I removed the link to the circuit diagram from your question because that site showed very bad internet etiquette. It's not that I'm objecting to the beautiful pictures on the ad that took over the screen, but to its refusal to allow simple navigation back to the site with the circuit. One would think that Ms. Rafaeli could get enough attention without resorting to such rudeness.
Here's a partial thought. Don't worry about "electromagnetic fields". The frequencies of this oscillator are low. Even at 20 kHz, the wavelength is 1.5 km, much bigger than any of the distances involved. So you need only consider simple electrostatics, ignoring magnetic fields. The basic idea is that your body provides a high-dielectric coefficient pathway to ground, with some conductance in parallel. Maybe you can simply treat the person as a near-short to ground and the person-antenna gap as a variable capacitor. The value of that variable capacitance (in cgs units) is roughly comparable to the area of the hand and antenna (say each is about 100 cm^2) divided by the hand to antenna gap (and by 4pi, to be faux-precise).
(1 cm cgs is about 1 pF SI.)
With only one op-amp and not very many circuit elements, it should then be possible to use techniques from standard electronics texts (e.g. Horowitz and Hill) to solve for the oscillation frequency.
For an experiment, you might see whether a hand behaved much differently from a metal plate of the same size connected by a wire to ground. That will give an idea of whether the approximation of treating the person as a short to ground is good at the relevant frequencies. (I'm not sure.)
(published on 02/11/11)