Here is another planet definition:

On the low-mass planethood criterion

Authors: Bojan Pecnik, Christopher Broeg

Comments: 13 pages, 1 table, submitted to journal of Planetary and Space Science

We propose a quantitative concept for the lower planetary boundary, requiring that a planet must keep its atmosphere in vacuum. The solution-set framework of Pecnik and Wuchterl (2005) enabled a clear and quantitative criterion for the discrimination of a planet and a minor body. Using a simple isothermal core-envelope model, we apply the proposed planetary criterion to the large bodies in the Solar System

http://arxiv.org/abs/astro-ph/0608367