Answers to Assignment 8, Chapter 8
OCG123, Spring 2001
Review Questions
2. There are three basic ways of determining the age of the earth in the absence
of surface rocks that go back to the beginning. The first is to measure the
isotopic ratios of lead (207/204 and 206/204) in chondritic meteorites and
assume it to the the same as the earth. An isochron diagram for doing this is
shown in Figure 8-2. The second way is to measure the age of the moon from rocks
brought back by Apollo astronauts. The third way is to measure lead-isotopic
ratios in lead minerals of various ages, which have "frozen" the
ratios of the magma from which they separated long ago. When those ratios are
plotted against the age of the rocks in which the lead minerals are embedded, it
is possible to extrapolate back and find the time at which the ratios matched
those of chondrites. That gives about 4.5 to 4.6 billion years for the age of
the earth. It also means that the earth formed when the chondrites did, i.e.,
when the rest of the solar system did.
4. The ocean and the atmosphere formed during the "heavy bombardment period" from 4.5 to 3.8 billion years ago, i.e., in the first billion years of the earth. The materials were released by impacts and brought in by the impacting bodies as well. The early atmosphere was mostly CO2, with smaller amounts of N2 and H2O. Oxygen did not begin to rise until after the first billion years.
6. The carbonate-silicate cycle could have helped solve the faint young sun problem by allowing CO2 to accumulate because there was little continent to weather and remove the CO2 in the process.
8. The Precambrian glaciations were different because they involved ice sheets at low latitudes, even at the equator. Glaciations since then have been at higher latitudes.
10. Land plants keep atmospheric CO2 in check by consuming it in photosynthesis. The greater the CO2, the faster the plants photosynthesize and remove it. This negative feedback loop keeps CO2 in check.
12. The recent global cooling may have been created by the collision of India and Asia, which created fresh, weatherable continental material in the Himalayas and on the Tibetan Plateau. The resulting weathering reduced the CO2 and the global greenhouse effect.
Critical-Thinking Problems
1. General comment: This problem can be unnecessarily confusing because it
assigns two different meaning to t, the age of the sun and the time
before the present. We must keep these uses sorted out as we work through the
parts of the problem. Big boo-boo on the part of the publisher!
a. S/S0 for the present (t = t0 = 4.6
billion years) is 1. S/S0 at 1.5 billion years ago (or t = 3.1
billion years after the sun formed) was 0.88, so the solar constant 1.5 billion
years ago was 88% of its present value. S/S0 at 3.0 billion years ago
(or t = 1.6 billion years after the sun formed) was 0.79, so the solar
constant 1.5 billion years ago was 79% of its present value.
b. Recall the formula from page 42, that Te = [S(1
- A)/4σ]0.25. Using S = S0
gives the well-known Te = 255 K that we calculated in Chapter 3. To
get the temperatures 1.5 and 3.0 billion years ago, we just use 0.88S0
and 0.79S0 instead. This gives 247 K and 240 K, respectively. (Hint:
calculate the value of [S0(1 - A)/4σ]
once and multiply it by 0.88 and 0.79 for the two other parts of the problem.)
c. To get the mean surface temperature of earth at these
three times, just add to the 255 K the values derived from the formula ΔTg
= 22 + 0.5(Te - 233). These values of the greenhouse effect are 33 K,
29 K, and 26 K. Adding these to the radiating temperature gives surface
temperatures of 288 K, 276 K, and 266 K for O, 1.5, and 3.0 billion years ago,
respectively. The actual surface temperature reaches the freezing point (273 K)
at about 2 billion years before the present (0.3 times the time between 1.5 and
3.0 billion years ago).