# Homework #6 Chapter 5: Earth and Moon Due: 15 Oct 2013

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1 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. 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? 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? 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?

2 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? 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? 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? 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

3 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-19 th century, d) in the 20 th century c) in the mid-19 th 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/m 3 4/3 ( m) 3 M = kg Surface gravity is the same as the acceleration due to gravity, g = GM/r 2. g = kg/ ( m) 2. g = 5.3 m/s 2. 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.

4 0.55 vescape = 11.2 = 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)r 3. The volume of the inner core is V inner = (4/3)r inner 3, so the ratio of the two is: (r inner / r) 3 = (1300/6378) 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 ( )/ = 0.16, or about 16% of Earth s total volume. The mantle is about 3000 km thick: ( )/ = 0.85, or 85% of the volume of Earth. The crust is only 15 km thick. Following the reasoning above, the crust comprises only ( )/ = 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 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.

5 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) d = 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, Each pixel covered an estimated 50 to 100 meters, which agrees very well the above estimate.

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