Thailand Tokamak-1 (TT-1) is a small tokamak under the operation of the Thailand Institute of Nuclear Technology. In our future plans, TT-1 has the feasibility of being equipped with external heating systems to achieve high-performance plasma operation and conduct physics associated with fast ions generated by the external heating system. One of the potential external heating systems under consideration is a positive-ion-source-based neutral beam injection (NBI) heating system. The primary source of fast ions for the NBI can be either hydrogen or deuterium-doped hydrogen beams. This study examines how hydrogen and deuterium ions, namely protons and deuterons, respectively, move in orbits, using the Lorentz orbit (LORBIT) code to track their full gyromotion. The energy of the ions has been varied between 200 eV and 40 keV. Three trajectory motions have been characterized, i.e., counter-passing ion, co-passing ion, and trapped ion. The average Larmor radius, dependent on the ion energies, has been investigated. The Larmor radius significantly increases with increasing ion energy in the case of trapped ions, while in the case of counter- and co-passing ions, the Larmor radius exhibits a slight increase with increasing ion energy. Furthermore, the pitch angle range of the lost ion in the TT-1 has been investigated. The results demonstrate the feasibility of utilizing a deuterium-doped hydrogen beam in TT-1 to study fast ion physics. To avoid a large number of lost ions, it is possible to use a deuterium-doped hydrogen beam with an energy not exceeding approximately 10 keV in the TT-1.