This paper presents a compact and low-profile slotted waveguide antenna (SWA), designed to achieve dual-frequency performance within the Ku-band, targeting low-earth-orbit (LEO) satellite applications. This study introduces an approach by parameter sweeping of the slot offset in the SWA design, revealing a new optimal slot offset that significantly outperforms the traditional Stevenson method for calculating uniform slot offsets. Additionally, this investigation modifies the conventional calculations for the slot length and width, leading to the development of a new SWA configuration that achieves dual-frequency performance within the Ku band for the first time, overcoming the limitations of the conventional SWAs. The SWA features 10 longitudinal slots with optimized uniform offsets, lengths, and widths on the broad wall of the waveguide, operating at 14.3 GHz and 16.7 GHz. It achieves high performance with total antenna efficiency exceeding 99% and gains exceeding 15 dBi. The proposed SWA exhibits linear polarization with low side lobe levels (SLLs), and low reflection coefficients. Two prototypes, weighing 24 g and 22 g respectively, were fabricated using 3D printing with different methods, measured with a Vector Network Analyzer (VNA), and compared with the electromagnetic simulation results. The proposed SWA enhances the antenna's adaptability for dual-frequency applications within the Ku band, making it particularly effective for the frequency variations of LEO satellite systems.