The Determination of Jupiter's Mass from Large Perturbations on Cometary Orbits in Jupiter's Sphere of Action

Abstract

Necessary and sufficient conditions are formulated for determining the mass of Jupiter from large perturbations induced in cometary orbits in the sphere of action of Jupiter. A procedure for the investigation has been developed and programmed for an electronic computer. Comparison of heliocentric and jovicentric computations shows that the perturbations on P/Wolf could be determined with great accuracy when this comet passed through Jupiter's sphere of action in 1922. The first attempt has been made to determine the mass of Jupiter using this passage and the observations of the comet in 1925. The resulting value for the reciprocal mass is 1047.345.