  We estimate the carbon footprint of astronomical research infrastructures,
including space telescopes and probes and ground-based observatories. Our
analysis suggests annual greenhouse gas emissions of $1.2\pm0.2$ MtCO$_2$e
yr$^{-1}$ due to construction and operation of the world-fleet of astronomical
observatories, corresponding to a carbon footprint of 36.6$\pm$14.0 tCO$_2$e
per year and average astronomer. We show that decarbonising astronomical
facilities is compromised by the continuous deployment of new facilities,
suggesting that a significant reduction in the deployment pace of new
facilities is needed to reduce the carbon footprint of astronomy. We propose
measures that would bring astronomical activities more in line with the
imperative to reduce the carbon footprint of all human activities.
