Space weather phenomena threaten the space assets that bring us services via space technologies, such as the Global Positioning System, communication systems with satellite relays, and most global TV broadcast networks, which have provided unprecedented convenience to everyday life and opportunities to businesses. A hazard among phenomena1 is the population of relativistic electrons in the region called Van Allan radiation belts2. These electrons can be trapped for years once produced by either natural3 or artificial processes4 and can damage the electronics and degrade the solar panels on satellites. Intense investigations have begun with recently launched NASA satellites, Van Allen Belt Probes A and B in 20125-13. To remedy the threat and reduce the resulting damage, artificial processes can be introduced to shorten the lifetime of these particles14 with mechanisms such as pitch-angle diffusion through wave-particle interaction15-17 by transmitting very-low-frequency (VLF) waves into radiation belts. To directly transmit the VLF waves in space is an extremely challenging task, and previous theoretical and numerical predictions of the radiation impedance differ more than five orders in magnitude18-23. Here we show the measurements of radiation impedance from high-power VLF wave transmission experiments in the radiation belts to help settle the dispute of the previous studies. The measured radiation reactance disagrees with the most influential theoretical model18,19,22 and the vacuum model, but proves the plasma sheath model and simulation of the antenna-plasma interaction20,21,23. A new discovery is that the measured radiation resistance decreases as the transmission frequency increases. Our results demonstrate the possibility to transmit high power in space and validated the design and technology for further high-power space-borne VLF transmitters. The physical understanding obtained in this study will also provide a guide to laboratory whistler mode wave injection experiments24, especially in controlled fusion25.