Path Object Is Going To Travel

Hey guys,

just wanted to know if there's any way to get the path of where an object is going to go, with physics factored in of course, and Print it in the form of something like a dotted line in front of the object.

Some random examples of what I'm talking about:

So say if there's a sphere moving along the screen and it's on a collision course with whatever. The line in front of it would show where the object will be traveling to and at which angle it would bounce off the object it collides with, like this:

Or say if the object was something like a meteor and it passes by a planets gravity field. The line in front would show where the meteor is going to traveling and how its going to bend around the planet based on its gravity, like this:

Just asking how because I have not a clue. Don't care if you don't know anything about the subject, just trying to find a starting point. Thanks.