Assume we have a sun-plannet system in a perfect, stable orbit. The gravitation force cancel out with the centrifugal force which equates into: Gm1m2/r^2 = m2v^2/r where m1= mass of the sun, m2 = mass of planet simplify the equation above I get: Gm1/r = v^2 This implies that if we move the plannet faster in tangent direction, the distance between 2 bodies must reduce to achieve a stable orbit. The opposite is true. Slowing down the planet will have to move further away from the sun to attain stable orbit. Let's consider kepler's second law and conservation of momentum. Basically, the law said that when the planet is half radius of a reference position, the velocity increase with the factor of 2. But according the the equation above, the velocity should increase with the factor of 4. Who can shed some light into this?