 Solution

Three detection methods are exoplanet transit photometry, the radial-velocity method, and exoplanet direct imaging. Transits detect obscuration of the star; radial velocities detect stellar reflex motion; imaging separates the planet's own reflected or thermal light from the star.

Exoplanet transit photometry supports wavelength-dependent exoplanet transmission spectra, while the same orbital geometry supports exoplanet secondary eclipses and phase-resolved planetary spectra. Exoplanet direct imaging provides resolved light for atmospheric spectroscopy. Stellar radial-velocity discovery alone does not measure an atmosphere, although high-resolution follow-up can separate a moving planetary molecular spectrum through its changing Doppler effect.

Two favorable conditions for detecting wide-orbit planets by exoplanet direct imaging are:

A wide orbit improves separation but weakens reflected-light illumination and lengthens the orbital period. These conditions therefore describe imaging sensitivity, not an assertion that every detection method becomes easier at large separation.