Final answer:
Astronauts detect planets around distant stars by looking for a dimming in the star's light or a wobble in its motion, caused by the gravitational effects of an orbiting planet. The Doppler effect is instrumental in measuring these changes in the star's spectrum, indicating the presence of a planet.
Step-by-step explanation:
One way that astronauts detect planets around distant stars is by observing to see if there is a dimming in the light that reaches us from a particular star. The reason that the star moves away or toward us is a wobble due to gravitational effects of the planet.
When a planet orbits a star, it exerts a gravitational pull on the star, causing the star to move slightly. This motion can be along our line of sight, causing the star to move toward or away from us. The Doppler effect can be used to measure this motion by observing the shift in the star's spectrum. If the star's light appears to wobble or its brightness dims at regular intervals, it suggests the presence of a planet. High-resolution stellar spectroscopy allows astronomers to detect such changes in radial velocity, and the pattern of dimming associated with the planet passing in front of the star helps determine the planet's size and orbital period.