Ross, I'm not real clear on the vector stuff. Let me ask the question this way. Suppose you are in a rocket that can magically propell itself, ie doesn't loose mass via acceleration. You point the nose of the rocket in the direction of the orbit, so that the rocket is tangencial to the earth. If you fire the rocket wouldn't that take you to a higher orbit. I'm visualizing a circle with a tangent drawn on it. At the center or the circle is a point representing the sun. One segment of the tangent is the rocket thrust and the other the direction the rocket seems to me it would head. No? I just can't see how the rocket would get closer to the sun and not farther away. To get clocer it seems to me that you would have to turn the rocket engine away from the some small degree outside the tangent so that the nose would point inside the circle.
Edit: This would be like firing a rocket at the horizon. Assuming it doesn't hit a mountain or run out of fuel, it will eventually head out into space. Meanwhile, as the rocket sat there ready for launch, it's orbit around the earth is at its minimum. The only variable here would be acceleration which would take it into orbit upon firing.