The data set collected during the night of the discovery of a minor body constitutes a too-short arc (TSA), resulting in failure of the differential correction procedure. This makes it necessary to recover the object during subsequent nights to gather more observations that will allow a preliminary orbit to be calculated. In this work, we present a recovery technique based on sampling the admissible region (AdRe) by the constrained Delaunay triangulation. We construct the AdRe in its topocentric and geocentric variants, using logarithmic and exponential metrics, for the following near-Earth-asteroids: (3122) Florence, (3200) Phaethon, 2003 GW, (1864) Daedalus, 2003 BH84 and 1977 QQ5; and the main-belt asteroids: (1738) Oosterhoff, (4690) Strasbourg, (555) Norma, 2006 SO375, 2003 GE55 and (32811) Apisaon. Using our sampling technique, we established the ephemeris region for these objects, using intervals of observation from 25 minutes up to 2 hours, with propagation times from 1 up to 47 days. All these objects were recoverable in a field of vision of 95’ × 72’, except for (3122) Florence and (3200) Phaethon, since they were observed during their closest approach to the Earth. In the case of 2006 SO375, we performed an additional test with only two observations separated by 2 minutes, achieving a recovery of up to 28 days after its discovery, which demonstrates the potential of our technique.

The observation of stellar occultations constitutes one of the most important techniques for determining the dimensions and establishing the physical parameters of small Solar System bodies. The most substantial calculations are obtained from multiple observations of the same event, which turns the observation of stellar occultations into highly collaborative work and groups teams of observers through international networks. The above situation also requires the participation of both professional and amateur observers in these collaborative networks. With the aim of promoting the participation of professional and amateur groups in the collaborative observation of stellar occultations, we present the methodology developed by the Astronomical Observatory of the Technological University of Pereira (OAUTP) for the observations of occultations due small Solar System bodies. We expose the three fundamental phases of the process: the plan to make observations, the capture of the events, and the treatment of the data. We apply our methodology using a fixed station and a mobile station to observe stellar occultations due to MBAs (354) Eleonora (61) Danae (15112) Arlenewolfe (3915) Fukushima (61788) 2000 QP181 (425) Cornelia (257) Silesia (386) Siegena and (41) Daphne, and due to TNOs 1998BU48 and (529823) 2010 PP81. The positive detections for the objects (257) Silesia (386) Siegena and (41) Daphne allow us to derive lower limits in the diameter of the MBAs of 63.1 km, 166.2 km and 158.7 km and offsets in the astrometric position (Δαc cosδc, Δδc) of 622.30 ± 0.83, 15.23 ± 9.88 mas, 586.06 ± 1.68, 43.03 ± 13.88 mas and –413.44 ± 9.42, 234.05 ± 19.12 mas, respectively.

This paper presents a methodology for Initial Orbit Determination (IOD) based on a modification of the Laplace’s geocentric method. The orbital elements for Near-Earth asteroids (1864) Daedalus, 2003 GW, 2019 JA8, a Hungaria-type asteroid (4690) Strasbourg, and the asteroids of the Main Belt (1738) Oosterhoff, (2717) Tellervo, (1568) Aisleen and (2235) Vittore were calculated. Input data observations from the Minor Planet Center MPC database and Astronomical Observatory of the Technological University of Pereira (OAUTP; MPC code W63) were used. These observations cover observation arcs of less than 22 days. The orbital errors, in terms of shape and orientation for the estimated orbits of the asteroids, were calculated. The shape error was less than 53 × 10–3 AU, except for the asteroid 2019 JA8. On the other hand, errors in orientation were less than 0.1 rad, except for (4690) Strasbourg. Additionally, we estimated ephemerides for all bodies for up to two months. When compared with actual ephemerides, the errors found allowed us to conclude that these bodies can be recovered in a field of vision of 95’ × 72’ (OAUTP field). This shows that Laplace’s method, though simple, may still be useful in the IOD study, especially for observatories that initiate programs of minor bodies observation.