As of 2024, astronomers have confirmed the existence of over 5,500 exoplanets. A primary objective of modern astrophysics is to detect and characterize Earth-twin planets—planets of similar size and mass to Earth orbiting within the habitable zone (around 1 AU1\text{ AU}1 AU) of Sun-like (G-type) stars.
Discuss the physical principles and the specific observational challenges associated with using the following three methods to detect such a planet:
In your answer, compare these methods and suggest which has been, or is likely to be, the most successful for detecting this specific class of planet, justifying your choice.
