We study information-theoretical security for space links between a satellite and a ground station.Quantum key distribution (QKD) is a well-established method for information-theoretical secure communication, giving the eavesdropper unlimited access to the channel and technological resources limited by only the laws of quantum physics. But QKD for space links is extremely challenging, the achieved key rates are extremely low, and daytime operating impossible. However, eavesdropping on a channel in free space without being noticed seems complicated, given the constraints imposed by orbital mechanics. If we also exclude the eavesdropper's presence in a given area around the emitter and receiver, we can guarantee that he has access to only a fraction of the optical signal. In this setting, quantum key-less private (direct) communication based on the wiretap channel model is a valid alternative to provide information-theoretical security. Like for QKD, we assume that the legitimate users are limited by state-of-the-art technology, while the potential eavesdropper is only limited by physical laws: either by specifying her detection strategy (Helstrom detector) or by bounding her knowledge, assuming the most powerful strategy through the Holevo information. Nevertheless, we demonstrate information-theoretical secure communication rates (positive keyless private capacity) over a classical-quantum wiretap channel using on-off keying of coherent states. We present numerical results for a setting equivalent to the recent experiments with the Micius satellite and compare them to the fundamental limit for the secret key rate of QKD. We obtain much higher rates compared with QKD with an exclusion area of less than 13 m for low earth orbit satellites. Moreover, we show that the wiretap channel quantum keyless privacy is much less sensitive to noise and signal dynamics and daytime operation is possible.