Download Homework #6 Chapter 5: Earth and Moon Due

Homework #6
Chapter 5: Earth and Moon
Due: 15 Oct 2013
Review and Discussion:
RD5.1 Explain how the Moon produces tides in Earth’s oceans.
Answer:
The Moon pulls on the side of Earth facing it with a stronger force than it exerts on the center of Earth.
Likewise, the Moon pulls with a weaker force on the far side of Earth than it exerts on the center of
Earth. The result is two high tides raised on Earth’s surface, one facing the Moon and one on Earth’s
opposite side.
.
RD5.2What does it mean to say the Moon is in a synchronous orbit around Earth? How did the Moon
come to be in such an orbit?
Answer:
A synchronous orbit is when the rotational period of an object matches its orbital period. The tidal
effect of Earth on the Moon is much stronger than that of the Moon on Earth. Earth’s rotation is
being slowed by tidal friction. The same happened for the Moon. But the Moon is also much
smaller than Earth, so Earth was able to slow the Moon’s rotation until it became synchronized
with the Moon’s orbit.
RD5.3 What is convection? Whatg effect does it have on a) Earth’s atmosphere and b) Earth’s
interior?
Answer:
Convection is the upwelling of hot material and the downward flow of cooler material to take its
place. (a) In Earth’s atmosphere it transports heat from the surface into the atmosphere and is
responsible for many of the weather patterns. (b) In Earth’s interior it helped form the crust,
mantle, and core of the planet. It currently is responsible for volcanism and plate tectonics.
RD5.4 In contract to Earth, the Moon undergoes extreme temperatures. Why?
Answer:
The extreme temperature variations of the Moon are, in part, due to the Moon’s lack of an atmosphere.
An atmosphere helps to insulate the surface from cooling at night. The Moon’s very long day (slow
rotational period) also plays a role. The Sun is up for a long period, allowing the rock to heat up. With an
equally long night, there is ample time to cool down to a low temperature. Earth, in contrast to the
Moon, rotates rapidly and has less time to heat up to high temperatures or cool down to low
temperatures.
RD5.8 Give two reasons why geologists think that part of the Earth’s core is liquid?
Answer:
Certain types of seismic waves, S-waves, cannot travel through liquid rock. Another type, P-waves, can
travel through liquid but are refracted. The “shadow zones” for both types of waves, or areas on Earth’s
surface where the different waves cannot be detected after an earthquake, indicate that part of Earth’s
interior must be liquid. This region is now mapped out as being the outer core. The inner core appears
to be solid.
RD5.9 What clue does Earth’s differentiation provide to our planet’s history?
Answer:
The fact that Earth is differentiated, structured in layers of decreasing density toward the surface,
suggests that Earth must have been molten in its past. If it was molten, then high-density material could
slowly sink to the interior while lower-density material would float to the surface. This is what is
observed today.
RD5.14 Give a brief description of Earth’s magnetosphere. Why does the Moon have no
magnetosphere?
Answer:
The magnetosphere is that region around a planet that is most influenced by the planet’s magnetic field.
The magnetic field can trap charged particles. Very early satellites detected the fast-moving particles
that were trapped in our magnetic field. The regions for Earth in which the particles were found are
called the Van Allen Belts. The Moon does not have a magnetosphere because a rapid rotation and a
liquid metallic core are necessary for generating a magnetic field. The Moon has neither of these
properties
Conceptual Self Test:
CST5.1 Because of tidal forces, the Moon is in a synchronous orbit around Earth
TRUE
CST5.4 Earth’s magnetic field is the result of our planet’s large, permanently magnetized iron
core
FALSE
CST5.5 Motion of the crustal plates is driven by convection in Earth’s upper mantle
TRUE
CST5.12 If Earth ahd no Moon, then tides would a) not occur, b) occur more often and with more
intensity, c)still occur, but not really measurable, d) occur with the same frequency, but would not be as
strong.
d) occur with the same frequency, but would not be as strong.
CST5.15 The first figure in Discovery 5-2 shows the CO2 levels in Earth’s atmosphere began to rise
rapidly a) in the middle ages, b) 1600, c) in the mid-19th century, d) in the 20th century
c) in the mid-19th century
Problems:
P5.01: What would Earth’s surface gravity and escape speed be if the entire planet had a density
equal to that of the crust (3000 kg/m^3, say)?
ANSWER:
Mass is equal to density times the volume:
M = 3000 kg/m3  4/3    (6.378 106 m)3
M = 3.26 1024 kg
Surface gravity is the same as the acceleration due to gravity, g = GM/r2. g = 6.67 10–11  3.26
1024 kg/ (6.378 106 m)2. g = 5.3 m/s2.
Escape speed is given in More Precisely 5-1. The mass, in Earth masses, is 3.26/5.97 = 0.55 and the
radius is 1.0.
vescape = 11.2
0.55
= 8.3 km/s.
1.0
P5.05: (Baed on the data presented in the text, estimate the fractions of Earth’s volume represented
by a) inner core, b) out core, c) mantle, and d) crust.
The total volume of Earth is V = (4/3)r3.
The volume of the inner core is Vinner = (4/3)rinner3, so the ratio of the two is:
(rinner / r)3 = (1300/6378) 3 = 8.4  10-3.
The outer core has a radius of 3500 km, so its volume is the volume of a sphere of radius 3500 km
minus the volume of the inner core: V = (4/3)(3500)3 – (4/3)(1300)3. The ratio of this to the total
volume of Earth is (35003 – 13003)/63783 = 0.16, or about 16% of Earth’s total volume.
The mantle is about 3000 km thick:
(63633 – 33633)/63783 = 0.85, or 85% of the volume of Earth.
The crust is only 15 km thick. Following the reasoning above, the crust comprises only
(63783 – 63633)/63783 = 0.007, or 0.7% of the volume of the Earth.
P5.08: Following an earthquake, how long would it take a P-wave moving in a straight line with
speed of 5km/s to reach the oppose side of the Earth?.
Earth’s diameter is 2 6378 km = 12,756 km. At 5 km/s, the time it will take is:
(12,756 km)/(5 km/s) = 2551 s, or about 43 minutes.
P5.10: The Hubble Space Telescope has a resolution of about 0.05 arc second. What is the smallest
object it could see on the surface of the Moon? Give your answer in meters.
Set up a ratio: the angle is to 360° as the distance on the Moon is to the circumference of a circle at the
Moon’s distance. Change degrees to arc seconds.
0.05"
d


2π(384,000 km)
360  3600" /

d = 0.093 km or 93 m.
Note: The advanced camera for surveys on the Hubble space telescope was used to image the
Aristarchus Crater on the Moon in UV/Vis on August 21, 2005. Each pixel covered an estimated 50
to 100 meters, which agrees very well the above estimate.