Final answer:
The Kepler mission detects Earth-like planets around other stars using the transit and Doppler methods. The transit method involves observing the slight dip in brightness of the central star as the planet transits. The Doppler method involves measuring the slight shift in position of the central star as it is tugged by the planet.
Step-by-step explanation:
The Kepler mission plan to detect Earth-like planets around other stars by observing the slight dip in brightness of the central star as the planet transits. This is known as the transit method. When a planet passes in front of its host star, it blocks a small fraction of the star's light, causing a decrease in brightness. By carefully measuring these dips in brightness over time, astronomers can determine the presence and characteristics of the planet.
In addition to the transit method, the Doppler method is also used. This involves measuring the slight shift in position of the central star as it is tugged to and fro by the planet. As a planet orbits its star, it exerts a gravitational pull that causes the star to wobble. This motion causes a slight shift in the wavelengths of the star's spectral lines, known as the Doppler shift. By analyzing these shifts, astronomers can infer the presence and properties of the planet.