The antennas on remote sensing satellites play a crucial role in receiving and transmitting wireless signals, affecting data acquisition quality. Among them, Luneburg lens antennas have been successfully applied in satellite tracking due to their high-gain property. However, reducing the flat Luneburg lens(FLL) profile while maintaining performance and addressing manufacturing challenges remains a limitation. This paper first utilizes transformation optics theory to derive the permittivity distribution of the FLL. Moreover, an innovative approach is introduced by multiplying the distribution with a coefficient “g” to achieve the desired lower permittivity required for fabrication. Then, a layered implementation is used to design a circular FLL and improve its performance by compressing its horizontal profile. Therefore, a unique elliptic FLL is proposed by making a trade-off between the gain, beamwidth, and focal length of the lens antenna. The antenna achieves a 22.9 dB maximum gain with beamwidths of 9.5°(E-plane) and 7.4°(H-plane). The elliptic FLL was fabricated using 3D printing technology, and the measured results showed a small deviation from the simulated results within an acceptable range of error. The elliptic FLL possesses design flexibility and holds immense potential in applications such as remote sensing satellite communication.