Final answer:
Astronomers use the transit and Doppler methods together to determine exoplanet densities; the transit method measures size via the star's dimming during a transit, and the Doppler method estimates mass via the star's radial velocity changes.
Step-by-step explanation:
Astronomers usually determine the densities of exoplanets by using a combination of the transit method and the Doppler method. The transit method involves detecting the slight dimming of a star as the planet crosses in front of it, which allows astronomers to measure the planet's size.
The Doppler method involves measuring the radial velocity of the star to detect wobbles caused by the gravitational influence of orbiting planets, which gives an estimate of a planet's mass. By knowing both the size from the transit data and the mass from the Doppler data, the average density of the exoplanet can be calculated.
For instance, the exoplanet orbiting the star HD 209458 was detected using the transit method and it was found that the planet transits across its parent star for about 3 hours every 3.5 days.
Combining this with the Doppler measurements, scientists discovered that the planet has approximately 70% the mass of Jupiter and a radius about 35% larger than Jupiter’s. From this data, we infer that HD 209458b is a gas and liquid world similar to Jupiter or Saturn, based on its density.