A fully integrated spectrometer system-on-a-chip (SoC) is demonstrated for the first time to support the back-end processing of spaceborne telescopic sensing. Like with all space-borne instruments, payload size, weight, and power are critically restricted by the launch vehicle capacity and available solar power. A custom integrated circuit (IC) approach naturally prevails over FPGA-based discrete solutions in these areas. Rather than concocting a system out of circuitries intended for different applications, as in , each component in this work is optimized along the operating principle of radio-frequency (RF) spectroscopy. Running at 2.6 GHz, the presented spectrometer features a three-bit flash ADC, an 8192-point polyphase filter bank (PFB), a 2048-point FFT processor, and a billion-count accumulator (ACC), all running off clocks derived from an integrated phase locked loop (PLL). The entire system consumes a peak power of 650 mW. It achieves the highest level of integration and best efficiency among current spectrometer solutions, and serves as the baseline component for upcoming NASA astrophysics spectroscopy missions.