Fusion: Practice and Applications FPA 2692-4048 2770-0070 10.54216/FPA https://www.americaspg.com/journals/show/4156 2018 2018 Mustansiriyah University, College of Science, Department of Mathematics, Baghdad, Iraq Ahmed Ahmed Mustansiriyah University, College of Science, Department of Mathematics, Baghdad, Iraq Ali Abdulhussein Mustansiriyah University, College of Science, Department of Mathematics, Baghdad, Iraq Laheeb Muhsen Noman The main goal of this paper is to obtain a special form of asymptotic solutions to the scalar version of the two body problem whenever the two bodies collide on the real line at the collision time. It has been shown that the desired asymptotic solution maintains certain properties when t approaches the collision time. However, it is not easy to Handel such a mission without the employment of successive approximations technique. The successive approximations technique has been modified and adjusted to serve as the main tool in the process of obtaining such solution. Moreover, it has been shown that the series of successive approximations converges absolutely and uniformly to a continuous function that approaches to 0 when t attains the collision time in a certain interval. The problem of one dimensional collision between the two bodies has been solved asymptotically at the collision time. 2026 2026 307 335 10.54216/FPA.210122 https://www.americaspg.com/articleinfo/3/show/4156