In this note the tensorial Taylor series (5) is used to calculate the change in the Hooke / Newton inverse square law due to the vacuum, and it is shown to second order that the orbital precession of UFT377 is due to the vacuum. It may be concluded that all precessions are due to the vacuum, or aether, or spacetime. This is a major discovery. The <delta r dot delta r > needed to induce orbital precession is given to second order in Eqs. (18) to (20). It would be very interesting to graph Eq. (5) to higher orders of the tensor Taylor series. Note carefully that the same tensor Taylor series is used in the theory of the Lamb shift in atomic H. So we achieve unification of concept in the description of atomic and orbital physics.