[size=150]Kepler’s 1[sup]st[/sup] law arises from the 2[sup]nd[/sup] and 3[sup]rd[/sup] Kepler’s laws and from the fact that the gravitational force diminishes as R[sup]-2[/sup] (the inverse square ofthe distance law of gravity).[/size][br][br][size=150]Feynman proved that to equal anglescorrespond equal velocity changes. He illustrated this property by two diagrams: an orbit diagram and a velocity diagram. From the construction (and from the relevant physical laws) follows that the velocity diagram is always of the shape of the regular polygon[/size]

[size=150]Feynman found the geometrical correspondence of these two diagrams based on the equality of the angle swept by a planet with the relevant central angle in the velocity diagram, see the figure below.  [br][/size][br][br][br]

[size=150]Rotating the velocity diagramand using the properties of ellipse that we mentioned above he proved that the shape of the planet’s path is an ellipse.[br][/size][br]