The goal of this lab is to use observations of the craters and
``seas'' of the moon to learn about the geological history of the moon.
The Earth, the Moon, and all the other planets
are subjected to a continuing bombardment
of comets, meteorites, and asteroids. For example,
Jupiter was just the target of a spectacular bombardment
by the comet Shoemaker-Levy (image). In this lab
you will measure the distirbution of crater sizes to estimate
the mass distribution of meteors that impacted and
you will crudely measure the distribution in time of the impacts.
Select two regions of the moon that you will study (show on
a complete figure of the moon). One of the regions should be
heavily cratered and another should be in either the Mare
tranquillitatis (Sea of Tranquility) or the Mare Serenitatis
(Sea of Serenity). There is a small-scale map
here and a very large
scale map here. Measure the sizes of the telescope's field of view (in
km so that you can estimate the fraction of the moon that you
are observing - you should have this information from the previous
lunar lab, or at least be able to measure it easily).
The distribution of impacts
In your heavily cratered area count the number of craters as
a function of their size (i.e. measure the distribution of
crater sizes). Bin the data into about 5 bins (e.g. 1 to 10 km
craters, 10 to 20 km, 20 to 30 km and so forth). Plot
size vs. number within these bins. Describe the distribution
(are there more small craters, more larger craters, equal numbers of
each size, etc. ). Now use the same data to make a plot
of natural logarithm of the size versus natural logarithm of
the number of craters in the bin. Draw the line that best goes through the
points (on average - it will probably not go through any particular point, let
alone every point!). A straight line fit to
these data will have a slope that corresponds to the power
index,
where N is the number of craters of size r and A is a
normalization constant (which you can estimate from the
y-intercept of your fit.) Compare the normalizations you get for the high
and low impact areas. How many times larger is the normalization for the
high impact area. What can you conclude from this? Examine the slopes,
what can you conclude from this?
The time distribution of impacts
You can arrive at a rough estimate of the rate of cratering
at various epochs. For example, you can deduce that a crater
is younger than another crater if it lies on top of the first
crater. Likewise, you can determine the rate of cratering
since a particular Mare was created by counting the number
of craters on that Mare (since the creation of the Mare
must have destroyed all previous craters). Take the area
of heavy cratering that you observed before. That area
(and the number of craters in that area) are representative
of the entire cratering history of the moon.
Measure the number of craters/square km in either of the
two Mares listed below and compare with the number within
the heavily cratered region.
The age of the Mare Tranquillitatis is 3.57 to 3.88 billion years.
The age of the Mare Serenitatis is 3.87 billion years. You can examine
just a small area of either Mare and assume that the area you chose
is representative of the entire Mare.
Finally, measure the number of craters/sq. km in the Copernicus
crater (use an area about twice as large as the crater to determine
the number of craters/sq. km around Copernicus).
The age of the Copernicus crater is 0.9 billion years.
Use the ages of the features as given above to calculate
the cratering rate from the time the moon was formed (about
4.5 Gyr ago) to about 3.8 Gyr, from 3.8 Gyr to 0.9 Gyr,
and from 0.9 Gyr to the present. What can you say about the
cratering history, and therefore about the rate of
meteoritic impacts during the history of the solar system?
, in the expression
