  The Twinkle space telescope has been designed for the characterisation of
exoplanets and Solar System objects. Operating in a low Earth, Sun-synchronous
orbit, Twinkle is equipped with a 45 cm telescope and visible (0.4 - 1um) and
infrared (1.3 - 4.5um) spectrometers which can be operated simultaneously.
Twinkle is a general observatory which will provide on-demand observations of a
wide variety of targets within wavelength ranges that are currently not
accessible using other space telescopes or accessible only to oversubscribed
observatories in the short-term future. Here we explore the ability of
Twinkle's spectrometers to characterise the currently-known exoplanets. We
study the spectral resolution achievable by combining multiple observations for
various planetary and stellar types. We also simulate spectral retrievals for
some well-known planets (HD 209458 b, GJ 3470 b and 55 Cnc e). From the
exoplanets known today, we find that with a single transit or eclipse, Twinkle
could probe 89 planets at low spectral resolution (R < 20) as well as 12
planets at higher resolution (R > 20) in channel 1 (1.3 - 4.5um). With 10
observations, the atmospheres of 144 planets could be characterised with R < 20
and 81 at higher resolutions. Upcoming surveys will reveal thousands of new
exoplanets, many of which will be located within Twinkle's field of regard.
TESS in particular is predicted to discover many targets around bright stars
which will be suitable for follow-up observations. We include these anticipated
planets and find that the number of planets Twinkle could observe in the near
infrared in a single transit or eclipse increases to 558 for R > 20 and 41 at
lower resolutions. By stacking 10 transits or eclipses, there are 1185
potential targets for study at R < 20 as well as 388 planets at higher
resolutions.
