goes into orbit:
Imagine I'm on the moon
, and I have a bunch of tennis ball
s. If I throw a ball parallel
to the ground, but not very quickly
, it'll go for a while, but eventually gravity
will pull it to the ground and it'll stop. Now, as I throw the balls with greater and greater velocity
, they'll get farther and farther, but they'll all fall eventually. But then I throw one really, really fast
, and it never hits the ground! How can this be?
Let's examine the curved path of the ball as it travels any horizontal distance-- for simplicity's sake, 1 meter
. Within that distance, it will fall away from a perfectly horizontal
path (the path it would take if there were no gravity) by a certain amount; let's call it dvert
, and it increases as horizontal velocity increases, since it can travel farther before it hits the ground. Now, let's look at the planet we're on (in this case, the moon); more specifically, 1 meter of it. Since the planet isn't flat
(last time I checked
), it'll curve away from a perfectly flat distance by a certain amount within this 1-meter length.
Now here's the crazy part: If dvert
(the amount the ball falls away from horizontal as it travels 1 meter) ever equals the amount that the planet curves away from the horizontal, the ball will never hit the ground
! Because the earth is curving away at the same rate that the ball is, it will go into orbit.