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The number of lunar craters with a diameter greater than 15 km and the age of less than 1.1 billion years has been compared with estimates of the number of craters of such sizes that could have formed over 1.1 billion years if the number of near-Earth objects and their orbital elements during this time were equal to their present values. Comparison was made for craters on the entire surface of the Moon and for the region of the Ocean of Storms (Oceanus Procellarum) and the seas of the visible side of the Moon. In these estimates, we used the values of the characteristic times that passed before the collisions of these objects with the Moon, and the dependence of the diameters of the craters on the diameters of the impactors. Our estimates do not contradict to the increase in the number of near-Earth objects after possible catastrophic destruction of large asteroids of the main belt, which could have occurred over the past 300 million years. In particular, they are consistent with the conclusion of [1] that the probability of a collision with the Moon increased 2.6 times 290 million years ago. The number of craters with an age of less than 1.1 billion years per unit area for the region of the Ocean of Storms and the seas of the visible side of the Moon exceeds the similar average number for the entire surface of the Moon. For craters with a diameter of at least 15 km, the ratio of these numbers was 1.45 and 3.5 for two methods [1, 2] for determining the age of craters.