Future space missions will be driven by factors such as the need for reduced cost of spacecraft without diminished performance, new services and capabilities including reconfigurability, autonomous operations, target observation with improved resolution and servicing (or proximity) operations. Small satellites, deployed as a sensor network in space, can through inter-satellite communication (ISC) enable the realization of these future goals. Developing the communication subsystem that can facilitate ISC within this distributed network of small satellites require a complex range of design trade-offs. For small satellites, the general design parameters that are to be optimized for ISC are size, mass, and power, as well as cost (SMaP-C). Novel and efficient design techniques for implementing the communication subsystem are crucial for building multiple small satellite networks with capability for achieving significant data-rates along the inter-satellite links (ISLs). In this paper, we propose an alternative approach to RF and laser ISLs for ISC among small satellites deployed as a sensor network in low Earth orbit (LEO). For short to medium range ISLs, we present an LED-based visible light communication (VLC) system that addresses the SMaP constraints, including capability for achieving significant data rates. Our research is focused on the development of the physical layer for pico-/nano class of satellites with prime consideration for the impact of solar background illumination on link performance. We develop an analytical model of the inter-satellite link (ISL) in MATLAB and evaluate its feasibility and performance for different intensity modulation and direct detection (IM/DD) schemes.