  Determining the size distribution of asteroids is key for understanding the
collisional history and evolution of the inner Solar System. We aim at
improving our knowledge on the size distribution of small asteroids in the Main
Belt by determining the parallaxes of newly detected asteroids in the Hubble
Space Telescope (HST) Archive and hence their absolute magnitudes and sizes.
Asteroids appear as curved trails in HST images due to the parallax induced by
the fast orbital motion of the spacecraft. The parallax effect can be computed
to obtain the distance to the asteroids by fitting simulated trajectories to
the observed trails. Using distance, we can obtain the object's absolute
magnitude and size estimation assuming an albedo value, along with some
boundaries for its orbital parameters. In this work we analyse a set of 632
serendipitously imaged asteroids found in the ESA HST Archive. An
object-detection machine learning algorithm was used to perform this task
during previous work. Our raw data consists of 1,031 asteroids trails from
unknown objects (not matching any entries in the MPC database). We also found
670 trails from known objects (objects featuring matching entries in the MPC).
After an accuracy assessment and filtering process, our analysed HST set
consists of 454 unknown objects and 178 known objects. We obtain a sample
dominated by potential Main Belt objects featuring absolute magnitudes (H)
mostly between 15 and 22 mag. The absolute magnitude cumulative distribution
confirms the previously reported slope change for 15 < H < 18, from 0.56 to
0.26, maintained in our case down to absolute magnitudes around H = 20, hence
expanding the previous results by approximately two magnitudes. HST archival
observations can be used as an asteroid survey since the telescope pointings
are statistically randomly oriented in the sky and they cover long periods of
time.
