Kepler's Laws as Modified by Newton

This is a Java applet illustrating Kepler's laws, as modified by Newton to include the effect of the center of mass, for a binary star system. Applet Controls: The star on the left is labeled by the index 1 and the star on the right by the index 2. The slider bar at the bottom controls the eccentricity of the orbits. The masses of the two stars (M1 for the star on the left and M2 for the star on the right) are controlled by the sliders on the left.

The slider 'zf' on the right side controls the zoom factor for the display, and the slider 'a1' sets the length of the semimajor axis of star 1 (the left star). The scale is indicated by the legend in the lower right of the display. The applet is set up to scale the distances always to a fixed amount (set by the zoom factor slider 'zf'), so changing the slider 'a1' does not change the locations of the stars, but it changes the distance scale indicated by the legend in the lower right.

The buttons on the top toggle on and off lines joining the stars to the focii of the ellipses, the orbits, and display of numerical information. The rightmost pulldown menu controls the speed of the animation. The motion may be toggled on and off by clicking anywhere in the applet display.

Data Display: When the info display is toggled on, the data displayed in the main window corresponds to the semimajor axes of the two stars [a(1) and a(2)], the masses of the two stars [M(1) and M(2)], the reduced mass M, the eccentricity e, the period, the separations of the two stars from the center of mass [R(1) and R(2)], the separation between the two stars R, and the elapsed time. All times are in Earth years, all distances in A.U., and all masses in solar units.