Internet connectivity on aircraft is becoming more and more popular, while its performance is lacking behind the offer on ground. In order to provide a high throughput to aircraft, an air-to-ground network combining direct air-to-ground, satellite and air-to-air connectivity is needed. To provide a fair throughput allocation to aircraft, we define a 5G-based air-to-ground architecture and introduce a heuristic algorithm to fairly distribute the capacity among aircraft. We evaluate the algorithm in an European scenario using real aircraft traces. We show that our algorithm can fairly distribute the throughput per aircraft. During high-aircraft-density times, the maximum difference to the ideally distributed throughput is only 3.9%. Additionally, we introduce a weighted-fair allocation, corresponding to the aircraft size, to distribute the throughput according to the number of users per aircraft.