What properties of extrasolar planets can be determined by astronomers. your answer should list two properties and discuss briefly what data is collected to determine each property.

The properties that can be determine are: the mass and its orbital period.

Mass (data: radial velocity, mass of the star and semi-major axis)

orbital period (data: period of the Doppler shift)  

Explanation:

The mass of an extrasolar planet can be determine by collecting the light (spectrum) from its host star. The spectrum will have a shift in its absorption lines by means of the gravitational effect of the planet over the star (as they orbit its mutual center of mass). The lines will shift toward the red part of the spectrum when the star move away from the observer and to the blue part of the spectrum when is moving toward the observer. The Doppler Effect can be use to find out the radial velocity, with the orbital period it can be estimate the semi-major axis using Kepler third law. Then using the Newton form for Kepler's third law it can be estimate the mass of the exoplanet:

  (1)    

The orbital period will be given by the period in which the variation from the spectral lines occurs.