Information technology organizations and companies are seeking greener alternatives to traditional terrestrial data centers to mitigate global warming and reduce carbon emissions. Currently, terrestrial data centers consume a significant amount of energy, estimated at about 1.5% of worldwide electricity use. Furthermore, the increasing demand for data-intensive applications is expected to raise energy consumption, making it crucial to consider sustainable computing paradigms. In this study, we propose a data center-enabled High Altitude Platform (HAP) system, where a flying data center supports the operation of terrestrial data centers. We conduct a detailed analytical study to assess the energy benefits and communication requirements of this approach. Our findings demonstrate that a data center-enabled HAP is more energy-efficient than a traditional terrestrial data center, owing to the naturally low temperature in the stratosphere and the ability to harvest solar energy. Adopting a data center-HAP can save up to 14% of energy requirements while overcoming the offloading outage problem and the associated delay resulting from server distribution. Our study highlights the potential of a data center-enabled HAP system as a sustainable computing solution to meet the growing energy demands and reduce carbon footprint.