  We consider corrections in the form of $\Delta L(R_{ijkl}R^{ijkl})$ to the
Einstein-Hilbert Lagrangian. Then we compute the corrections to the
Schwarszchild geometry due to the inclusion of this general term to the
Lagrangian. We show that $\Delta L_3=\alpha_{{1/3}}(R_{ijkl}R^{ijkl})^{{1/3}}$
gives rise to a constant anomalous acceleration for objects orbiting the Sun
onward the Sun. This leads to the conclusion that $\alpha_{{1/3}}=(13.91\pm
2.11) \times 10^{-26}(\frac{1}{\text{meters}})^{{2/3}}$ would have covariantly
resolved the Pioneer anomaly if this value of $\alpha_{{1/3}}$ had not
contradicted other observations.
  We notice that the experimental bounds on $\Delta L_3$ grows stronger in case
we examine the deformation of the space-time geometry around objects lighter
than the Sun. We therefore use the high precision measurements around the Earth
(LAGEOS and LLR) and obtain a very strong constraint on the corrections in the
form of $\Delta L(R_{ijkl}R^{ijkl})$ and in particular $\Delta
L=\alpha_n(R_{ijkl}R^{ijkl})^n$. This bound requires
$\alpha_{{1/3}}\leq6.12\times 10^{-29}(\frac{1}{\text{meters}})^{{2/3}}$.
Therefore it refutes the covariant resolution of the Pioneer anomaly.
