Both those facts amaze me.
I mean, all you need do is fire off a spaceship backwards relative to the earth's orbit such that it is stationary relative to the sun, then let gravity do the rest, right?
Except that you need to accelerate the space ship to the orbital speed of the earth to get its own orbital speed to zero, a mere 107,000 km/h
I get it, mathematically, but I don't get it intuitively.