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There are increasing concerns about the Arctic region and the Antarctic region, which are known as indicators of the global change. To conduct research on the global change issue, especially for the two-polar regions of the Earth, the long-term continuous Earth observations are required. However, the existing Earth observation systems lack the ability to meet this need. In this paper, we propose to use the Moon as an Earth observation platform. This Moon-based platform could have large spatial coverage and long temporal duration. In addition, the site selection is a complex issue for the Moon-based platform because of the vast space on the Moon surface. We research this problem by placing the sensor at four potential sites on the Moon, respectively - the North Pole, the South Pole, the Sinus Iridum area and the Mare Nectaris area. Furthermore, the latitude and longitude of nadir point, the time length, the observation duration and the time length during a single observation duration of the four sites are calculated. Analyses are conducted to compare some observation performances of the four sites. Finally, we found that the latitude variation of the nadir point has an impact on the time window and the observation duration. If the sensor is placed at the polar regions of the Moon, there will be an 18.6-year period between the two adjacent longest observation duration. Thus, we give the next best time window to observe the two-polar regions of the Earth, when the sensor is placed at the polar region of the Moon. If the sensor is placed at the lower latitude regions of the Moon, there will be a 9.3-year period between the two adjacent longest observation duration. Moreover, on account of the observation duration and the time length during a single observation duration, the sites with relative low latitudes on the Moon are good choices.