  We explore the prospects for Twinkle to determine the atmospheric composition
of the nearby terrestrial-like planet LTT 1445 Ab, including the possibility of
detecting the potential biosignature ammonia (NH$_{3}$). At a distance of 6.9
pc, this system is the second closest known transiting system and will be
observed through transmission spectroscopy with the upcoming Twinkle mission.
Twinkle is equipped with a 0.45 m telescope, covers a spectral wavelength range
of 0.5 - 4.5 $\mu$m simultaneously with a resolving power between 50 - 70, and
is designed to study exoplanets, bright stars, and solar system objects. We
investigate the mission's potential to study LTT 1445 Ab and find that Twinkle
data can distinguish between a cold Haber World (N$_2$-H$_2$-dominated
atmosphere) and a Hycean World with a H$_2$O-H$_2$-dominated atmosphere, with a
$\chi_{\nu}^{2}$ = 3.01. Interior composition analysis favors a Haber World
scenario for LTT 1445 Ab, which suggests that the planet probably lacks a
substantial water layer. We use petitRADTRANS and a Twinkle simulator to
simulate transmission spectra for the more likely scenario of a cold Haber
World for which NH$_{3}$ is considered to be a biosignature. We study the
detectability under different scenarios: varying hydrogen fraction,
concentration of ammonia, and cloud coverage. We find that ammonia can be
detected at a $\sim$ 3$\sigma$ level for optimal (non-cloudy) conditions with
25 transits and a volume mixing ration of 4.0 ppm of NH$_{3}$. We provide
examples of retrieval analysis to constrain potential NH$_{3}$ and H$_{2}$O in
the atmosphere. Our study illustrates the potential of Twinkle to characterize
atmospheres of potentially habitable exoplanets.
