An approximate height formula for tropospheric ray tracing

A simple approximate formula for the height above the earth'S surface of a radio ray propagating through a spherically stratified smoothly varying atmosphere is derived. For the purpose of illustration an exponential model atmosphere is numerically evaluated, and examples show the significant improvement that resuits compared with the usual "effective earth's radius" approximations, especially for large surface gradients. Key words in this communication are ray tracing, troposphere, and approximate height.