  The well-known analogy between a special limit of General Relativity and
electromagnetism is explored in the context of the Lorentz-violating
Standard-Model Extension (SME). An analogy is developed for the minimal SME
that connects a limit of the CPT-even component of the electromagnetic sector
to the gravitational sector. We show that components of the post-newtonian
metric can be directly obtained from solutions to the electromagnetic sector.
The method is illustrated with specific examples including static and rotating
sources. Some unconventional effects that arise for Lorentz-violating
electrostatics and magnetostatics have an analog in Lorentz-violating
post-newtonian gravity. In particular, we show that even for static sources,
gravitomagnetic fields arise in the presence of Lorentz violation.
