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When a planet travels in front of a star, the total flux/luminosity of the star drops by some amount.

If we measure a periodic drop in flux, we can surmise that there might be a planet orbiting the star.

Another way to detect exoplanets is by using the radial velocity/wobble of a star. If there are planets orbiting the star, the planets will exert a gravitational pull on the star, causing it to wobble around. Sometimes the star will be travelling towards the Earth, and sometimes it will be travelling away from the Earth. This change in velocity causes a Doppler shift in the light from the star, which we can measure.