Source of the post
I assume U means constant velocity, or acceleration independent of time?
Nah, U is the potential energy of the barrier (660MJ in this case... and don't ask me why physicists use U for potential energy). It's also the same thing as the V0
in the formulae you showed -- you can think of it as V for voltage, since usually in the context of electron tunneling it's with an electrostatic barrier.
The velocity of the particle is considered in the "E", for kinetic energy. In this case it ends up being pretty much irrelevant -- it's the height (U), width (L), and your mass (m) that make the probability so small for tunneling to Saturn. (I hope I didn't just call you fat.)
Comparing to the probability of picking the same atom out of all atoms in the observable universe is fun. There are about 10^80 of them. If I pick one at random, the odds of you picking the same atom is 1 in 10^80. Ok, that's not so impressive after all. The first picker hasn't changed the odds. But what if more people pick atoms at random? If three people do it then the odds that all three pick the same atom are 1 in (10^80)^2. The extra exponent is simply the number of people who pick, minus 1. What if every person on Earth picks an atom out of the universe at random?
Then the odds that every person picks the same atom is still
better than the odds of tunneling to Saturn! (It's 1 in (10^80)^(7.5x10^9), which is about 10^-10^12). Long story short, the probability for tunneling to another planet is as ridiculous as the idea. And now I've talked enough about quantum mechanics; someone else should talk about green things.