  The $5S_{1/2}\rightarrow 5D_{5/2}$ two-photon transition in Rb is of interest
for the development of a compact optical atomic clock. Here we present a
rigorous calculation of the 778.1~nm ac-Stark shift ($2.30(4)
\times10^{-13}$(mW/mm$^2$)$^{-1}$) that is in good agreement with our measured
value of $2.5(2) \times10^{-13}$(mW/mm$^2$)$^{-1}$. We include a calculation of
the temperature-dependent blackbody radiation shift, we predict that the clock
could be operated either with zero net BBR shift ($T=495.9(27)$~K) or with zero
first-order sensitivity ($T=368.1(14)$~K). Also described is the calculation of
the dc-Stark shift of 5.5(1)$\times 10^{-15}$/(V/cm$^2$) as well as clock
sensitivities to optical alignment variations in both a cat's eye and flat
mirror retro-reflector. Finally, we characterize these Stark effects discussing
mitigation techniques necessary to reduce final clock instabilities.

Atomic Physics