Increasingly, autonomous vehicles that optimally collect/harvest external fields from highly dynamic environments have grown in relevance for Planet Earth. This includes path planning for optimal energy harvesting (solar, wind, wave, thermal, etc.) or optimal cleanup or collections in dynamic environments. In this work, we develop an exact partial differential equation-based methodology that predicts collection-time optimal paths for autonomous vehicles navigating in dynamic environments. The governing differential equations solve the multi-objective optimization problem of navigating a vehicle autonomously in a highly dynamic flow field to any destination to minimize travel time while also maximizing the collected amounts of fields harvested by the vehicle. Using Hamilton-Jacobi theory for reachability, our methodology computes the exact set of Pareto optimal solutions to the multi-objective path planning problem. Our approach applies to path planning in various environments; however, we primarily present examples of navigating in dynamic ocean flows. First, we validate our methodology using steady and unsteady benchmark cases. We then showcase optimal fish growth paths for moving fish farms, optimal algae growth and collection paths for autonomous carbon capture, and optimal plastic collection paths for marine cleanup. Overall, we find that our exact planning equations and efficient schemes are promising to address several pressing challenges for our planet.