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Based on telescopic observations of Jupiter-family comets (JFCs), there is predicted to be a paucity of objects at sub-kilometre sizes. However, several bright fireballs and some meteorites have been tenuously linked to the JFC population, showing metre-scale objects do exist in this region. In 2017, the Desert Fireball Network (DFN) observed a grazing fireball that redirected a meteoroid from an Apollo-type orbit to a JFC-like orbit. Using orbital data collected by the DFN, in this study, we have generated an artificial dataset of close terrestrial encounters that come within $1.5$ lunar distances (LD) of the Earth in the size-range of $0.01-100$kg. This range of objects is typically too small for telescopic surveys to detect, so using atmospheric impact flux data from fireball observations is currently one of the only ways to characterise these close encounters. Based on this model, we predict that within the considered size-range $2.5\times 10^{8}$ objects ($0.1\%$ of the total flux) from asteroidal orbits ($T_{J}>3$) are annually sent onto JFC-like orbits ($2<T_{J}<3$), with a steady-state population of about $8\times 10^{13}$ objects. Close encounters with the Earth provide another way to transfer material to the JFC region. Additionally, using our model, we found that approximately $1.96\times 10^{7}$ objects are sent onto Aten-type orbits and $\sim10^{4}$ objects are ejected from the Solar System annually via a close encounter with the Earth.