Wireless connectivity in airplanes is becoming more important, demanded, and common. One of the largest bottlenecks with the in-flight Internet is that the airplane is far away from both the satellites and the ground base stations during most of the flight time. Maintaining a reliable and high-rate wireless connection with the airplane over such a long-range link thus becomes a challenge. Microwave frequencies allow for long link distances but lack the data rate to serve up to several hundreds of potential onboard customers. Higher bands in the millimeter-wave spectrum (30 GHz-300 GHz) have, therefore, been utilized to overcome the bandwidth limitations. Still, the per-user throughput with state-of-the-art millimeter-wave systems is an order of magnitude lower than the one available with terrestrial wireless networks. In this paper, we take a step further and study the channel characteristics for the terahertz band (THz, 0.3 THz-10 THz) in order to map the feasibility of this band for aviation. We first propose a detailed channel model for aerial THz communications taking into account both the non-flat Earth geometry and the main features of the frequency-selective THz channel. We then apply this model to estimate the characteristics of aerial THz links in different conditions. We finally determine the altitudes where the use of airplane-to-satellite THz connection becomes preferable over the airplane-to-ground THz link. Our results reveal that the capacity of the airborne THz link may reach up to 120 Gbit/s, thus enabling cellular-equivalent data rates to the passengers and staff during the entire flight.