  We demonstrate how the total luminosity in satellite galaxies is a powerful
probe of dark matter halos around central galaxies. The method cross-correlates
central galaxies in spectroscopic galaxy samples with fainter galaxies detected
in photometric surveys. After background subtraction, the excess galaxies
around the central galaxies represent faint satellite galaxies within the dark
matter halo. Using abundance matching models, we show that the the total galaxy
luminosity, L_sat, scales linearly with host halo mass, making L_sat an
excellent proxy for M_h. L_sat is also sensitive to the formation time of the
halo, as younger halos have more substructure at fixed M_h. We demonstrate that
probes of galaxy large-scale environment can break this degeneracy. Although
this is an indirect probe of the halo, it can yield a high-S/N measurement for
galaxies expected to occupy halos at $<10^{12}$ M_sol, where other methods
suffer from larger errors. In this paper we focus on observational and
theoretical systematics in the L_sat method. We test the robustness of our
method of finding central galaxies and our methods of estimating the number of
background galaxies. We implement this method on central galaxies in SDSS data,
with satellites identified in faint imaging from the DESI Legacy Imaging
Surveys. We find excellent agreement between our theoretical predictions and
the observational measurements. Finally, we compare our L_sat measurements to
weak lensing estimates of M_h for red and blue subsamples. In the stellar mass
range where the measurements overlap, we find consistent results, where red
galaxies live in larger halos. However, the L_sat approach allows us to probe
significantly lower mass galaxies. At these masses, the L_sat values are
equivalent. This example shows the potential of L_sat as a probe of dark halos.
(Abridged)

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics