In this thesis, I present my work on the discovery and characterisation of long-period transiting exoplanets. Detecting exoplanets via the transit method is inherently biased towards short-period planets. Due to the nature of its observing strategy, the Transiting Exoplanet Survey Satellite (TESS) is particularly susceptible to this detection bias. To increase the number of long-period planets, I use TESS ‘duotransits’ — planet candidates with two observed transits separated by a large gap, typically two years. From the two non-consecutive transits the orbital period is unknown, but there exists a discrete set of allowed period aliases. With the CHaracterising ExOPlanet Satellite (CHEOPS), I perform targeted follow-up of TESS duotransits to determine their true periods and confirm them as long-period planets.

I begin by describing the specialised pipeline that I created to discover TESS duotransits. My pipeline reads in TESS lightcurves, detrends them using a time-windowed sliding mean, runs a box least squares (BLS) transit search and outputs duotransit candidates. The process was optimised to discover duotransits suitable for CHEOPS follow-up by using injection-recovery tests and selecting BLS parameters based on typical duotransit properties. After running my pipeline on ∼ 40,000 stars, I discovered five duotransit systems that have since been observed by CHEOPS: HD 5806, TOI-5678, TIC 182992572, TIC 130843507 and HD 185619. For the four that have had their orbital period confirmed so far, I performed a joint TESS and CHEOPS analysis to derive each planet’s properties. I also present the TESS and CHEOPS discovery of two warm sub-Neptunes transiting the bright K-dwarf HD 15906, as reported in a publication which I led.

In total, I contributed to the discovery of 19 long-period planets as a core member of the CHEOPS Duotransit Program. All of these new discoveries have orbital periods longer than 20 days, radii smaller than 5 R_⊕ and host stars brighter than a Gaia magnitude of 12. These small planets on long-period orbits around bright stars are amenable to detailed characterisation studies, for example radial velocity follow-up to measure their masses or transmission spectroscopy to probe their atmospheres. That makes them particularly valuable for understanding how exoplanet properties change as a function of stellar irradiation and improving our understanding of planet formation and evolution.