Gravitational slingshot - please explain

well it's like that, except instead of snow under yr runners you have gravity hanging onto yr head - either way it helps you turn the corner without YOU using any energy

so you get into orbit, speed up while still IN orbit , then let go at the precisely decided moment on yr orbit and fly very exactly in a straight line in the direction you wanted) (if you tried to point yrself in that direction before you got off the earth eg you wd expend enormous unnecessary energy fighting the pull)

escape velocity straight up is way more than escape velocity sideways (that's why it's more tiring going upstairs and walking along the landing)