Impact Basin Models The Search for the Source of the Far Side Crust

Recently, using the refined data from the Clementine laser altimeter that is shown in Figures 13.2 and 13.3, I undertook a search for a basin whose ejecta covers the far side of the Moon.

The first step was to form a generalized model of an impact basin. Projectiles from beyond Earth's orbit cause impact: maverick stony or metallic bodies from the asteroid belt or icy comets from the Kuiper belt. They arrive at the Moon with velocities far in excess of the speed of sound in

Figure 13.1. The eastern limb of the Moon, taken by the mapping camera in the Apollo 16 Command Module. Mare Smythii and, above that, Mare Marginis are mostly on the near side. The limb (90° east longitude) runs through the right hand edge of Mare Smythii, which is on the lunar equator. The far side is to the right. Photo a16_m_3021, NASA, LPI.

Figure 13.1. The eastern limb of the Moon, taken by the mapping camera in the Apollo 16 Command Module. Mare Smythii and, above that, Mare Marginis are mostly on the near side. The limb (90° east longitude) runs through the right hand edge of Mare Smythii, which is on the lunar equator. The far side is to the right. Photo a16_m_3021, NASA, LPI.

North Pole

North Pole

South Pole

-6000 -4000 -2000 0 2000 1000 6000 Sevalton(ir)

South Pole

-6000 -4000 -2000 0 2000 1000 6000 Sevalton(ir)

Figure 13.2. Elevation map of the Moon, centered on its near side. This geographic map displays elevation as a grayscale against latitude from 90° south to 90° north, and longitude from 180° west to 180° east. The data, called topogrd1, was derived from the Clementine LIDAR instrument. NRL, Zuber, 2004.

Figure 13.3. This elevation map is the same as that of Figure 13.2 except that it is centered on the far side. Note that the East Limb is the western limb of the far side. The dark depression is the South Pole-Aitken Basin. The large Korolev Basin is just north of the South Pole-Aitken Basin, at the top of the far side bulge. The bulge would be approximately circular if it were not for the impact of the South Pole-Aitken Basin.

Figure 13.3. This elevation map is the same as that of Figure 13.2 except that it is centered on the far side. Note that the East Limb is the western limb of the far side. The dark depression is the South Pole-Aitken Basin. The large Korolev Basin is just north of the South Pole-Aitken Basin, at the top of the far side bulge. The bulge would be approximately circular if it were not for the impact of the South Pole-Aitken Basin.

the surface material, in other words at hypervelocity. In such circumstances, the effect is nearly the same as a powerful explosion. The most important property of the impactor is simply its kinetic energy. The angle of the impact is of secondary importance. Only if the approach is less than 30 from the horizontal does the shape of the impact basin become significantly elliptical, rather than circular.

Through a discipline called dimensional analysis, impacts of all sizes can be compared to normalized models. The technique covers size ranges from laboratory experiments all the way up to the large lunar basins. Figure 13.4 shows radial profiles of several lunar basins that are first measured using Clementine elevation data and then normalized by both depth and diameter. It also shows a model radial profile that matches key features of the selected basins.

The depth and the diameter of the profiles were each normalized separately because the ratio of depth to diameter depends on many factors including the energy of the impact and the nature of the target surface. For example, the density, porosity, layering, and curvature of the target surface all influence how the energy of impact is dissipated. Further, isostatic compensation can act to decrease the vertical scale of a basin over time. This effect would be especially strong for a very large and very early basin, which is exactly what is being sought.

The model of an impact basin and its ejecta shown in Figure 13.4 fits the medium-sized basins, but could not be c o o 3E

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Figure 13.5. This radial profile of ejection velocity, together with the assumptions supported by dimensional analysis and experiment, produces the model ejecta pattern of Figure 13.4.

Figure 13.4. The solid line is a radial profile of a generalized impact basin. The light lines are radial profiles of several lunar basins ranging from 200 to 900 km in diameter. A radial profile of a basin is a plot of the average height or depth around a circle, as a function of the radius from the center of the basin. Some of these basins have inner and outer rings and have been partially filled with mare, features that are neglected in the model. The sample basins were measured using the high-resolution Clementine database topogrd2.

expected to fit a basin of the size of the South Pole-Aitken Basin or larger because of the curvature of the Moon. For the smaller basins, the ejecta can be assumed to follow approximately ballistic trajectories, like the flight of a cannon ball. But actually, the ejected material is launched in an elliptical orbit into the vacuum of space. Therefore its launch velocity (speed and angle) must be estimated and included in the model.

How the ejected material is launched at the edge of the expanding explosion is known from laboratory measurements. The angle of launch is nearly constant at about 45 and the mass rate of ejection per angle of azimuth is nearly independent of radius. However, the velocity varies strongly with the radius of launch, being very high at the point of impact and falling to zero at what will become the edge of the impact basin. Figure 13.5 shows the radial profile of velocity that is consistent with the ejecta model of Figure 13.4. Recently, a theoretical study (Richardson, 2007) of the ejection velocity has been published that agrees well with the empirical curve of Figure 13.5, and agrees precisely out to a radius of 0.91.

Another important difference between the ejecta pattern of very large basins and medium basins is the area available for the circular ring of ejecta to occupy. On an approximately flat surface, the depth of a ring of ejecta at a given radius from the center is simply its volume divided by the width of the ring multiplied by the circumference of a circle of equivalent radius. But when the basin is so large that its ejecta must be considered as falling on a spherical surface, the circumference of the circle is reduced. In fact, when the ejecta, in its orbit, reaches the far side of the Moon (the antipode of the impact point), the ejecta from all directions converges, theoretically at a point. Of course, variations from the assumptions actually spread the ejecta out somewhat in the vicinity of the antipode.

Figure 13.5. This radial profile of ejection velocity, together with the assumptions supported by dimensional analysis and experiment, produces the model ejecta pattern of Figure 13.4.

Now that I had a general model of an impact basin, I was ready to search for the basin that had left its debris on the far side.

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