How does hybrid gravity bend light and shift planetary orbits?

Hybrid metric-Palatini gravity blends two different geometric descriptions of curvature into a single function, propagating the usual graviton plus two massive scalar fields. Working directly from the field equations — no shortcuts — the authors derive the gravitational potential (standard Newtonian plus two Yukawa correction terms) and the light-bending parameter, then use Solar System planetary precession data to constrain the scalar masses. The constraints spell out exactly when this theory is indistinguishable from Einstein's and when it isn't.