In this paper, we investigate the effect of the strong time-varying transmission distance on the performance of the low-earth orbit (LEO) satellite-terrestrial transmission (STT) system. We propose a new analytical framework using finite-state Markov channel (FSMC) model and time discretization method. Moreover, to demonstrate the applications of the proposed framework, the performances of two adaptive transmissions, rate-adaptive transmission (RAT) and power-adaptive transmission (PAT) schemes, are evaluated for the cases when the transmit power or the transmission rate at the LEO satellite is fixed. Closed-form expressions for the throughput, energy efficiency (EE), and delay outage rate (DOR) of the considered systems are derived and verified, which are capable of addressing the capacity, energy efficiency, and outage rate performance of the considered LEO STT scenarios with the proposed analytical framework.