In order to meet the demands of `Internet above the clouds', we propose a multiple-antenna aided adaptive coding and modulation (ACM) for aeronautical communications. The proposed ACM scheme switches its coding and modulation mode according to the distance between the communicating aircraft, which is readily available with the aid of the airborne radar or the global positioning system. We derive an asymptotic closed-form expression of the signal-to-interference-plus-noise ratio (SINR) as the number of transmitting antennas tends to infinity, in the presence of realistic co-channel interference and channel estimation errors. The achievable transmission rates and the corresponding mode-switching distance-thresholds are readily obtained based on this closed-form SINR formula. Monte-Carlo simulation results are used to validate our theoretical analysis. For the specific example of 32 transmit antennas and 4 receive antennas communicating at a 5 GHz carrier frequency and using 6 MHz bandwidth, which are reused by multiple other pairs of communicating aircraft, the proposed distance-based ACM is capable of providing as high as 65.928 Mbps data rate when the communication distance is less than 25\,km.