November 20, 2015: Two studies in planetary dynamics: (i) Impact seasons on Mars, (ii) The mass function of planets in the Galaxy

I will present results of new calculations of the asteroidal impact flux on Mars.  Mars’ orbit is significantly eccentric and the planet orbits near the inner edge of the asteroid belt where the space density of asteroids has a large radial gradient.  The correlated secular dynamics of Mars and the asteroids plays a significant role in modulating the impact flux on this planet.  At the present epoch, this leads to a large variation — of about a factor of three — in the impact flux when Mars is near aphelion versus perihelion; significantly, the integrated annual impact flux is lower than would be expected in the absence of correlated secular dynamics.

The second part of the talk will describe some deductions about the planet mass function from the observational data of exoplanets and theoretical considerations of planetary dynamics.  I will describe analysis of the observational data from the Kepler space mission which indicates that planetary orbital separations have an approximately log-normal distribution.  Adopting some plausible ansatzs for the dynamical stability of N-planet systems to relate orbital separations to planet masses, it appears that the planet mass function is peaked in logarithm of mass, with the most probable value of log m/M⊕ ∼ (0.6 − 1.0); a modest extrapolation indicates that Earth mass planets are about ~1000 times more common than Jupiter mass planets.

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