Kepler's Laws Calculator

This is a Java applet illustrating visually both with geometry and algebra the calculation of Kepler's Laws problems for two masses. All quantities in the diagram and the algebraic equations are updated dynamically as variables are changed. For simplicity of display, circular orbits are drawn for the masses. None of the quantities calculated here depend on the eccentricity of the orbits. Applet Controls: There are 3 modes for the applet, chosen by the choice menu at the bottom right, which switches between the calculation of the period, the separation, and the sum of the masses, with appropriate changes in the input quantities. These have correspondingly different controls.

(1) Period: The three sliders allow the separation in astronomical units and the masses (in units of solar masses) to be input and the period in years is calculated.

(2) Separation: The three sliders allow the period in years and the masses in units of solar masses to be input and the separation in astronomical units is calculated.

(3) Sum of Masses: The three sliders allow the period in years, the separation, and the ratio of masses M(1)/M(2) to be input and the sum of the masses M(1) + M(2) and the individual masses are calculated. Note that Kepler's Laws alone allow only the sum of the masses to be calculated. The ratio M(1)/M(2) used to apportion masses between the two objects must be obtained independent of Kepler's Laws (for example, by observing the orbits and locating the center of mass).

Data Display: The upper left portion of the display area shows the quantity being calculated and the diagram for location of the masses and center of mass, and the orbits (assuming spherical orbits) as the parameters are varied with the sliders.

The lower left portion of the display area shows the algebraic equations that are being solved to construct the display in the upper left.