Cavity shape of large lunar impact features. Charles J. Byrne, Image Again, 39 Brandywine Way, Middletown,
NJ 07748, charles.byrne@verizon.net.
Introduction: The shape of the apparent crater of an
impact feature is sometimes described as a paraboloid. The
radial profiles of several large lunar impact features have
been examined and they are found to be better approxi-
mated with a negative cosine curve [1, 2, 3].
Alternate models of cavities: The radial profile of a
paraboloid, normalized in both radius and diameter, is:
Z = -1+ R^2
where Z is the depth of the cavity, normalized on the true
depth [4] at the center (assuming no central peak, as is the
case with the features reported here). R is the radius, nor-
malized on half the apparent diameter [4] of the cavity
(measured at the intercept of the apparent crater with the
target surface).
The radial profile of a negative cosine is given by:
Z = -Cos(2·R/π)
where Z and R are normalized as above.
The two models are compared in Figure 1.
Figure 1: The negative cosine curve compared with a parabola.
The difference between the two models is small if they are
each normalized in both radius and depth. However, if only
the slope near the rim can be measured, fitting a parabola
to that slope will result in an underestimate of the true
depth by 21%. This slope is the best available measure of
true depth when there is subsequent fill by mare or ejecta
from nearby features. Therefore, this difference is impor-
tant.
Figure 2 shows how well the negative cosine fits the cavity
of impact features when the cavity is well-exposed, has no
internal rings, and has little fill by mare or ejecta.
Figure 2: Radial profiles of (from the top) Copernicuse, Hilbert,
Grimaldi, Langrenus, and the Moscoviense Basin. The red lines are
negative cosine curves.
Lunar and Planetary Science XXXIX (2008)
1288.pdf
These radial profiles were calculated from Topogrd2, the
quarter-degree digital elevation map derived from