This is a real simulation based on the laws of gravity. Using a crushingly simple numerical integration to move the orbiter one step at a time, it's blown by the wind of physical laws and nothing else. While the computational accuracy of Macromedia Flash is probably less than ideal, it's sufficient for this particular example.

To move the orbiter, the following code runs over and over. Even if you are not a programmer, you can see the gist of it.

    // Carry orbiter forward one step

    // Radius vector and magnitude
    x = planet._x-orbiter._x;
    y = planet._y-orbiter._y;
    r_sq=x*x+y*y
    r = Math.sqrt(r_sq);

    // Acceleration due to gravity
	// Note m implicitly = 1.0
    ddx = (x/r)*(GM/r_sq);
    ddy = (y/r)*(GM/r_sq);

    // New velocity and position
    // Note time step implicitly = 1.0
    dx+=ddx;
    dy+=ddy;
    orbiter._x+=dx;
    orbiter._y+=dy;
    // Note orbiter velocity can be further changed by burns

As you may be able to see, in each step the orbiter travels according to the velocity it had at the end of the previous step, plus whatever velocity it picks up as a result of gravitational attraction. This is just like the stepwise mathematical model used by Isaac Newton to visualize orbital mechanics in the late 17th Century: linear motion with occasional centripetal impacts. Finally, using the rocket engine adds another small bit with which you can maneuver.

You may see that when you burn the engine, the orbiter will pass through the same point on the next orbit. So you change the velocity at the point of the burn, and the position on the far side of the orbit. To go from one circular orbit to another, you will always need two burns: one to move the far side of the orbit to the new radius, the second to circularize.