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In July 1994 the Comet Shoemaker-Levy 9 struck the planet Jupiter at a speed of around $60\textrm{ km s}^{-1}$ . Although it broke up before impact, the core of the original comet was around $5\textrm{ km}$ diameter. Its estimated density was $0.3 - 0.7\textrm{ g cm}^{-3}$.

Imagine that such a comet had struck the earth. How much would it have changed the earth's velocity relative to the sun? (Note that the mass of the earth is about $6\times 10^{24}\textrm{ kg}$).
Did you know ... ?

The mathematics of the orbits of comets and planets and cricket balls is identical and forms a large part of university applied mathematics courses.