Abstract The arrival of solid particles from outside our Solar System would present us with an invaluable source of scientific information. Attempts to detect such interstellar particles among the meteors observed in Earth’s atmosphere have almost exclusively assumed that those particles moving above the Solar System’s escape speed – particles on orbits hyperbolic with respect to the Sun – were precisely the extrasolar particles being searched for. Here we show that hyperbolic particles can be generated entirely within the Solar System by gravitational scattering of interplanetary dust and meteoroids by the planets. These particles have necessarily short lifetimes as they quickly escape our star system; nonetheless some may arrive at Earth at speeds comparable to those expected of interstellar meteoroids. Some of these are associated with the encounter of planets with the debris streams of individual comets: Comet C/1995 O1 Hale–Bopp’s 1996 pre-perihelion encounter with Jupiter could have scattered particles that would have reached our planet with velocities of almost 1kms−1 above the hyperbolic velocity at Earth; however, such encounters are relatively rare. The rates of occurrence of hyperbolically-scattered sporadic meteors are also quite low. Only one of every ∼104 optical meteors observed at Earth is expected to be such a locally generated hyperbolic and its heliocentric velocity is typically only a hundred metres per second above the heliocentric escape velocity at Earth’s orbit. The majority of such gravitationally-scattered hyperbolics originate at Mercury, though Venus and Mars also contribute. Mercury and Venus are predicted to generate weak ‘hyperbolic meteor showers’: the restrictive geometry of scattering to our planet means that a radiant near the Sun from which hyperbolic meteors arrive at Earth should recur with the planet’s synodic period. However, though planetary scattering can produce meteoroids with speeds comparable to interstellar meteors and at fluxes near current upper limits for such events, the majority of this locally-generated component of hyperbolic meteoroids is just above the heliocentric escape velocity and should be easily distinguishable from true interstellar meteoroids.