Satellite communications (SatComs) are anticipated to deliver global Internet access. Low Earth orbit (LEO) satellites (SATs) offer the advantage of higher downlink capacity due to their reduced link budget compared to medium Earth orbit (MEO) and geostationary Earth orbit (GEO) SATs. In this paper, beam broadening methods for uniform rectangular arrays (URAs) in LEO SatComs were studied. The proposed method is the first of its kind to jointly consider path loss variation from SAT to the user terminal (UT) due to the Earth's curvature to guarantee the quality of service (QoS), constant modulus constraints (CMCs) favored for maximizing power amplifier (PA) efficiency, and out-of-beam radiation suppression to avoid interference. A broadened-beam URA coefficient design problem is formulated and decomposed into two uniform linear array (ULA) design subproblems utilizing Kronecker product beamforming. With this decomposition, the number of beamforming coefficients that need to be optimized is significantly reduced compared to the original URA design problem. The non-convex ULA subproblems are addressed using the semidefinite relaxation (SDR) technique and a convex iterative algorithm. Simulation results reveal the advantages of the proposed method for suppressing the out-of-beam radiation and achieving the design criteria. In addition, channel capacity evaluations are carried out. It demonstrates that the proposed "broadened-beam" beamformers can offer capacities that are at least four times greater than those of beamformers employing an array steering vector when the beam transition time is considered. The proposed method holds potential for LEO SAT broadcasting applications, such as digital video broadcasting (DVB).