Say you're in orbit around the earth and you would trow a ball or some sort towards the edge of the earth far enough so it doesn't enter the atmosphere but instead slingshots around the earth so you can catch it again, all things considered wouldn't this thrust have propelled you in a direction?
So you throw a ball - which will move you in the opposite direction to the throw. Then catch it as it comes round and it will move you the way it was moving - back to where you were. Which direction did you want? Throw a ball and you move. Catch a ball and you move: but don't do both.
I guess you mean this effect could be utilised for propulsion ? It would be extremely inefficient and would only work in orbit. As Oli pointed out, the moment you catch it again you would move back towards your starting position, but not all the way (although most of the way) because some of the balls energy would also be converted to heat.
I tought that because it revolved halfway around the earth it would somewhat maintain it's energy but change direction causing a not 100% efficient boost in the same direction?
You or the spacecraft will probably be heavier then the ball, sending you in the opposite direction at (ball_mass/spacecraft_mass)*ball_speed. So the spacecraft and the ball wont be meeting halfway around the earth. This also answers your last question.
What you are suggesting is an unusual version of what is in common use for changing the orientation of a sattellite, called a "momentum wheel." for example, if you want to twist a sattelite about an axis, you spin up the momentum wheel of that axis and conservation of angular momentum causes the main body of the sattelite to rotate in the opposite direction (much more slowly in, practical cases). as the main body of the sattelite approaches the new orientation you desire, you begin to remove the angular momentum you added to the wheel that started the reorientation. Instead of a momentum wheel, you are suggesting giving some angular momentum to a "sub satellite." This will change your orbit and probably* the period of the orbit. If you time it correctly, the sub-satellite could complete exactly N orbits of the Earth and return to your position, be caught in a net, and then I think you would be back in basically the old original orbit. (Almost sure of this, but as there are several orbits with the same magnitude of angular momentum, I think that perhaps you might change the plane of the orbit). I am sure that there would be no net change in the magnitude of angular momentum, and doubt that even the plane of the orbit can be changed. It is an interesting question that should be explored more carefully. ------------------ * may be possible to make so the "launch point" is at the apogee of the new orbit (no change in major axis of the orbit) so that the period remains the same - do not want to think about this carefuly.
