Two Slingshots May Detect Ultraweak Features in the Sun’s Gravity

A space experiment aimed at specifying the law of the Sun’s gravity more precisely is discussed. An extended “standard flight” scheme with two gravity assist maneuvers (slingshots) of a space probe near Venus and Earth is suggested, where the slingshots serve as amplifiers of small deflections caused by a deviation of the gravity law from a chosen ansatz. The deviation of the probe’s trajectory from its classic (Newtonian) pattern is calculated in detail using the isotropic Eddington–Robertson metric for the Sun’s gravity field and the “patched conic approximation” method for description of each slingshot. The trajectory deviation in the two-slingshots scheme is roughly assessed, the results indicating a principal possibility to detect the ultraweak distinctive feature of relativistic gravity.