In this paper, energy optimal surveillance trajectories for unmanned aerial vehicles (UAV) are explored. The main objective is to have maximum sensor coverage range while maintaining a perpetual flight in the presence of uncertainties. A solar-powered UAV is equipped with photovoltaic cells mounted on its wings and rechargeable batteries. The photovoltaic cells generate solar energy based on the position of the sun, attitude of the UAV, and sky clarity. The vehicle aims to optimize the energy storage in the batteries and coverage during the day while the availability of solar radiation is uncertain and the sensor resolution diminishes because of altitude gain. A model for optimal coverage, path planning, and power allocation in a solar-powered UAV is proposed and the corresponding simulation results are presented. In addition, the effect of maximum altitude gain on the energy storage is studied based on a reduced hybrid model. An online setting is proposed to represent the solar radiation uncertainties. This approach demonstrates convergence to the best fixed strategy in both theory and simulation results.