The paper addresses the challenge of efficient beam coverage and interference mitigation in low-earth orbit (LEO) satellite networks, which are crucial for enabling ubiquitous coverage and massive connectivity in future 6G mobile communications. Conventional directional antennas and fixed-position antenna (FPA) arrays have limited degrees of freedom in beamforming to adapt to the time-varying coverage requirements of terrestrial users. To overcome this limitation, the authors propose the use of movable antenna (MA) arrays to enhance satellite beam coverage and interference mitigation. Specifically, they optimize the antenna position vector (APV) and antenna weight vector (AWV) of the satellite-mounted MA array over time to minimize average signal leakage power to the interference area while ensuring minimum beamforming gain over the coverage area. The continuous-time decision process is transformed into a discrete-time optimization problem, and an alternating optimization (AO) algorithm is developed using the successive convex approximation (SCA) technique. Additionally, a low-complexity MA scheme is proposed to reduce antenna movement overhead by using an optimized common APV over all time slots. Simulation results demonstrate that the proposed MA array-aided beam coverage schemes significantly reduce interference leakage compared to conventional FPA-based schemes, while the low-complexity MA scheme achieves comparable performance in terms of interference mitigation.The paper addresses the challenge of efficient beam coverage and interference mitigation in low-earth orbit (LEO) satellite networks, which are crucial for enabling ubiquitous coverage and massive connectivity in future 6G mobile communications. Conventional directional antennas and fixed-position antenna (FPA) arrays have limited degrees of freedom in beamforming to adapt to the time-varying coverage requirements of terrestrial users. To overcome this limitation, the authors propose the use of movable antenna (MA) arrays to enhance satellite beam coverage and interference mitigation. Specifically, they optimize the antenna position vector (APV) and antenna weight vector (AWV) of the satellite-mounted MA array over time to minimize average signal leakage power to the interference area while ensuring minimum beamforming gain over the coverage area. The continuous-time decision process is transformed into a discrete-time optimization problem, and an alternating optimization (AO) algorithm is developed using the successive convex approximation (SCA) technique. Additionally, a low-complexity MA scheme is proposed to reduce antenna movement overhead by using an optimized common APV over all time slots. Simulation results demonstrate that the proposed MA array-aided beam coverage schemes significantly reduce interference leakage compared to conventional FPA-based schemes, while the low-complexity MA scheme achieves comparable performance in terms of interference mitigation.