Optical space communication has been proven to be a reliable relay satellite transmission system. The difficulty that occurs in RF satellite communication (SatCom) can be alleviated by using free-space optical (FSO) or laser SatCom. In this work, we analyze a proposed laser downlink relay SatCom model with existing channel turbulence employing intensity modulation and direct detection (IM/DD), and amplify-and-forward (AF) technology and compare it with the optical direct link SatCom. Accounting for atmospheric attenuation and turbulence, the effect of model parameters such as zenith angle, receiver aperture radius, best number of optical ground stations (OGSs), and end-to-end operating wavelength on system performance is investigated for different OGS height scenarios. We provide exact closed-form expressions for the proposed model and optimize system performance by selecting the best number of OGSs using a selective diversity technique that can boost the system signal-to-noise (SNR) by up to 37 dB (99.9%).