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I'm an engineering student and have a few ideas to bat at the scientific community. First premise is based upon common sense. I understand that if I am standing on a skateboard on a relatively smooth surface and a stone of significant mass is thrown to me and I catch it, the momentum of the projectile is transferred to me causing a forward acceleration.

My question: Suppose that a system is designed to provided constant acceleration in space utilizing the aforementioned intuitive concept. In the simplest form I can idealize such a system as a basketball constantly striking a flat surface. Opposed to a ball consider an arbitrary mass striking a greater mass. I suppose that if creative means are applied to control the striking action (e.g. magnetism, mechanical means) then this action can be repeated to provide constant acceleration without the use of carrying fuel loads. Would it not be possible to reset the system to an initial state without canceling the resulting acceleration?

Due to the length of this question I will post the next question later. Thx

C Robbins
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The issue here is that the initial momentum needs to come from somewhere. I suppose, if we could track the momentum of various things in space, we could "hitch a ride" from it. Like netting a comet or taking advantage of space debris striking the craft. That's a properly analogous situation to your basketball/skateboard system.

However, you seem to be intent on an internal system. The problem with this is momentum conservation. Even though you have these two objects are hitting each other, you're slowing down the hitting-object so you can propel it to your flat surface again. That means that whatever momentum is generated by every collision is canceled out by slowing down your hitting-object.

It's like you on your skateboard trying to throw the ball to move yourself, but then catching that ball yourself so you can throw it again. This will result in you going nowhere; the momentum of the ship/hitter-object (or ball/you/skateboard) system never actually increases. This results in the two objects (the load and hitter-object) bouncing at each other, but not actually going anywhere.

To get a really good idea of why this works, you should find a really nice rolling chair in a pretty flat and level room, sit in it, and attempt to get to the other side of the room without touching anything but the chair.

PipperChip
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There is actually such a mechanism that you're describing. The means to achieve that is through radiation pressure from light. This is called solar sail, and would achieve space exploration without having to expend proppelents for the main movement production.

Ignacio Vergara Kausel
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You could imagine this. Say you have a railgun on the moon (to avoid atmosphere) that fires a projectile at the spacecraft. The projectile bounces elastically off the spacecraft, transferring twice its momentum. If you are happy to accelerate in exactly the correct direction, it could return to the moon to be fired again. The momentum is transferred to the moon, but as the moon is so massive we don't care. The energy is made from sunlight and renewable.

There are several problems to be solved-as I said, if you want to reset the system (as you asked) you need to accelerate in precisely the right direction so the rebound sends the projectile back to the moon. As the spacecraft leaves the moon, the flight time increases, so the time between impacts increases, lowering the average acceleration. As the spacecraft accelerates, the momentum transferred gets less-the transferred momentum is the amount in the CM frame. The limiting spacecraft velocity is the projectile velocity-at that point the projectile will never catch up.

Ross Millikan
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