FSO satellite communication enables data transfer at high bandwidths, low latency, and high security. Due to these benefits, FSO communication services with satellite constellations can hugely improve global connectivity and bandwidth, while maintaining sufficient security. Modeling a global FSO satellite communication service is beneficial for gaining insight into, and performing preliminary analysis on such missions. However, these missions are complex problems with several physical processes occurring at different time scales. Macroscopic processes in the order of minutes to hours consist of relative platform dynamics (eg. aircraft and satellite motion) and atmospheric attenuation. Microscopic processes consist of atmospheric turbulence- and platform disturbances in the order of milliseconds and transporting photons/bits in the order of nanoseconds. To our knowledge, there are currently no end-to-end models that accurately and efficiently simulate a combination of all these processes. To overcome this, a multi-scale method is proposed that simulates and combines the physics of the microscopic and macroscopic processes of a global FSO satellite communication mission. A bi-directional air-to-space link is chosen as a use case. The proposed model simulates a 1.5 hours communication mission in 6 minutes with 8 Gb random access memory (RAM). Platform dynamics and jitter are the most dominant effects. Including microscopic processes results in a performance difference in signal power of 10 dB to 80 dB depending on the strength of the atmospheric channel. Using the multi-scale method, we can efficiently and realistically simulate an FSO communication service end-toend between an aircraft and a satellite constellation.