<p>Upon the discovery of an asteroid, initial orbit determination (IOD) methods may fail due to the observations being too short arcs (TSAs), prompting the adoption of the admissible region approach (AR). The AR physically bounds two unobservable variables, creating a two-dimensional uniform distribution to complete the asteroid’s state. Then, to assess the asteroid’s potential impact on Earth, all virtual asteroids in the AR are propagated to compute collision probability and create the manifold of variations (MOV). Once a target is identified as a potential impactor, focusing on the sky region where it may appear becomes imperative. Consequently, we aim to develop a reliable algorithm for assessing the risk posed by asteroids detected on TSAs. Initially, we construct the Admissible State Region (ASR) based on the observations, encompassing six dimensions, which include the uncertainty of the attributable. The ASR is defined by boundaries set by the semi-major axis, perihelion, and minimum orbital intersection distance (MOID), all of which can be expressed using Taylor polynomial equations. For asteroids with orbits potentially intersecting with Earth’s orbit, the ASR is numerically forward propagated to establish a continuous and analytical MOV. Subsequently, determining collision probability becomes feasible using the asteroid’s state and uncertainty, allowing the identification of potential impactors within the ASR. In essence, our study focuses on assessing the risk of TSAs.</p>