Lab 5: Crater Dating
Introduction
Impact craters may also be used to estimate relative ages of planetary surfaces. If we
assume that impacts are a completely random process (they occur at any place on a planet
surface with equal probability), then if there enough impacts to form a valid statistical
sample, we can use the number of impact craters in a surface to estimate age.
For example, if the rate of formation of impact craters is 2 craters per million years, and a
planet has 5,760 craters, then the age of the planet's surface is number of craters divided
by the rate of crater formation:
5,760 / 2 per million years = 2,880 million years = 2.88 Ga (billion years)
The rate of crater formation has changed with time and cannot be extrapolated from
current crater rates. Also the number of craters also depends on the surface area, a large
area will, in general, have more craters than a small area. The area problem is taken into
account by using crater densities, which are calculated as the number of craters divided
by the area of the surface in which they are formed. Even without knowing the rate of
crater formation, if two areas on a planet have different crater densities, then the area
with the higher crater density is the older
. If an absolute age of a surface can be
determined independently of the crater age, then the crater density can be calibrated to
absolute age. The only planetary body for which this calibration is available is the Moon.
Using crater density data from the Moon and absolute ages of lunar samples returned to
Earth, the crater-count graph paper (below) has been calibrated in terms of absolute age.
A further complication in using craters to calculate ages is that craters come in a wide
range of diameters and not all sizes are equally probable. In general, small craters are
much more common than large craters. Observations suggest that as the diameter
decreases by a factor of 8
, the number of craters of that size increases by about 1,000
. For
example, for every crater about 16 km in diameter, there are 1,000 craters 2 km in
diameter. For every crater 128 km in diameter there are 1,000 craters 16 km in diameter
and 1,000,000 craters 2 km in diameter. Thus, when counting craters and calculating
crater densities, craters are divided into size ranges based on a factor of 2 (8 = 2 x 2 x 2),
as shown in the figure below.
In keeping with the observed distribution of crater sizes, crater counts are plotted on