Remote-sensing observations of Solar System objects with a space telescope offer a key method of understanding celestial bodies and contributing to planetary formation and evolution theories. The capabilities of Twinkle, a space telescope in a low Earth orbit with a 0.45-m mirror, to acquire spectroscopic data of Solar System targets in the visible and infrared are assessed. Twinkle is a general observatory that provides on-demand observations of a wide variety of targets within wavelength ranges that are currently not accessible using other space telescopes or that are accessible only to oversubscribed observatories in the short-term future. We determine the periods for which numerous Solar System objects could be observed and find that Solar System objects are regularly observable. The photon flux of major bodies is determined for comparison to the sensitivity and saturation limits of Twinkle’s instrumentation and we find that the satellite’s capability varies across the three spectral bands (0.4 to 1, 1.3 to 2.42, and 2.42 to 4.5  μm). We find that for a number of targets, including the outer planets, their large moons, and bright asteroids, the model created predicts that with short exposure times, high-resolution spectra (R  ∼  250, λ  <  2.42  μm; R  ∼  60, λ  >  2.42  μm) could be obtained with signal-to-noise ratio (SNR) of   >  100 with exposure times of <300  s. For other targets (e.g., Phobos), an SNR  >  10 would be achievable in 300 s (or less) for spectra at Twinkle’s native resolution. Fainter or smaller targets (e.g., Pluto) may require multiple observations if resolution or data quality cannot be sacrificed. Objects such as the outer dwarf planet Eris are deemed too small, faint or distant for Twinkle to obtain photometric or spectroscopic data of reasonable quality (SNR  >  10) without requiring large amounts of observation time. Despite this, the Solar System is found to be permeated with targets that could be readily observed by Twinkle.