Final answer:
Astronomers determine exoplanet masses using both the Doppler method, which measures the radial velocity changes of a star, and the transit method, which observes the dimming of a star as a planet transits in front of it. The combination allows for the measurement of both mass and size, enabling the calculation of the planet's average density.
Step-by-step explanation:
Astronomers usually determine the masses of exoplanets using a combination of Doppler method and transit method. The Doppler technique involves high-resolution stellar spectroscopy to measure the star's radial velocity change due to the gravitational influence of an orbiting planet, providing the minimum mass of the planet. However, it is the combination with the transit method, which detects the dimming of a star as a planet transits across its face and allows astronomers to measure the planet's size, that can yield the exoplanet's actual mass and, hence, its average density.
For example, in the case of the transiting planet orbiting the star HD 209458, the transit method showed that the planet transited its parent star for about 3 hours every 3.5 days, and the Doppler shift data helped to estimate that the planet has about 70% the mass of Jupiter, but with a radius approximately 35% larger.