Cleostratus is a lunar crater near the northwest limb of the Moon. It lies to the northeast of Xenophanes crater, and west-southwest of the prominent Pythagoras crater. From the Earth this crater appears highly elongated due to foreshortening.
The rim of this crater has become soft-shouldered due to steady impact erosion, and the formation is now just a depression in the surface surrounded by an eroded rise. A pair of small craters lie across the southwest rim, forming part of a short chain of craters leading to the west. Along the crest of the southern rim is a linear ridge. The satellite crater 'Cleostratus E' is attached to the northwest rim, and intrudes slightly into the inner wall. The interior floor of this crater is flat and nearly featureless, having only a few tiny craterlets marking the surface.
By convention these features are identified on lunar maps by placing the letter on the side of the crater mid-point that is closest to Cleostratus crater.
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