  We observed two secondary eclipses of the exoplanet WASP-12b using the
Infrared Array Camera on the Spitzer Space Telescope. The close proximity of
WASP-12b to its G-type star results in extreme tidal forces capable of inducing
apsidal precession with a period as short as a few decades. This precession
would be measurable if the orbit had a significant eccentricity, leading to an
estimate of the tidal Love number and an assessment of the degree of central
concentration in the planetary interior. An initial ground-based secondary
eclipse phase reported by Lopez-Morales et al. (0.510 +/- 0.002) implied
eccentricity at the 4.5 sigma level. The spectroscopic orbit of Hebb et al. has
eccentricity 0.049 +/- 0.015, a 3 sigma result, implying an eclipse phase of
0.509 +/- 0.007. However, there is a well documented tendency of spectroscopic
data to overestimate small eccentricities. Our eclipse phases are 0.5010 +/-
0.0006 (3.6 and 5.8 microns) and 0.5006 +/- 0.0007 (4.5 and 8.0 microns). An
unlikely orbital precession scenario invoking an alignment of the orbit during
the Spitzer observations could have explained this apparent discrepancy, but
the final eclipse phase of Lopez-Morales et al. (0.510 -0.006 / +0.007) is
consistent with a circular orbit at better than 2 sigma. An orbit fit to all
the available transit, eclipse, and radial-velocity data indicates precession
at <1 sigma; a non-precessing solution fits better. We also comment on analysis
and reporting for Spitzer exoplanet data in light of recent re-analyses.
