The Earth's albedo is one the least studied of the fundamental climate parameters. The albedo is a bi-directional property, and there is a high degree of anisotropy in the reflected light from a given surface. However, simultaneously observing all points on Earth from all reflecting angles is a practical impossibility. Therefore, all measurements from which albedo can be inferred require assumptions and/or modeling to derive a good estimate. Nowadays, albedo measurements are taken regularly either from low Earth orbit satellite platforms or from ground-based measurements of the earthshine in the dark side of the Moon. But the results from these different measurements are not in satisfactory agreement. Clearly, the availability of different albedo databases and their inter-comparisons can help to constrain the assumptions necessary to reduce the uncertainty of the albedo estimates. In recent years, there has been a renewed interest in the development of robotic and manned exploration missions to the Moon. This return to the Moon will enable diverse exploration and scientific opportunities. Here we discuss the possibility of a lunar-based Earth radiation budget monitoring experiment, the Lunar Terrestrial Observatory (LTO), and evaluate its scientific and practical advantages compared to the other, more standard, observing platforms.