A shift from the current Air Traffic Management (ATM) operational scheme to Trajectory-Based Operations (TBO) is imminent in both the United States and in Europe. An enabling technology is the four-dimensional trajectory (4DT) planner, which is the focus of this research. The aim is to consider the feasibility of a heuristic branching method for 4DT planning by developing such a planner and testing it against an established Dijkstra-like approach. Windfield and obstacle field complexities are varied and the solution effectiveness and runtimes of the tested planners are compared by the developed metrics. No significant statistical difference is found between the distributions of results for solution effectiveness of the two planners, but a significant reduction in runtime is shown by the newly developed planner. The study thus indicates the feasibility of a heuristic branching-based method for 4DT planning in the realm of ATM, which informs future research in this domain.