2.4 Lunar Landform and Topography
35
About 0.2(D/6)
Fig. 2.10 The profile of typical crater
In the rough mare, the cumulative number of craters N c,r (m
−2 ) larger than a certain
diameter in a unit area (1 m
2 ) can be expressed as
N c,r (D) =
10
−1
× D
−2
(D ≤ 100 m)
10 × D
−3
(D > 100 m)
(2.5)
where D is the diameter of crater.
The depth of crater is basically proportional to its diameter. The ratio is about 1:6.
The model of crater is:
h c =
D
2
12Π x
sin
2Π x
D
(2.6)
where h c is the height of crater and D is the diameter of crater.
The profile of typical crater is shown in Fig. 2.10.
The depth to diameter ratio and the height of crater lip to diameter ratio of the
crater vary with the different age (fresh, young, mature and old) of crater. The older is
the crater, the smaller is the ratio, and shallower is the crater. Therefore, the variation
of shape according to different age of crater should be taken into consideration in
constructing the model of crater. The ideal shapes of craters in various ages are shown
in Table 2.5.
According to the age of crater stated above, the ratio between the number of
craters with diameter over D and the diameter of crater in different ages is shown in
Fig. 2.11.