Which method of planetary detection works only for planets that happen to orbit their star with an orientation that causes them to pass directly in front of the star as seen from Earth?

The correct answer is Transit Method.

Explanation:

The Transit Method is a system currently used by astronomers to detect exoplanets. It works by measuring the fall of light that a star has at the moment that the planets pass in front of each of them, that is, they transit.

If this type of transit occurs periodically and during a certain time, then one could say that the planet is orbiting that star, in what we call an orbital period.

The decrease in intensity of each star during transit is directly associated with the size relationship between the star and the planet. If the planet is small, the attenuation will be small. And if the planet is large, the attenuation will be greater.

These attenuation changes are also periodic as well as orbitation, and for all these reasons this method is the best and most reliable way to analyze the existence of exoplanets.