Rigid-body motion planning is fundamental to robotic transport and manipulation, where both object position and orientation determine whether a body can move through cluttered environments. This coupling makes planning chal- lenging because translation and rotation can be constrained very differently by surrounding geometry. We propose Shape- Aware Neural Time Fields, a physics-informed neural motion planning framework that learns a reusable travel-time, or cost- to-go, representation for rigid-body motion while explicitly accounting for these distinct geometric restrictions. The learned field captures local motion difficulty in translation and rotation and is paired with a sampling-based planner that balances progress toward the goal with the cost of reaching nearby poses. We evaluate the framework across 2D and 3D rigid- body planning tasks and non-prehensile manipulation through object pushing in diverse environments. Results show substantial improvements in planning success and inference efficiency over physics-informed neural planning baselines, while remaining competitive with classical sampling-based planners at significantly lower planning times. Ablation studies further validate the contributions of both the learned representation and the proposed planning strategy. Finally, closed-loop pushing experiments under execution deviations and external disturbances demonstrate that fast replanning enables reactive and adaptive task execution.

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