Continuous uniform high-precision data on the Earth's radiation balance over many decades and hundreds of years are essential for reliable research and prediction of climate change. This necessarily requires the use of long-term fixed, stable space platforms at a sufficient distance from Earth. However, measurements by all low-orbit and geostationary satellites cannot provide high-precision identifications of the radiation balance, since they observe its limited areas. Two identical especial optical robotic telescopes, of which the Lunar Observatory (LO) consists of, are a single system of sequentially functioning in the automatic mode of Earth observations. Telescopes will be installed along the equatorial zone at opposite edges of the Moon, 80.9±0.1° distant from its visible center. LO provides measurements of the variations in the magnitude of the specific power reflected by the planet into the space of the total solar irradiance in the spectral range Δλ=0.2–4 μm and outgoing intrinsic thermal radiation of the Earth in the ranges Δλ=4–50 μm and the atmospheric transparency window Δλ=8–13 μm. The system of two telescopes, replacing each other, will sequentially survey the entire Earth's surface continuously for more than 94% of the time of a lunar day only at lunar night time. LO will make it possible to determine the parameters of the average annual values of total energies departing from the Earth into space with an error of the order of 0.1%, which is almost an order of magnitude more accurate than the errors in the measurement of these parameters by instruments of any orbital spacecraft. Monitoring of energy variations in the range Δλ=8–13 μm will make it possible to control and determine the relative contribution of the variation in the concentration of greenhouse gases in the atmosphere to climate change.