun is nowhere near the amount of fuel required to slow from 30 km/sec to zero.
Basically all we need to do is reach the moon... from there gravity does the work for us with the correct trajectory and a small amount of fuel to correct the trajectory.
You just have to change direction, not slow yourself down, as long as your path intersects the sun you're done... we have sent spacecraft to the sun... it's not beyond our technical capabilities.
Basically, it's like flying into a banked curve... as long as you're pointed at the Sun when you exit the curve you're going to hit the sun with out needing to bleed 30km/s.
The fundamental reason why it doesn't work is because it's really expensive get stuff into space...
If it was difficult to hit things with large gravitational forces we wouldn't see very many comets in the night sky...