Planets orbiting around other stars have been discovered by _____.

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The question asks how planets orbiting around other stars have been discovered. 
Option 1: accurate measurements of the stars' radial velocity. This refers to the Doppler method, which detects wobbles in a star's motion caused by the gravitational pull of an orbiting planet—one of the earliest and most successful exoplanet discovery techniques. 
Option 2: measuring the tides on the stars caused by a planet. In practice, planetary tides on stars are negligible for detectable signals; this is not a viable method for discovering exoplanets. 
Option 3: images of the stars and planets. Direct imaging of planets is extremely challenging due to the star’s glare, and while possible in some cases, it has not been the primary method for discovering planets. It typically requires specialized high-contrast imaging and is limited to young, distant, or massive planets. 
Option 4: using interferometry in large optical telescopes. Optical interferometry can improve resolution but has not been the standard or most common technique used to discover exoplanets; it is more commonly applied for stellar measurements and imaging of relatively bright targets, not routine planet detection. 
Option 5: using interferometry in large radio telescopes. Radio interferometry is powerful for studying certain astrophysical phenomena, but exoplanet discovery via radial velocity and transit methods is not done primarily with radio interferometry; most exoplanet detections come from optical measurements. 
In summary, the radial velocity method (Option 1) is the established approach for detecting planets around other stars, whereas the other options describe techniques that are not the standard discovery methods for exoplanets.

ASTRON 2140 AU2025 (23428) Final - 2025 Dec 12

Planets orbiting around other stars have been discovered by _____.

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