  Up to date planet ephemerides are becoming increasingly important as
exoplanet science moves from detecting exoplanets to characterising their
architectures and atmospheres in depth. In this work ephemerides are updated
for 22 Kepler planets and 4 Kepler planet candidates, constituting all Kepler
planets and candidates with sufficient signal to noise in the TESS 2min
dataset. A purely photometric method is utilised here to allow ephemeris
updates for planets even when they do not posses significant radial velocity
data. The obtained ephemerides are of very high precision and at least seven
years 'fresher' than archival ephemerides. In particular, significantly reduced
period uncertainties for Kepler-411d, Kepler-538b and the candidates
K00075.01/K00076.01 are reported. O-C diagrams were generated for all objects,
with the most interesting ones discussed here. Updated TTV fits of five known
multiplanet systems with significant TTVs were also attempted (Kepler-18,
Kepler-25, Kepler-51, Kepler-89, and Kepler-396), however these suffered from
the comparative scarcity and dimness of these systems in TESS. Despite these
difficulties, TESS has once again shown itself to be an incredibly powerful
follow-up instrument as well as a planet-finder in its own right. Extension of
the methods used in this paper to the 30min-cadence TESS data and TESS extended
mission has the potential to yield updated ephemerides of hundreds more systems
in the future.
