Summary: ASTR 5120: Numerical Project (due Monday 16th March)
Calculating the transfer probability for Martian meteorites
A small number of meteorites recovered from Antarctica have been securely identified
(via analysis of the composition of trapped gases) as being of Martian origin. Presumably
these rocks were lofted from the surface of Mars in impact events before finding their way
into Earthcrossing orbits and eventually impacting Earth. It is of some interest to know
(a) the probability for such events to occur and (b) how long the transfer typically takes
(and thus, whether life could conceivably survive the journey).
Useful data: Mars has a radius of 3400 km and a mass of M = 6.4 × 10 26 g. The
semimajor axis is 1.524 AU and the eccentricity is e = 0.0934. Earth has a radius of
6400 km and a mass of M = 6.0 × 10 27 g, The semimajor axis is 1.000 AU and the
eccentricity is e = 0.0167.
Consider meteorites ejected from Mars with velocities at infinity (i.e. after escaping
the Martian potential) of 1 km/s or 2 km/s. Determine (a) the cumulative probability of
collisions with the Earth in the first 10 Myr, and (b) the distribution of collision times.
It's probably OK to assume that the distribution of impacts on Mars (and hence the
directions of ejected bodies) is isotropic, but you might want to check whether the orbital
phase and the presence or absence of other planets (especially Jupiter and Venus) makes
any significant di#erence.
Methods: It's probably going to be easiest to track the trajectories using a Solar