Earth's velocity in orbit ~ 30 km/sec ~ 10^-4 c http://en.wikipedia.org/wiki/Earth%27s_orbit If we increase the speed, the orbit becomes eccentric (e>0): v/vcircular = sqrt(1+e) But if the eccentricity e equals or exceeds 1, then the Earth escapes from orbit. So, the maximum speed for such an Earth is sqrt(2)*30 km/sec ~ 42.43 km/sec ~ 1/7000 c (so we shouldn't need Einstein). Now, the same calculations apply to an object of _any_ mass, so long as it isn't large relative to the Sun's mass. http://www.eso.org/public/outreach/eduoff/aol/market/experiments/hb/ In particular, we can have a highly eccentric comet that comes into the Earth's orbit at its closest point; we know that the speed of this comet at its closest point will lie between 30 and 42.43 km/sec. Note that if our comet is orbiting in the same plane as the Earth, and in the same direction, any potential collision with the Earth will occur at a significant speed, but far less than if it had a retrograde orbit, or an orbit perpendicular to the Earth's orbital plane; or a hyperbolic (extra-solar system) "orbit". This highly eccentric comet can have just about any semi-major axis that we choose; let's choose a semi-major axis of ~ 10,000 AU; this will give the comet an orbital period of ~ 1 million years. Thus, our comet may have revolved around the Sun ~ 4600 times during the lifetime of the solar system. This is a very small number, relative to the current upper limit estimates of 150,000,000 years (150 million Earth orbits) for the main body of the solar system to "relax" into its current configuration, during which our comet would have entered the inner solar system only 150 times. We also note that our comet (or some like it) may have run out of luck 65.5 million years ago (4600 minus 65 revolutions) and possibly caused the K-T event. http://en.wikipedia.org/wiki/Cretaceous%E2%80%93Tertiary_extinction_event Such comets need not have come from outside the solar system -- they might very well have been produced by close encounters of early small planets/planetoids that nearly got ejected from the solar system. Current N-body models of the early solar system seem to ignore bodies that have been "ejected"; once they achieve certain speeds and/or distances, they are ignored for future time-steps of the models. While ignoring them is appropriate for figuring out what happens to what's left in the solar system, it isn't when you are interested in what might happen to such bodies that didn't get completely ejected.