  Using the Spitzer Space Telescope, we observed a transit at 3.6um of KELT-11b
(Pepper et al. 2017). We also observed three partial transits from the ground.
We simultaneously fit these observations, ground-based photometry from Pepper
et al. (2017), radial velocity data from Pepper et al. (2017), and an SED model
utilizing catalog magnitudes and the Hipparcos parallax to the system. The only
significant difference between our results and Pepper et al. (2017) is that we
find the orbital period is shorter by 37 seconds, $4.73610\pm0.00003$ vs.
$4.73653\pm0.00006$ days, and we measure a transit center time of BJD_TDB
$2457483.4310\pm0.0007$, which is 42 minutes earlier than predicted. Using our
new photometry, we measure the density of the star KELT-11 to 4%. By combining
the parallax and catalog magnitudes of the system, we are able to measure
KELT-11b's radius essentially empirically. Coupled with the stellar density,
this gives a parallactic mass and radius of $1.8\,{\rm M}_\odot$ and $2.9\,{\rm
R}_\odot$, which are each approximately $1\,\sigma$ higher than the adopted
model-estimated mass and radius. If we conduct the same fit using the expected
parallax uncertainty from the final Gaia data release, this difference
increases to $4\,\sigma$. This demonstrates the role that precise Gaia
parallaxes, coupled with simultaneous photometric, RV, and SED fitting, can
play in determining stellar and planetary parameters. With high precision
photometry of transiting planets and high precision Gaia parallaxes, the
parallactic mass and radius uncertainties of stars become 1% and 3%,
respectively. TESS is expected to discover 60 to 80 systems where these
measurements will be possible. These parallactic mass and radius measurements
have uncertainties small enough that they may provide observational input into
the stellar models themselves.
