Can you explain (or link to) "Fun fact, this means that if we ever wanted to dispose of nuclear waste by dumping it in a star, we'd need much less rocket fuel to hit Alpha Centauri than the Sun."
It's not making much sense to my tired mind today.
It takes less energy to accelerate an object away from both the Earth and sun (assuming your launch pad is on an appropriate spot on the Earth surface), than to accelerate an object away from the Earth but into the sun without just getting the object stuck in an orbit like Venus or Mercury.