  The Kepler mission reveals a peculiar trough-peak feature in the orbital
spacing of close-in planets near mean-motion resonances: a deficit and an
excess that are a couple percent to the narrow, respectively wide, of the
resonances. This feature has received two main classes of explanations, one
involving eccentricity damping, the other scattering with small bodies. Here,
we point out a few issues with the damping scenario, and study the scattering
scenario in more detail. We elucidate why scattering small bodies tends to
repel two planets. As the small bodies random-walk in energy and angular
momentum space, they tend to absorb, fractionally, more energy than angular
momentum. This, which we call "ping-pong repulsion", transports angular
momentum from the inner to the outer planet and pushes the two planets apart.
Such a process, even if ubiquitous, leaves identifiable marks only near
first-order resonances: diverging pairs jump across the resonance quickly and
produce the MMR asymmetry. To explain the observed positions of the
trough-peaks, a total scattering mass of order a few percent of the planet
masses is required. Moreover, if this mass is dominated by a handful of
Mercury-sized bodies, one can also explain the planet eccentricities as
inferred from transit-time-variations. Lastly, we suggest how these conditions
may have naturally arisen during the late stages of planet formation.
